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Call number: | 10310727:ONLINE Show nearby items on shelf |
Title: | A Guide to Microsoft Excel 2007 for scientists and engineers [electronic resource] |
Author(s): |
Bernard V. Liengme David J. Ellert |
Date: | 2009 |
Size: | 1 online resource (336 p.) |
Contents: | 1. The Microsoft Excel Window 2. Basic Operations 3. Printing a Worksheet 4. Using Functions 5. Decision Functions 6. Charts 7. Curve Fitting 8. User-defined Functions 9. Modelling I 10. Solving Equations 11. Numerical Integration 12. Differential Equations 13. Modelling II 14. Statistics for Experimenters 15. Report Writing |
ISBN: | 9780123746238 |
Series: | ebrary eBook |
Series: | eBooks |
Keywords: | Engineering - Data processing , Microsoft Excel (Computer file) , Science - Data processing |
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Location: | ONLINE |
Call number: | TA357.H574::1988 Show nearby items on shelf |
Title: | Numerical computation of internal and external flows |
Author(s): |
Charles Hirsch |
Date: | 1988 |
Publisher: | Wiley |
Note: | v. 1. Fundamentals of numerical discretization -- v. 2. Computational methods for inviscid and viscous flows |
Contents: | THE NUMERICAL COMPUTATION OF POTENTIAL FLOWS. The Mathematical Formulations of the Potential Flow Model. The Discretization of the Subsonic Potential Equation. The Computation of Stationary Transonic Potential Flows. THE NUMERICAL SOLUTION OF THE SYSTEM OF EULER EQUATIONS. The Mathematical Formulation of the System of Euler Equations. The Lax-Wendroff Family of Space-Centered Schemes. The Central Schemes with Independent Time Integration. The Treatment of Boundary Conditions. Upwind Schemes for the Euler Equations. Second Order Upwind and High-Resolution Schemes. THE NUMERICAL SOLUTION OF THE NAVIER-STOKES EQUATIONS. The Properties of the System of Navier-Stokes Equations. Discretization Methods for the Navier-Stokes Equations |
ISBN: | 0471923516 |
Series: | Wiley series in numerical methods in engineering |
Keywords: | Fluid dynamics , Mathematical models , Fluids , Flows , Simulations , Numerical methods |
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Location: | MAIN |
Call number: | TA330.J44::2002 Show nearby items on shelf |
Title: | Advanced engineering mathematics |
Author(s): |
Alan Jeffrey |
Date: | 2002 |
Publisher: | Harcourt Academic Press |
Note: | Volume 2 is the solutions manual |
Contents: | Review of Prerequisites |
Vectors and Matrices | |
Vectors and Vector Spaces | |
Matrices and Systems of Linear Equations | |
Eigenvalues, Eigenvectors and Diagonalization | |
Ordinary Differential Equations | |
First Order Differential Equations | |
Second and Higher Order Linear Differential Equations and Systems | |
The Laplace Transform | |
Series Solutions of Differential Equations, Special Functions, and Sturm-Liouville Equations | |
Fourier Series | |
Fourier Integrals and the Fourier Transform | |
Vector Calculus | |
Vector Differential Calculus | |
Vector Integral Calculus | |
Complex analysis | |
Analytic Functions | |
Complex Integration | |
Laurent Series, Residues, and Contour Integration | |
The Laplace Inversion Integral | |
Particla Differential Equations | |
Numerical Mathematics | |
ISBN: | 012382592X |
Keywords: | Engineering mathematics |
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Location: | MAIN |
Call number: | SPRINGER-2016-9783319335070:ONLINE Show nearby items on shelf |
Title: | Monte Carlo and Quasi-Monte Carlo Methods MCQMC, Leuven, Belgium, April 2014 |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (57 p.) |
Note: | 10.1007/978-3-319-33507-0 |
Contents: | Part I Invited papers -- Multilevel Monte Carlo Implementation for SDEs driven by Truncated Stable Processes -- Construction of a Mean Square Error Adaptive Euler–Maruyama Method With Applications in Multilevel Monte Carlo -- Vandermonde Nets and Vandermonde Sequences -- Path Space Markov Chain Monte Carlo Methods in Computer Graphics -- Walsh Figure of Merit for Digital Nets: An Easy Measure for Higher Order Convergent QMC -- Some Results on the Complexity of Numerical Integration -- Approximate Bayesian Computation: A Survey on Recent Results -- Part II Contributed papers -- Multilevel Monte Carlo Simulation of Statistical Solutions to the Navier–Stokes Equations -- Unbiased Simulation of Distributions with Explicitly Known Integral Transforms -- Central Limit Theorem for Adaptive Multilevel Splitting Estimators in an Idealized Setting -- Comparison between LS-Sequences and β -adic van der Corput Sequences -- Computational Higher Order Quasi-Monte Carlo Integration -- Numerical |
Computation of Multivariate Normal Probabilities using Bivariate Conditioning -- Non-nested Adaptive Timesteps in Multilevel Monte Carlo Computations -- On ANOVA Decompositions of Kernels and Gaussian Random Field Paths -- The Mean Square Quasi-Mont e Carlo Error for Digitally Shifted Digital Nets -- Uncertainty and Robustness in Weather Derivative Models -- Reliable Adaptive Cubature Using Digital Sequences -- Optimal Point Sets for Quasi-Monte Carlo Integration of Bivariate Periodic Functions with Bounded Mixed Derivatives -- Adaptive Multidimensional Integration Based on Rank-1 Lattices -- Path Space Filtering -- Tractability of Multivariate Integration in Hybrid Function Spaces -- Derivative-based Global Sensitivity Measures and Their Link with S obol’ Sensitivity Indices -- Bernstein Numbers and Lower Bounds for the Monte Carlo Error -- A Note on the Importance of Weak Convergence Rates for SPDE Approximations in Multilevel Monte Carlo Schemes -- A Strategy for Parallel | |
Implementations of Stochastic Lagrangian Simulation -- A New Rejection Sampling Method for Truncated Multivariate Gaussian Random Variables Restricted to Convex Sets -- Van der Corput and Golden Ratio Sequences Along the Hilbert Space-Filling Curve -- Uniform Weak Tractability of Weighted Integration -- Incremental Greedy Algorithm and Its Applications in Numerical Integration -- On “Upper Error Bounds for Quadrature Formulas on Function Classes” by K K Frolov -- Tractability of Function Approxi mation With Product Kernels -- Discrepancy Estimates for Acceptance-Rejection Samplers Using Stratiﬁed Inputs -- List of Participants -- Index | |
ISBN: | 9783319335070 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Springer Proceedings in Mathematics & Statistics: 163 |
Keywords: | Mathematics , Applied mathematics , Engineering mathematics , Computer mathematics , Mathematics , Computational Mathematics and Numerical Analysis , Applications of Mathematics |
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Call number: | SPRINGER-2016-9783319302560:ONLINE Show nearby items on shelf |
Title: | Introduction to Scientific Computing and Data Analysis |
Author(s): |
Mark H Holmes |
Date: | 2016 |
Size: | 1 online resource (138 p.) |
Note: | 10.1007/978-3-319-30256-0 |
Contents: | Introduction to Scientific Computing -- Solving a Nonlinear Equation -- Matrix Equations -- Eigenvalue Problems -- Interpolation -- Numerical Integration -- Initial Value Problems -- Optimization -- Data Analysis -- Appendices |
ISBN: | 9783319302560 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Texts in Computational Science and Engineering: 13 |
Keywords: | Mathematics , Partial differential equations , Computer mathematics , Mathematical optimization , Mathematics , Computational Science and Engineering , Optimization , Partial Differential Equations |
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Call number: | SPRINGER-2016-9783319278735:ONLINE Show nearby items on shelf |
Title: | New Trends in Applied Harmonic Analysis Sparse Representations, Compressed Sensing, and Multifractal Analysis |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (19 p.) |
Note: | 10.1007/978-3-319-27873-5 |
Contents: | Multifractal Analysis of Cantor-like Measures -- Multifractal Analysis and Wavelets -- An Introduction to Mandelbrot Cascades -- Lebesgue-type Inequalities for Greedy Approximation -- Results on Non-linear Approximation for Wavelet Bases in Weighte d Function Spaces -- Consequences of the Marcus/Spielman/Srivastava Solution of the Kadison-Singer Problem -- Model Sets and New Versions pf Shannon Sampling Theorem -- Stylometry and Mathematical Study of Authorship -- Thoughts on Numerical and Conceptua l Harmonic Analysis |
ISBN: | 9783319278735 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Harmonic analysis , Fourier analysis , Measure theory , Computer science , Computer mathematics , Mathematics , Fourier Analysis , Abstract Harmonic Analysis , Signal, Image and Speech Processing , Measure and Integration , Mathematical Applications in Computer Science |
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Call number: | SPRINGER-2016-9783319272658:ONLINE Show nearby items on shelf |
Title: | Basic Concepts in Computational Physics |
Author(s): |
Benjamin A Stickler |
Date: | 2016 |
Edition: | 2nd ed. 2016 |
Size: | 1 online resource (409 p.) |
Note: | 10.1007/978-3-319-27265-8 |
Contents: | Some Basic Remarks -- Part I Deterministic Methods -- Numerical Differentiation -- Numerical Integration -- The KEPLER Problem -- Ordinary Differential Equations – Initial Value Problems -- The Double Pendulum -- Molecular Dynamics -- |
Numerics of Ordinary Differential Equations - Boundary Value Problems -- The One-Dimensional Stationary Heat Equation -- The One-Dimensional Stationary SCHRÖDINGER Equation -- Partial Differential Equations -- Part II Stochastic | |
Methods -- Pseudo Random Number Generators -- Random Sampling Methods -- A Brief Introduction to Monte-Carlo Methods -- The ISING Model -- Some Basics of Stochastic Processes -- The Random Walk and Diffusion Theory -- MARKOV-Chain | |
Monte Carlo and the POTTS Model -- Data Analysis -- Stochastic Optimization -- Appendix: The Two-Body Problem -- Solving Non-Linear Equations. The NEWTON Method -- Numerical Solution of Systems of Equations -- Fast Fourier Transform -- | |
Basics of Probability Theory -- Phase Transitions -- Fractional Integrals and Derivatives in 1D -- Least Squares Fit -- Deterministic Optimization | |
ISBN: | 9783319272658 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Physics , Chemistry, Physical and theoretical , Computer mathematics , Applied mathematics , Engineering mathematics , Physics , Numerical and Computational Physics , Appl.Mathematics/Computational Methods of Engineering , Computational Mathematics and Numerical Analysis , Theoretical and Computational Chemistry |
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Call number: | SPRINGER-2016-9781493927852:ONLINE Show nearby items on shelf |
Title: | Mathematics for Natural Scientists Fundamentals and Basics |
Author(s): |
Lev Kantorovich |
Date: | 2016 |
Edition: | 1st ed. 2016 |
Size: | 1 online resource (118 p.) |
Note: | 10.1007/978-1-4939-2785-2 |
Contents: | I. Fundamentals -- Basic Knowledge -- Functions -- II. Basics -- Derivatives -- Integral -- Functions of Many Variables: Differentiation -- Functions of Many Variables: Integration -- Infinite Numerical and Functional Series -- |
Ordinary Differential Equations | |
ISBN: | 9781493927852 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Physics , Chemometrics , Mathematical physics , Applied mathematics , Engineering mathematics , Physics , Mathematical Methods in Physics , Appl.Mathematics/Computational Methods of Engineering , Math. Applications in Chemistry , Mathematical Applications in the Physical Sciences , Numerical and Computational Physics |
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Call number: | SPRINGER-2014-9788132218357:ONLINE Show nearby items on shelf |
Title: | A First Course in Ordinary Differential Equations [electronic resource] : Analytical and Numerical Methods |
Author(s): |
Martin Hermann Masoud Saravi |
Date: | 2014 |
Publisher: | New Delhi : Springer India : Imprint: Springer |
Size: | 1 online resource |
Note: | This book presents a modern introduction to analytical and numerical techniques for solving ordinary differential equations (ODEs). Contrary to the traditional formatthe theorem-and-proof formatthe book is focusing onanalytical and numerical methods. The book supplies a variety of problems and examples, ranging from the elementary to the advanced level, to introduce and study the mathematics of ODEs. The analytical part of the book deals withsolution techniques for scalar first-order and second-order linear ODEs, and systems of linear ODEswith a special focus on the Laplace transform, operator techniques and power series solutions. In the numerical part, theoretical andpractical aspects of Runge-Kutta methods for solving initial-value problems and sh ooting methods for linear two-point boundary-value problems are considered. The book is intended as a primary text for courses on the theory of ODEs andnumerical treatment of ODEs for advanced undergraduate and early graduate students. It is assumed that the reader has a basic grasp of elementary calculus, in particular methods of integration, and of numerical analysis. Physicists,chemists, biologists, computer scientists and engineers whose work involves solving ODEs will also find the book useful as a r eference work and tool for independent study. The book has been prepared within the framework of aGermanIranian research project on mathematical methods for ODEs, which was started in early 2012 |
Contents: | Chapter 1. Basic Concepts of Differential Equations |
Chapter 2. First | |
Order Differential Equations | |
Chapter 3. Second | |
Order Differential Equations | |
Chapter 4. Laplace Transforms | |
Chapter 5. System of Linear Differential Equations | |
Chapter 6. Power Series Solutions | |
Chapter 7. Numerical Methods for Initial Value Problems | |
Chapter 8. Shooting Methods for Linear Boundary | |
Appendix A. Power Series | |
Appendix B. Some elementary integration formulae | |
Appendix C. Table of Laplacetransforms. | |
ISBN: | 9788132218357 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differential Equations , Numerical analysis , Materials |
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Call number: | SPRINGER-2014-9783642453670:ONLINE Show nearby items on shelf |
Title: | Scientific Computing with MATLAB and Octave [electronic resource] |
Author(s): |
Alfio Quarteroni Fausto Saleri Paola Gervasio |
Date: | 2014 |
Edition: | 4th ed. 2014 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | This textbook is an introduction to Scientific Computing, in which several numerical methods for the computer-based solution of certain classes of mathematical problems are illustrated. The authors show how to compute the zeros,the extrema, and the i ntegrals of continuous functions, solve linear systems, approximate functions using polynomials and construct accurate approximations for the solution of ordinary and partial differential equations. To make theformat concrete and appealing, the programmin g environments Matlab and Octave are adopted as faithful companions. The book contains the solutions to several problems posed in exercises and examples, often originating from importantapplications. At the end of each chapter, a specific section is devot ed to subjects which were not addressed in the book and contains bibliographical references for a more comprehensive treatment of the material. From the review:.... This carefully written textbook, the third English edition, contains substantial new devel opments on the numerical solution of differential equations. It is typeset in a two-color design and is written in a style suited forreaders who have mathematics, natural sciences, computer sciences or economics as a background and who are interested in a well-organized introduction to the subject. Roberto Plato (Siegen), Zentralblatt MATH 1205.65002 |
Contents: | 1. What can' t be ignored |
2. Nonlinear equations | |
3. Approximation of functions and data | |
4. Numerical differentiation and integration | |
5. Linear systems | |
6. Eigenvalues and eigenvectors | |
7. Numerical optimization | |
8. Ordinary differential equations | |
9. Numerical approximation of boundary | |
value problems | |
10. Solutions of the exercises | |
References | |
Index | |
ISBN: | 9783642453670 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Texts in Computational Science and Engineering, 1611-0994 : v2 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Chemistry , Computer science , Visualization , Engineering |
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Call number: | SPRINGER-2014-9783319077406:ONLINE Show nearby items on shelf |
Title: | Quantum Radiation in Ultra-Intense Laser Pulses [electronic resource] |
Author(s): |
K. Felix Mackenroth |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Scientific advances and several technical breakthroughs have led to a remarkableincrease in available laser intensities over the past decades. In available ultra-intense laser fields, photon fluxes may become so high that freecharge carriers interact coherentlywith several of the field's photons. In this thesis such nonlinear interactions are investigatedfor the prime example of radiation emission by electrons scattered from intense laser pulses ofarbitrary temporal structure. To this end, nonlinear quantum field theory is employed taking the interaction with the laser into account exactly. After an in-depth introduction to classical particle dynamics as well as quantum fieldtheory in nonlinearly intense laser fields the emission of one and two photo ns is explicitly analyzed. The results are then translated to viable technical applications, such as a scheme for the determination of the carrier-envelopephase of ultra-intense laser pulses and a proposal for detecting the strongly suppressed two-photon signal |
Contents: | Interaction of Electrons with Laser Fields |
Nonlinear Single Compton Scattering | |
Nonlinear Double Compton Scattering | |
Numerical Integration of Strongly Oscillating Functions | |
ISBN: | 9783319077406 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Theses, Recognizing Outstanding Ph.D. Research, 2190-5053 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Quantum theory |
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Call number: | SPRINGER-2014-9783319060743:ONLINE Show nearby items on shelf |
Title: | Functional Analysis and Applied Optimization in Banach Spaces [electronic resource] : Applications to Non-Convex Variational Models |
Author(s): |
Fabio Botelho |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | This book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physicsand engineering probl ems. The book includes introductory and advanced concepts in measure and integration, as well as an introduction to Sobolev spaces. The problems presented are nonlinear, with non-convex variational formulation.Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to an appropriate weak cluster point of minimizing sequences for the primal one. Indeed, the dualapproach more readily facilitates numerical computations for some of the selected models. While intended primarily for applied mathematicians, the text will also be of interest to engineers, physicists, and other researchers in relatedfields |
Contents: | 1. Topological Vector Spaces |
2. The Hahn | |
Bananch Theorems and Weak Topologies | |
3. Topics on Linear Operators | |
4.Basic Results on Measure and Integration | |
5. The Lebesgue Measure in Rn | |
6. Other Topics in Measure and Integration | |
7. Distributions | |
8. The Lebesque and Sobolev Spaces | |
9. Basic Concepts on the Calculus of Variations | |
10. Basic Concepts on Convex Analysis | |
11. Constrained Variational Analysis | |
12. Duality Applied to Elasticity | |
13. Duality Applied to a Plate Model | |
14. About Ginzburg | |
Landau Type Equations: The Simpler Real Case | |
15. Full Complex Ginzb | |
ISBN: | 9783319060743 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Fourier analysis , Functional analysis , Numerical analysis |
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Call number: | SPRINGER-2014-9783319056692:ONLINE Show nearby items on shelf |
Title: | Lobachevsky Geometry and Modern Nonlinear Problems [electronic resource] |
Author(s): |
Andrey Popov |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | This monograph presents the basic concepts of hyperbolic Lobachevsky geometry and their possible applications to modern nonlinear applied problems in mathematics and physics, summarizing the findings of roughly the last hundredyears. The central sect ions cover the classical building blocks of hyperbolic Lobachevsky geometry, pseudo spherical surfaces theory, net geometrical investigative techniques of nonlinear differential equations in partial derivatives,and their applications to the analysis of th e physical models. As the sine-Gordon equation appears to have profound geometrical roots and numerous applications to modern nonlinear problems, it is treated as a universalobject of investigation, connecting many of the problems discussed. The aim of th is book is to form a general geometrical view on the different problems of modern mathematics, physics and natural science in general in the contextof non-Euclidean hyperbolic geometry |
Contents: | Introduction |
1 Foundations of Lobachevsky geometry: axiomatics, models, images in Euclidean space | |
2 The problem of realizing the Lobachevsky geometry in Euclidean space | |
3 The sine | |
Gordon equation: its geometry and applications of current interest | |
4 Lobachevsky geometry and nonlinear equations of mathematical physics | |
5 Non | |
Euclidean phase spaces. Discrete nets on the Lobachevsky plane and numerical integration algorithms for 2 | |
equations | |
Bibliography | |
Index | |
ISBN: | 9783319056692 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Differential equations, partial |
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Call number: | SPRINGER-2014-9783319024356:ONLINE Show nearby items on shelf |
Title: | Basic Concepts in Computational Physics [electronic resource] |
Author(s): |
Benjamin A. Stickler Ewald Schachinger |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | With the development of ever more powerful computers a new branch of physics and engineering evolved over the last few decades: Computer Simulation or Computational Physics. It serves two main purposes: - Solution of complexmathematical problems such as, differential equations, minimization/optimization, or high-dimensional sums/integrals. - Direct simulation of physical processes, as for instance, molecular dynamics or Monte-Carlo simulation ofphysical/chemical/technical processes. Consequently, the book is divided into two main parts: Deterministic methods and stochastic methods. Based on concrete problems, the first part discusses numerical differentiation and integration,and the treatment of ordinary differential equations. This is augmented by n otes on the numerics of partial differential equations. The second part discusses the generation of random numbers, summarizes the basics of stochastics whichis then followed by the introduction of various Monte-Carlo (MC) methods. Specific emphasis is on MARKOV chain MC algorithms. All this is again augmented by numerous applications from physics. The final two chapters on Data Analysisand Stochastic Optimization share the two main topics as a common denominator. The book offers a number of appendices to provide the reader with more detailed information on various topics discussed in the main part. Nevertheless, thereader should be familiar with the most important concepts of statistics and probability theory albeit two appendices have been dedicated to provide a rudimentary discussion |
Contents: | Some Basic Remarks |
Part I Deterministic Methods: Numerical Differentiation | |
Numerical Integration | |
The KEPLER Problem | |
Ordinary Differential Equations Initial Value Problems | |
The Double Pendulum | |
Molecular Dynamics | |
Numerics of Ordinary Differential Equations | |
Boundary Value Problems | |
The One | |
Dimensional Stationary Heat Equation | |
The One | |
Dimensional Stationary SCHRDINGER Equation | |
Numerics of Partial Differential Equations | |
Part II Stochastic Methods | |
Pseudo Random Number Generators | |
Random Sampling Methods | |
A Brief Introduction to Monte | |
Carlo Methods | |
The | |
ISBN: | 9783319024356 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Chemistry , Computer science Mathematics , Engineering mathematics |
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Call number: | SPRINGER-2014-9783319022314:ONLINE Show nearby items on shelf |
Title: | Strong and Weak Approximation of Semilinear Stochastic Evolution Equations [electronic resource] |
Author(s): |
Raphael Kruse |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | In this book we analyze the error caused by numerical schemes for the approximation of semilinear stochastic evolution equations (SEEq) in a Hilbert space-valued setting. The numerical schemes considered combine Galerkin finiteelement methods with Eu ler-type temporal approximations. Starting from a precise analysis of the spatio-temporal regularity of the mild solution to the SEEq, we derive and prove optimal error estimates of the strong error ofconvergence in the first part of the book. The second part deals with a new approach to the so-called weak error of convergence, which measures the distance between the law of the numerical solution and the law of the exact solution.This approach is based on Bismuts integration by parts formula and the Malli avin calculus for infinite dimensional stochastic processes. These techniques are developed and explained in a separate chapter, before the weak convergenceis proven for linear SEEq |
Contents: | Introduction |
Stochastic Evolution Equations in Hilbert Spaces | |
Optimal Strong Error Estimates for Galerkin Finite Element Methods | |
A Short Review of the Malliavin Calculus in Hilbert Spaces | |
A Malliavin Calculus Approach to Weak Convergence | |
Numerical Experiments | |
Some Useful Variations of Gronwalls Lemma | |
Results on Semigroups and their Infinitesimal Generators | |
A Generalized Version of Lebesgues Theorem | |
References | |
Index | |
ISBN: | 9783319022314 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2093 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differential equations, partial , Numerical analysis , Distribution (Probability theory) |
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Call number: | SPRINGER-2014-9783319013008:ONLINE Show nearby items on shelf |
Title: | Current Challenges in Stability Issues for Numerical Differential Equations [electronic resource] : Cetraro, Italy 2011, Editors: Luca Dieci, Nicola Guglielmi |
Author(s): |
Wolf-Jrgen Beyn Luca Dieci Nicola Guglielmi Ernst Hairer Jess Mara Sanz-Serna Marino Zennaro |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | This volume addresses some of the research areas in the general field of stability studies for differential equations, with emphasis on issues of concern for numerical studies. Topics considered include: (i) the long timeintegration of Hamiltonian Or dinary DEs and highly oscillatory systems, (ii) connection between stochastic DEs and geometric integration using the Markov chain Monte Carlo method, (iii) computation of dynamic patterns in evolutionarypartial DEs, (iv) decomposition of matrices dependi ng on parameters and localization of singularities, and (v) uniform stability analysis for time dependent linear initial value problems of ODEs. The problems considered in this volumeare of interest to people working on numerical as well as qualitative as pects of differential equations, and it will serve both as a reference and as an entry point into further research |
Contents: | Studies on current challenges in stability issues for numerical differential equations |
Long | |
Term Stability of Symmetric Partitioned Linear Multistep Methods | |
Markov Chain Monte Carlo and Numerical Differential Equations | |
Stability and Computation of Dynamic Patterns in PDEs | |
Continuous Decompositions and Coalescing Eigen values for Matrices Depending on Parameters | |
Stability of linear problems: joint spectral radius of sets of matrices | |
ISBN: | 9783319013008 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2082 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Matrix theory , Differential Equations , Differential equations, partial , Computer science Mathematics , Algorithms |
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Call number: | SPRINGER-2014-9781461496380:ONLINE Show nearby items on shelf |
Title: | Real Analysis for the Undergraduate [electronic resource] : With an Invitation to Functional Analysis |
Author(s): |
Matthew A Pons |
Date: | 2014 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | This undergraduate textbook introduces students to the basics of real analysis, provides an introduction to more advanced topics including measure theory and Lebesgue integration, and offers an invitation to functional analysis.While these advanced t opics are not typically encountered until graduate study, the text is designed for the beginner. The authors engaging style makes advanced topics approachable without sacrificing rigor. The text alsoconsistently encourages the reader to pick up a pencil a nd take an active part in the learning process. Key features include: - examples to reinforce theory - thorough explanations preceding definitions, theorems and formal proofs -illustrations to support intuition - over 450 exercises designed to develop con nections between the concrete and abstract. This text takes students on a journey through the basics of real analysis and provides those who wish to delvedeeper the opportunity to experience mathematical ideas that are beyond the standard undergraduate cu rriculum |
Contents: | The Real Numbers |
Sequences in R | |
Numerical Series | |
Continuity | |
The Derivative | |
Sequence and Series of Functions | |
The Riemann Integral | |
Lebesgue Measure on R | |
Lebesgue Integration | |
ISBN: | 9781461496380 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Functional analysis |
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Call number: | SPRINGER-2014-9781461490906:ONLINE Show nearby items on shelf |
Title: | Solar System Astrophysics [electronic resource] : Planetary Atmospheres and the Outer Solar System |
Author(s): |
Eugene F Milone William J.F Wilson |
Date: | 2014 |
Edition: | 2nd ed. 2014 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | The second edition of Solar System Astrophysics: Planetary Atmospheres and the Outer Solar System provides a timely update of our knowledge of planetary atmospheres andthe bodies of the outer solar system and their analogs inother planetary systems. This volume begins with an expanded treatment of the physics, chemistry, and meteorology of the atmospheres of the Earth, Venus, and Mars, moving on to their magnetospheres and then to a full discussion of thegas and ice giants and their properties. From here, attention switches to the small bodies of the solar system, beginning with the natural satellites. Then comets, meteors, meteorites, and asteroids are discussed in order, and thevolume concludes with the origin and evolution of our solar system. Fin ally, a fully revised section on extrasolar planetary systems puts the development of our system in a wider and increasingly well understood galactic context. Allof the material is presented within a framework of historical importance. This book and its s ister volume, Solar System Astrophysics: Background Science and the Inner Solar system, are pedagogically well written, providing clearlyillustrated explanations, for example, of such topics as the numerical integration of the Adams-Williamson equation, t he equations of state in planetary interiors and atmospheres, Maxwells equations as applied to planetaryionospheres and magnetospheres, and the physics and chemistry of the Habitable Zone in planetary systems. Together, the volumes form a comprehensive te xt for any university course that aims to deal with all aspects of solar andextra-solar planetary systems. They will appeal separately to the intellectually curious who would like to knowjust how far our knowledge of the solar system has progressed in rec ent years |
Contents: | Planetary Atmospheres |
Planetary Ionospheres and Magnetospheres | |
The Giant Planets | |
Satellite and Ring Systems | |
Comets and Meteors | |
Meteorites, Asteroids, and the Age and Origin of Planetary Systems | |
Extra | |
solar Planetary Systems | |
ISBN: | 9781461490906 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Astronomy and Astrophysics Library, 0941-7834 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Planetology , Astronomy |
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Call number: | SPRINGER-2014-9781461488484:ONLINE Show nearby items on shelf |
Title: | Solar System Astrophysics [electronic resource] : Background Science and the Inner Solar System |
Author(s): |
Eugene F Milone William J.F Wilson |
Date: | 2014 |
Edition: | 2nd ed. 2014 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | The second edition of Solar System Astrophysics: Background Science and the Inner Solar System provides new insights into the burgeoning field of planetary astronomy. As in the first edition, this volume begins with a rigoroustreatment of coordinate frames, basic positional astronomy, and the celestial mechanics of two and restricted three body system problems. Perturbations are treated in the same way, with clear step-by-step derivations. Then theEarths gravitational potential field and the Earth-Mo on system are discussed, and the exposition turns to radiation properties with a chapter on the Sun. The exposition of the physical properties of the Moon and the terrestrialplanets are greatly expanded, with much new information highlighted on the Moon, Mercury, Venus, and Mars. All of the material is presented within a framework of historical importance. This book and its sister volume, Solar SystemAstrophysics: Planetary Atmospheres and the Outer Solar System, are pedagogically well written, providing clearly illustrated explanations, for example, of such topics as the numerical integration of the Adams-Williamson equation, theequations of state in planetary interiors and atmospheres, Maxwells equations as applied to planetary ionospheres and magnetosp heres, and the physics and chemistry of the Habitable Zone in planetary systems. Together, the volumesform a comprehensive text for any university course that aims to deal with all aspects of solar and extra-solar planetary systems. They will appeal separ ately to the intellectually curious who would like to know just how far ourknowledge of the solar system has progressed in recent years |
Contents: | Perceptions of the Solar System in History |
Basic Tools and Techniques | |
Celestial Mechanics | |
The Core of the Solar System: The Sun | |
General Properties of Terrestrial Planets | |
Planetary Heat Flow and Temperatures | |
Rocks and Minerals | |
The Moon's Surface, Structure, and Evolution | |
Surface Science of our Terrestrial Planets | |
ISBN: | 9781461488484 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Astronomy and Astrophysics Library, 0941-7834 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Planetology , Astronomy |
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Call number: | SPRINGER-2013-9783642351587:ONLINE Show nearby items on shelf |
Title: | Computational Flexible Multibody Dynamics [electronic resource] : A Differential-Algebraic Approach |
Author(s): |
Bernd Simeon |
Date: | 2013 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This monograph, written from a numerical analysis perspective, aims to provide a comprehensive treatment of both the mathematical framework and the numerical methods for flexible multibody dynamics. Not only is this fieldpermanently and rapidly growi ng, with various applications in aerospace engineering, biomechanics, robotics, and vehicle analysis, its foundations can also be built on reasonably established mathematical models. Regarding actualcomputations, great strides have been made over the last two decades, as sophisticated software packages are now capable of simulating highly complex structures with rigid and deformable components. The approach used in this bookshould benefit graduate students and scientists working in computational mechanics and related disciplines as well as those interested in time-dependent partial differential equations and heterogeneous problems with multiple timescales. Additionally, a number of open issues at the frontiers of research are addressed by taking a differe ntial-algebraic approach and extending it to the notion of transient saddle point problems |
Note: | Springer eBooks |
Contents: | A Point of Departure |
Rigid Multibody Dynamics | |
Elastic Motion | |
Flexible Multibody Dynamics | |
Spatial Discretization | |
Stiff Mechanical Systems | |
Time Integration Methods | |
Numerical Case Studies | |
ISBN: | 9783642351587 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Differential-Algebraic Equations Forum |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differential Equations , Differential equations, partial , Numerical analysis , Mechanics |
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Call number: | SPRINGER-2013-9783642324758:ONLINE Show nearby items on shelf |
Title: | Amorphous Nanophotonics [electronic resource] |
Author(s): |
Carsten Rockstuhl Toralf Scharf |
Date: | 2013 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book represents the first comprehensive overview over amorphous nano-optical and nano-photonic systems. Nanophotonics is a burgeoning branch of optics that enables many applications by steering the mould of light on lengthscales smaller than the wavelength with devoted nanostructures. Amorphous nanophotonics exploits self-organization mechanisms based on bottom-up approaches to fabricate nanooptical systems. The resulting structures presented in thebook are characterized by a deterministic unit cell with tailored geometries but their spatial arrangement is not controlled. Instead of periodic, the structures appear either amorphous or random. The aim of this book is to discussall aspects related to observable effects in amorphous nanophotonic mat erial and aspects related to their design, fabrication, characterization and integration into applications. The book has an interdisciplinary nature withcontributions from scientists in physics, chemistry and materials sciences and sheds light on the topi c from many directions |
Note: | Springer eBooks |
Contents: | Dielectric amorphous photonics materials and structures |
Photonic quasi | |
crystals | |
Solar cells with scattering and nanostructures | |
Disordered photonic crystals | |
Light localization in dielectric media | |
Amorphous plasmonics | |
Fabrication methods | |
Structural characterization techniques | |
Numerical means to describe optics in amorphous media | |
Analytical and quasi | |
analytical treatment | |
Homogenization techniques and the problem of how to deal with different length scales | |
Electromagnetic characterization techniques | |
New physical (electromagnetic) phenomena emerging due to irregu | |
ISBN: | 9783642324758 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Nano-Optics and Nanophotonics, 2192-1970 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Engineering , Optical materials |
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Call number: | SPRINGER-2013-9783642275555:ONLINE Show nearby items on shelf |
Title: | Differential-Algebraic Equations: A Projector Based Analysis [electronic resource] |
Author(s): |
Ren Lamour Roswitha Mrz Caren Tischendorf |
Date: | 2013 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Differential algebraic equations (DAEs), including so-called descriptor systems, began to attract significant research interest in applied and numerical mathematics in the early 1980s, no more than about three decades ago. In thisrelatively short tim e, DAEs have become a widely acknowledged tool to model processes subjected to certain constraints in order to simulate and to control processes in various application fields such as network simulation, chemicalkinematics, mechanical engineering and syste ms biology. DAEs and their more abstract versions in infinite dimensional spaces comprise a great potential forthe future mathematical modeling of complex coupled processes. The purpose ofthe book is to expose the impressive complexity of general DAEs fro m an analytical point of view, to describe the state of the art as well as open problems andin sodoing to motivate further researchof this versatile,extraordinary topic from a broader mathematical perspective. The book elaborates on a new general, structu ral analysis capturing linear and nonlinear DAEs in a hierarchical way. The DAE structure is exposed by means of specialprojector functions. Some issues on numerical integration and computational aspects are also treated in this context |
Note: | Springer eBooks |
Contents: | Notations |
Introduction | |
Part I. Projector based approach | |
1 Linear constant coefficient DAEs | |
.2 Linear DAEs with variable coefficients | |
3 Nonlinear DAEs | |
Part II. Index | |
1 DAEs: Analysis and numerical treatment | |
4 Analysis | |
5 Numerical integration | |
6 Stability issues | |
Part III. Computational aspects | |
7 Computational linear algebra aspects | |
8 Aspects of the numerical treatment of higher index DAEs | |
Part IV. Advanced topics | |
9 Quasi | |
regular DAEs | |
10 Nonregular DAEs | |
11 Minimization with constraints described by DAEs | |
12 Abstract differential algebraic equations | |
ISBN: | 9783642275555 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Differential-Algebraic Equations Forum |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differential Equations , Computer science Mathematics |
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Call number: | SPRINGER-2013-9783319004013:ONLINE Show nearby items on shelf |
Title: | Computational Physics [electronic resource] : Simulation of Classical and Quantum Systems |
Author(s): |
Philipp O.J Scherer |
Date: | 2013 |
Edition: | 2nd ed. 2013 |
Publisher: | Heidelberg : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This textbook presents basic and advanced computational physics in a very didactic style. It contains very-well-presented and simple mathematical descriptions of many of the most important algorithms used in computational physics.Many clear mathemati cal descriptions of important techniques in computational physics are given. The first part of the book discusses the basic numerical methods. A large number of exercises and computer experiments allows to study theproperties of these methods. The second part concentrates on simulation of classical and quantum systems. It uses a rather general concept for the equation of motion which can be applied to ordinary and partial differential equations.Several classes of integration methods are discussed includin g not only the standard Euler and Runge Kutta method but also multistep methods and the class of Verlet methods which is introduced by studying the motion in Liouville space.Besides the classical methods, inverse interpolation is discussed, together with the popular combined methods by Dekker and Brent and a not so well known improvement by Chandrupatla. A general chapter on the numerical treatment ofdifferential equations provides methods of finite differences, finite volumes, finite elements and boundar y elements together with spectral methods and weighted residual based methods. A comparison of several methods for quantumsystems is performed, containing pseudo-spectral methods, finite differences methods, rational approximation to the time evolution op erator, second order differencing and split operator methods. The book gives simple but non trivialexamples from a broad range of physical topics trying to give the reader insight into the numerical treatment but also the simulated problems. Rotational mo tion is treated in much detail to describe the motion of rigid rotors which canbe just a simple spinning top or a collection of molecules or planets. The behaviour of simple quantum systems is studied t |
Note: | Springer eBooks |
Contents: | Part I Numerical Methods |
Error Analysis | |
Interpolation | |
Numerical Differentiation | |
Numerical Integration | |
Systems of Inhomogeneous Linear Equations | |
Roots and Extremal Points | |
Fourier Transformation | |
Random Numbers and Monte | |
Carlo Methods | |
Eigenvalue Problems | |
Data Fitting | |
Discretization of Differential Equations | |
Equations of Motion | |
Part II Simulation of Classical and Quantum Systems | |
Rotational Motion | |
Molecular Dynamics | |
Thermodynamic Systems | |
Random Walk and Brownian Motion | |
Electrostatics | |
Waves | |
Diffusion | |
Nonlinear Systems | |
Simple Quantum S | |
ISBN: | 9783319004013 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Graduate Texts in Physics, 1868-4513 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Chemistry , Engineering mathematics |
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Call number: | SPRINGER-2013-9783319000718:ONLINE Show nearby items on shelf |
Title: | Stochastic World [electronic resource] |
Author(s): |
Sergey S Stepanov |
Date: | 2013 |
Publisher: | Heidelberg : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book is an introduction into stochastic processes for physicists, biologists and financial analysts. Using an informal approach, all the necessary mathematical tools and techniques are covered, including the stochasticdifferential equations, mea n values, probability distribution functions, stochastic integration and numerical modeling. Numerous examples of practical applications of the stochastic mathematics are considered in detail, ranging fromphysics to the financial theory. A reader with bas ic knowledge of the probability theory should have no difficulty in accessing the book content |
Note: | Springer eBooks |
Contents: | Random Events |
Stochastic Equations | |
Mean Values | |
Probabilities | |
Stochastic Integrals | |
Systems of Equations | |
Stochastic Nature | |
Stochastic Society | |
Computer Modeling | |
ISBN: | 9783319000718 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematical Engineering, 2192-4732 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Electronic data processing , Distribution (Probability theory) , Mathematical physics , Statistics |
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Call number: | SPRINGER-2013-9781461478287:ONLINE Show nearby items on shelf |
Title: | Integral Methods in Science and Engineering [electronic resource] : Progress in Numerical and Analytic Techniques |
Author(s): |
Christian Constanda Bardo E.J Bodmann Haroldo F. de Campos Velho |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Advances in science and technology are driven by the development of rigorous mathematical foundations for the study of both theoretical and experimental models.With certain methodological variations, this type of study alwayscomes down to the applica tion of analytic or computational integration procedures, making such tools indispensible. With a wealth of cutting-edge research in the field, Integral Methods in Science and Engineering: Progress in Numericaland Analytic Techniquesprovides a detailed po rtrait of both the construction of theoretical integral techniques and their application to specific problems in science and engineering. The chapters in this volume are based on talksgiven by well-known researchers at the Twelfth International Conferenc e on Integral Methods in Science and Engineering, July 2327, 2012, in Porto Alegre, Brazil. They address a broad range of topics, from problems of existence anduniqueness for singular integral equations on domain boundaries to numerical integration via fi nite and boundary elements, conservation laws, hybrid methods, and other quadrature-related approaches. The contributing authors bringtheir expertise to bear on a number of topical problems that have to date resisted solution, thereby offering help and gu idance to fellow professionals worldwide. Integral Methods in Science and Engineering:Progress in Numerical and Analytic Techniques will be a valuable resource forresearchers in applied mathematics, physics, and mechanical and electrical engineering, forg raduate students in these disciplines, and for various otherprofessionals who use integration as an essential tool in their work |
Note: | Springer eBooks |
Contents: | 1 Multiphase Flow Splitting in Looped Pipelines |
2 Greens Function Decomposition Method for Transport Equation | |
3 Integral Neutron Transport and New Computational Methods: A Review | |
4 Scale Invariance and Some Limits in Transport Phenomenology: Existence of a Spontaneous Scale | |
5 On Coherent Structures from a Diffusion | |
Type Model | |
6 Numerical Simulation of the Dynamics of Molecular Markers Involved in Cell Polarization | |
7 Analytical Study of Computational Radiative Fluxes in a Heterogeneous Medium | |
8 A Novel Approach to the Hankel Transform Inversion of the Neutron Diffusion P | |
ISBN: | 9781461478287 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Integral equations , Differential Equations , Differential equations, partial , Computer science Mathematics , Engineering mathematics , Materials |
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Call number: | SPRINGER-2013-9781461468684:ONLINE Show nearby items on shelf |
Title: | Seamless R and C++ Integration with Rcpp [electronic resource] |
Author(s): |
Dirk Eddelbuettel |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Rcpp is the glue that binds the power and versatility of R with the speed and efficiency of C++. With Rcpp, the transfer of data between R and C++ is nearly seamless, and high-performance statistical computing is finallyaccessible to most R users. Rc pp should be part of every statistician's toolbox. Michael Braun, MIT Sloan School of Management Seamless R and C++ Integration with Rcpp is simply a wonderful book. For anyone who uses C/C++and R, it is an indispensable resource. The writing is outstandi ng. A huge bonus is the section on applications. This section covers the matrix packages Armadillo and Eigen and the GNU Scientific Library as well as RInside whichenables you to use R inside C++. These applications are what most of us need to know to rea lly do scientific programming with R and C++. I love this book. Robert McCulloch, University of Chicago Booth School of Business Rcpp isnow considered an essential package for anybody doing serious computational research using R. Dirk's book is an excelle nt companion and takes the reader from a gentle introduction to more advanced applications via numerous examples andefficiency enhancing gems. The book is packed with all you might have ever wanted to know about Rcpp, its cousins (RcppArmadillo, RcppEigen etc.), modules, package development and sugar. Overall, this book is a must-have on yourshelf. Sanjog Misra, UCLA Anderson School of Management The Rcpp package represents a major leap forward for scientific computations with R. With very few lines of C+ + code, one has R's data structures readily at hand for furthercomputations in C++. Hence, high-level numerical programming can be made in C++ almost as easily as in R, but often with a substantial speed gain. Dirk is a crucial person in these development s, and his book takes the reader from thefirst fragile steps on to using the full Rcpp machinery. A very recommended book! Sren Hjsgaard, Department of Mathematical S |
Note: | Springer eBooks |
Contents: | Preface |
Introduction | |
A Gentle Introduction to Rcpp | |
Tools and Setup | |
Core Data Types | |
Data Structures: Part One | |
Data Structures: Part Two | |
Advanced Topics | |
Using Rcpp in your package | |
Extending Rcpp | |
Modules | |
Sugar | |
Applications | |
RInside | |
RcppArmadillo | |
RcppGSL | |
RcppEigen Appendix | |
C++ for R programmers | |
Indices | |
References | |
ISBN: | 9781461468684 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Use R! : v64 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Statistics , Computer science , Mathematical statistics |
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Call number: | SPRINGER-2013-9781461459620:ONLINE Show nearby items on shelf |
Title: | Foundations of Abstract Analysis [electronic resource] |
Author(s): |
Jewgeni H Dshalalow |
Date: | 2013 |
Edition: | 2nd ed. 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Foundations of Abstract Analysis is the first of a two book series offered as the second (expanded) edition to the previously published text Real Analysis. It is written for a graduate-level course on real analysis and presentedin a self-contained wa y suitable both for classroom use and for self-study. While this book carries the rigor of advancedmodern analysis texts, it elaborates the material in much greater details and therefore fills a gap betweenintroductory level texts (with topics developed in Euclidean spaces) and advanced level texts (exclusively dealing with abstract spaces) making it accessible for a much wider interested audience. To relieve the reader of thepotential overload of new words, definitions, and concepts, the book (in its u nique feature) provides lists of new terms at the end of each section, in a chronological order. Difficult to understand abstract notions are preceded byinformal discussions and blueprints followed by thorough details andsupported by examples and figures. To further reinforce the text, hints and solutions to almost a half of more than 580 problems are provided at the end of thebook, still leaving ample exercises for assignments. This volume covers topics in point-set topology and measure and integration. P rerequisites include advanced calculus, linear algebra, complex variables, and calculus basedprobability |
Note: | Springer eBooks |
Contents: | Set |
Theoretic and Algebraic Preliminaries | |
Analysis of Metric Spaces | |
Elements of Point | |
Set Topology | |
Measurable Spaces and Measurable Functions | |
Measures | |
Integration in Abstract Spaces | |
Solutions to Selected Problems | |
Bibliography | |
List of Symbols | |
Index of Names and Terms | |
ISBN: | 9781461459620 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Functional analysis , Numerical analysis |
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Call number: | SPRINGER-2013-9780817683948:ONLINE Show nearby items on shelf |
Title: | The CourantFriedrichsLewy (CFL) Condition [electronic resource] 80 Years After Its Discovery |
Author(s): |
Carlos A de Moura Carlos S Kubrusly |
Date: | 2013 |
Publisher: | Boston : Birkhuser Boston : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Thisvolume comprises a carefully selectedcollection ofarticlesemerging from and pertinent to the 2010 CFL-80 conference in Rio de Janeiro,celebrating the80th anniversary of the CourantFriedrichsLewy (CFL)condition. A major result in the field of nume rical analysis, the CFL condition has influenced the research of many important mathematicians over the past eight decades, and this work is meant to take stock of its most important andcurrent applications. The CourantFriedrichsLewy (CFL) Condition: 80 Y ears After its Discovery will be of interest to practicing mathematicians, engineers, physicists, and graduate students who work with numerical methods.Contributors: U. Ascher B. Cockburn E. Deriaz M.O. Domingues S.M. Gomes R. Hersh R. Jeltsch D. Kolomens kiy H. Kumar L.C. Lax P. Lax P. LeFloch A. Marica O. Roussel K. Schneider J. Tiexeira Cal Neto C. Tomei K. van den Doel E. Zuazua |
Note: | Springer eBooks |
Contents: | Foreword |
Stability of Different Schemes | |
Mathematical Intuition: Poincar, Plya, Dewey | |
Three | |
dimensional Plasma Arc Simulation using Resistive MHD | |
A Numerical Algorithm for Ambrosetti | |
Prodi Type Operators | |
On the Quadratic Finite Element Approximation of 1 | |
D Waves: Propagation, Observation, Control, and Numerical Implementation | |
Space | |
Time Adaptive Mutilresolution Techniques for Compressible Euler Equations | |
A Framework for Late | |
time/stiff Relaxation Asymptotics | |
Is the CFL Condition Sufficient? Some Remarks | |
Fast Chaotic Artificial Time Integration | |
Appendix A | |
Han | |
ISBN: | 9780817683948 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Information theory , Differential equations, partial , Computer science Mathematics , Engineering mathematics |
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Call number: | SPRINGER-2013-9780817683856:ONLINE Show nearby items on shelf |
Title: | New Foundations in Mathematics [electronic resource] : The Geometric Concept of Number |
Author(s): |
Garret Sobczyk |
Date: | 2013 |
Publisher: | Boston : Birkhuser Boston : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple androbust means of expressi ng a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematicsand physics. Much of the material presented h as been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modernabstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. The book begins with a discussion of modular numbers (clock arithmetic) and modularpolynomials. This leads to the idea of a spectral basis, the complex and hyperbolic numbers, and finally to geometric algebra, which lays the groundwork for the remainder of the text. Many topics are presented in a new light,including: * vector spaces and matrices * structure of linear operators and quadratic forms * Hermitian inner product spaces * geometry of moving planes * spacetime of special relativity * classical integration theorems *differential geometry of curves and smooth surfaces * projective geometry * Lie groups and Lie algebras. Exercises with selected solutions are provided, and cha pter summaries are included to reinforce concepts as they are covered.Links to relevant websites are often given, and supplementary material is available on the authors website. New Foundations in Mathematics will be of interest to undergraduate and grad uate students of mathematics and physics whoare looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a s |
Note: | Springer eBooks |
Contents: | 1 Modular Number Systems |
2 Complex and Hyperbolic Numbers | |
3 Geometric Algebra | |
4 Vector Spaces and Matrices | |
5 Outer Product and Determinants | |
6 Systems of Linear Equations | |
7 Linear Transformations on R^n | |
8 Structure of a Linear Operator | |
9 Linear and Bilinear Forms | |
10 Hermitian Inner Product Spaces | |
11 Geometry of Moving Planes | |
12 Representations of the Symmetric Group | |
13 Calculus on m | |
Surfaces | |
14 Differential Geometry of Curves | |
15 Differential Geometry of k | |
Surfaces | |
16 Mappings Between Surfaces | |
17 Non | |
Euclidean and Projective Geometries | |
18 Lie Gr | |
ISBN: | 9780817683856 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory , Matrix theory , Topological Groups , Mathematical physics , Engineering mathematics |
Availability: | Click here to see Library holdings or inquire at
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Call number: | SPRINGER-2013-9780817683702:ONLINE Show nearby items on shelf |
Title: | Geography of Order and Chaos in Mechanics [electronic resource] : Investigations of Quasi-Integrable Systems with Analytical, Numerical, and Graphical Tools |
Author(s): |
Bruno Cordani |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This original monograph aims to explore the dynamics in the particular but very important and significant case of quasi-integrable Hamiltonian systems, or integrable systems slightly perturbed by other forces. With both analyticand numerical methods, the book studies several of these systemsincluding for example the hydrogen atom or the solar system, with the associated Arnold webthrough modern tools such as the frequency-modified fourier transform,wavelets, and the frequency-modulation indicator. Me anwhile, it draws heavily on the more standard KAM and Nekhoroshev theorems. Geography of Order and Chaos in Mechanics contains many figures that illuminate its concepts in novelways, but perhaps its most useful feature is its inclusion of software to rep roduce the various numerical experiments. The graphical user interfaces of five supplied MATLAB programs allows readers without any knowledge of computerprogramming to visualize and experiment with the distribution of order, chaos and resonances in variou s Hamiltonian systems. This monograph will be a valuable resource for professional researchers and certain advanced undergraduatestudents in mathematics and physics, but mostly will be an exceptional reference for Ph.D. students with an interest in pertur bation theory |
Note: | Springer eBooks |
Contents: | Preface |
List of Figures | |
1 Introductory Survey | |
2 Analytical Mechanics and Integrable Systems | |
3 Perturbation Theory | |
4 Numerical Tools I: ODE Integration | |
5 Numerical Tools II: Detecting Order, Chaos, and Resonances | |
6 The Kepler Problem | |
7 TheKEPLER Program | |
8 Some Perturbed Keplerian Systems | |
9 The Multi | |
Body Gravitational Problem | |
Bibliography | |
Index | |
ISBN: | 9780817683702 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematical Physics : v64 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differential equations, partial , Global differential geometry , Mathematical physics |
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Call number: | SPRINGER-2012-9789400713666:ONLINE Show nearby items on shelf |
Title: | Numerical Methods with Worked Examples: Matlab Edition [electronic resource] |
Author(s): |
C Woodford C Phillips |
Date: | 2012 |
Edition: | Second Edition |
Publisher: | Dordrecht : Springer Netherlands |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book is for students following an introductory course in numerical methods, numerical techniques or numerical analysis. It introduces MATLAB as a computing environment for experimenting with numerical methods. It approachesthe subject from a pra gmatic viewpoint theory is kept at a minimum commensurate with comprehensive coverage of the subject and it contains abundant worked examples which provide easy understanding through a clear and concisetheoretical treatment. This edition places even great er emphasis on learning by doing than the previous edition. Fully documented MATLAB code for the numerical methods described in the book will be available as supplementarymaterial to to the book on http://extras.springer.com |
Note: | Springer eBooks |
Contents: | 1. Basic Matlab |
2. Linear Equations | |
3.Nonlinear Equations | |
4.Curve Fitting | |
5.Numerical Integration | |
6.Numerical Differentiation | |
7. Linear Programming | |
8.Optimization | |
9.Ordinary Differential Equations | |
10.Eigenvalues and Eigenvectors | |
11. Statistics | |
ISBN: | 9789400713666 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Chemistry , Biology Data processing , Engineering mathematics |
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Call number: | SPRINGER-2012-9783642259838:ONLINE Show nearby items on shelf |
Title: | Spherical Harmonics and Approximations on the Unit Sphere: An Introduction [electronic resource] |
Author(s): |
Kendall Atkinson Weimin Han |
Date: | 2012 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | These notes provide an introduction to the theory of spherical harmonics in an arbitrary dimension as well as an overview of classical and recent results on some aspects of the approximation of functions by spherical polynomialsand numerical integrat ion over the unit sphere. The notes are intended for graduate students in the mathematical sciences and researchers who are interested in solving problems involving partial differential and integral equations onthe unit sphere, especially on the unit sphe re in three-dimensional Euclidean space. Some related work for approximation on the unit disk in the plane is also briefly discussed, with results being generalizable to the unit ball in moredimensions |
Note: | Springer eBooks |
Contents: | 1 Preliminaries |
2 Spherical Harmonics | |
3 Differentiation and Integration over the Sphere | |
4 Approximation Theory | |
5 Numerical Quadrature | |
6 Applications: Spectral Methods | |
ISBN: | 9783642259838 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2044 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Integral equations , Differential equations, partial , Functions, special , Numerical analysis |
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Call number: | SPRINGER-2012-9780817682590:ONLINE Show nearby items on shelf |
Title: | Numerical Analysis [electronic resource] |
Author(s): |
Walter Gautschi |
Date: | 2012 |
Edition: | Second Edition |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The book reads like an unfolding story... Topics are motivated with great care and ingenuity that might be given to establishing the drive behind characters in a good novel... Clarity is never sacrificed for elegance. Above all,the pace is always liv ely and brisk, the writing concise, and the author never lets the exposition bog down... [The book] successfully conveys the author's interest and experience in the subject to the reader. SIAM Review(on theFirst Edition) Revised andupdated, this second ed ition of Walter Gautschi's successful Numerical Analysistextbook explorescomputational methodsfor problems arising in areassuch asclassical analysis, approximation theory,nonlinear equations, and ordinary differential equations. Topics included in the boo k are presented with a view toward stressing basic principles and maintaining simplicity and teachability as far as possible, while subjects requiringa higher level of technicality are referenced in detailed bibliographic notes at the end of each chapter. Readers are thus given the guidance and opportunity to pursue advanced modern topics in more depth. Along with updatedreferences, new biographical notes, and enhanced notational clarity,this second editionincludes the expansion of an alreadylarge collect ion of exercises and assignments, both the kind that deal with theoretical and practicalaspects of the subject and those requiring machine computation and the use of mathematical software. Perhaps most notably, the author has carefully developed and polis hedacomplete solutions manual for this edition, which isavailable through the publisher and will serve as an exceptionally valuable resource for instructors. The text is geared to a one- or two-semester graduate course in numerical analysis for students w ho have a good background incalculus and advanced calculus and some knowledge of linear algebra, complex analysis, and differential equations. Previous exposure to numerical m |
Note: | Springer eBooks |
Contents: | Preface to the Second Edition |
Preface | |
Prologue | |
Chapter 1. Machine Arithmetic and Related Matters | |
Chapter 2. Approximation and Interpolation | |
Chapter 3. Numerical Differentiation and Integration | |
Chapter 4. Nonlinear Equations | |
Chapter 5. Initial Value Problems for ODEs | |
One | |
Step Methods | |
Chapter 6. Initial Value Problems for ODEs | |
Multi | |
Step Methods | |
Chapter 7. Two | |
Point Boundary Value Problems for ODEs | |
References | |
Subject Index | |
ISBN: | 9780817682590 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Differential Equations , Computer science Mathematics , Computer science , Numerical analysis |
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Call number: | SPRINGER-2011-9783642196867:ONLINE Show nearby items on shelf |
Title: | Numerical Methods for Two-phase Incompressible Flows [electronic resource] |
Author(s): |
Sven Gross Arnold Reusken |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book is the first monograph providing an introduction to and an overview of numerical methods for the simulation of two-phase incompressible flows. The Navier-Stokes equations describing the fluid dynamics are examined incombination with models for mass and surfactant transport. The book pursues a comprehensive approach: important modeling issues are treated, appropriate weak formulations are derived, level set and finite element discretizationtechniques are analyzed, efficient iterative solvers are investigated, implementational aspects are considered and the results of numerical experiments are presented. The book is aimed at M Sc and PhD students and other researchers inthe fields of Numerical Analysis and Computational Engineering Science in terested in the numerical treatment of two-phase incompressible flows |
Note: | Springer eBooks |
Contents: | Introduction |
Part I One | |
phase incompressible flows | |
Mathematical models | |
Finite element discretization | |
Time integration | |
ISBN: | 9783642196867 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Series in Computational Mathematics, 0179-3632 : v40 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Computer science Mathematics , Engineering mathematics , Hydraulic engineering , Mechanical engineering |
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Call number: | SPRINGER-2011-9783642160042:ONLINE Show nearby items on shelf |
Title: | Sparse Grid Quadrature in High Dimensions with Applications in Finance and Insurance [electronic resource] |
Author(s): |
Markus Holtz |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book deals with the numerical analysis and efficient numerical treatment of high-dimensional integrals using sparse grids and other dimension-wise integration techniques with applications to finance and insurance. The bookfocuses on providing in sights into the interplay between coordinate transformations, effective dimensions and the convergence behaviour of sparse grid methods. The techniques, derivations and algorithms are illustrated by manyexamples, figures and code segments. Numerical exper iments with applications from finance and insurance show that the approaches presented in this book can be faster and more accurate than (quasi-) Monte Carlo methods, even forintegrands with hundreds of dimensions |
Note: | Springer eBooks |
ISBN: | 9783642160042 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Computational Science and Engineering, 1439-7358 : v77 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Finance , Computer science Mathematics |
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Call number: | SPRINGER-2011-9783642153587:ONLINE Show nearby items on shelf |
Title: | Stochastic Analysis 2010 [electronic resource] |
Author(s): |
Dan Crisan |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Stochastic Analysis aims to provide mathematical tools to describe and model high dimensional random systems. Such tools arise in the study of Stochastic Differential Equations and Stochastic Partial Differential Equations,Infinite Dimensional Stocha stic Geometry, Random Media and Interacting Particle Systems, Super-processes, Stochastic Filtering, Mathematical Finance, etc. Stochastic Analysis has emerged as a core area of late 20th century Mathematicsand is currently undergoing a rapid scientific d evelopment. The special volume Stochastic Analysis 2010 provides a sample of the current research in the different branches of the subject. It includes the collected works of theparticipants at the Stochastic Analysis section of the 7th ISAAC Congress org anized at Imperial College London in July 2009 |
Note: | Springer eBooks |
Contents: | D.Crisan: Introduction to the Volume |
V. Bally and E. Clment: Integration by Parts Formula with Respect to Jump Times for Stochastic Differential Equations | |
V. Ortiz | |
Lpez and M. Sanz | |
Sol: A Laplace Principle for a Stochastic Wave Equation in Spatial Dimension Three | |
X | |
M. Li: Intertwinned Diffusions Operators by Examples | |
L. G. Gyurk and T. Lyons: Effcient and practical implementations of Cubature on Wiener space | |
T. Kurtz: Equivalence of Stochastic Equations and Martingale Problems | |
I. Gyngy and N.V. Krylov: Accelerated Numerical Schemes for PDEs and SPDEs | |
A. Papavasi | |
ISBN: | 9783642153587 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Distribution (Probability theory) |
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Call number: | SPRINGER-2011-9783642150142:ONLINE Show nearby items on shelf |
Title: | Topological Methods in Data Analysis and Visualization [electronic resource] : Theory, Algorithms, and Applications |
Author(s): |
Valerio Pascucci Xavier Tricoche Hans Hagen Julien Tierny |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Topology-based methods are of increasing importance in the analysis and visualization of datasets from a wide variety of scientific domains such as biology, physics, engineering, and medicine. Current challenges of topology-basedtechniques include th e management of time-dependent data, the representation large and complex datasets, the characterization of noise and uncertainty, the effective integration of numerical methods with robust combinatorialalgorithms, etc. While there is an increasing number of high-quality publications in this field, many fundamental questions remain unsolved. New focused efforts are needed in a variety of techniques ranging from the theoreticalfoundations of topological models, algorithmic issues related to the representat ion power of computer-based implementations as well as their computational efficiency, user interfaces for presentation of quantitative topologicalinformation, and the development of new techniques for systematic mapping of science problems in topological constructs that can be solved computationally. The editors have brought together the most prominent and best recognizedresearchers in the field of topology-based data analysis and visualization for a joint discussion and scientific exchange of the latest results in the field. The 2009 TopoInVis workshop in Snowbird, Utah, follows the two successfulworkshops in 2005 (Budmerice, Slovakia) and 2007 (Leipzig, Germany) |
Note: | Springer eBooks |
Contents: | Foundations of Computational Topology |
Hierarchical Topological Data | |
Structures | |
Topological Feature Extraction Algorithms | |
Applications in Scientific Data Analysis and Visualization | |
Topological Analysis of Large | |
Scale Scientific Data | |
Indices | |
ISBN: | 9783642150142 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Visualization, 1612-3786 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Computer graphics , Visualization , Geometry , Topology , Engineering , Mechanical engineering |
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Call number: | SPRINGER-2011-9783642116407:ONLINE Show nearby items on shelf |
Title: | Numerical Techniques for Global Atmospheric Models [electronic resource] |
Author(s): |
Peter Lauritzen Christiane Jablonowski Mark Taylor Ramachandran Nair |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book surveys recent developments in numerical techniques for global atmospheric models. It is based upon a collection of lectures prepared by leading experts in the field. The chapters reveal the multitude of steps thatdetermine the global atmos pheric model design. They encompass the choice of the equation set, computational grids on the sphere, horizontal and vertical discretizations, time integration methods, filtering and diffusion mechanisms,conservation properties, tracer transport, and con siderations for designing models for massively parallel computers. A reader interested in applied numerical methods but also the many facets of atmospheric modeling should find thisbook of particular relevance |
Note: | Springer eBooks |
Contents: | Part I: Equations of motion and some basic ideas on discretizations |
Pat II. Conservation laws, finite | |
volume methods, remapping techniques and spherical grids | |
Part III. Some aspects of atmospheric dynamical cores | |
ISBN: | 9783642116407 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Computational Science and Engineering, 1439-7358 : v80 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Meteorology , Differential equations, partial , Computer science Mathematics |
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Call number: | SPRINGER-2011-9781441986788:ONLINE Show nearby items on shelf |
Title: | Computational Ocean Acoustics [electronic resource] |
Author(s): |
Finn B Jensen William A Kuperman Michael B Porter Henrik Schmidt |
Date: | 2011 |
Edition: | 2 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Since the mid-1970s, the computer has played an increasingly pivotal role in the field of ocean acoustics. Faster and less expensive than actual ocean experiments, and capable of accommodating the full complexity of the acousticproblem, numerical mod els are now standard research tools in ocean laboratories. The progress made in computational ocean acoustics over the last thirty years is summed up in this authoritative and innovatively illustrated new text.Written by some of the field's pioneers, all Fellows of the Acoustical Society of America, Computational Ocean Acoustics presents the latest numerical techniques for solving the wave equation in heterogeneous fluidsolid media. Theauthors discuss various computational schemes in detail, emphasizing t he importance of theoretical foundations that lead directly to numericalimplementations for real ocean environments. To further clarify the presentation, thefundamental propagation features of the techniques are illustrated in color. Computational Ocean A cousticsconveys the state-of-the-art of numerical modeling techniques for graduate and undergraduate students of acoustics, geology andgeophysics, applied mathematics, and ocean engineering. It is also an essential addition to the libraries of ocean resea rch institutions that use propagation models |
Note: | Springer eBooks |
Contents: | Series Preface |
Preface to the Second Edition | |
Preface to the First Edition | |
Fundamentals of Ocean Acoustics | |
Wave Propagation Theory | |
Ray Methods | |
Wavenumber Integration Techniques | |
Normal Modes | |
Parabolic Equations | |
Finite Differences and Finite Elements | |
Broadband Modeling | |
Ambient Noise | |
Signals in Noise | |
Name Index | |
Subject Index | |
ISBN: | 9781441986788 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Modern Acoustics and Signal Processing |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Oceanography , Computer simulation , Acoustics , Acoustics in engineering |
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Call number: | SPRINGER-2011-9781441978653:ONLINE Show nearby items on shelf |
Title: | Time Series Analysis and Its Applications [electronic resource] : With R Examples |
Author(s): |
Robert H Shumway David S Stoffer |
Date: | 2011 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Time Series Analysis and Its Applications presents a balanced and comprehensive treatment of both time and frequency domain methods with accompanying theory. Numerous examples using nontrivial data illustrate solutions to problemssuch as discovering natural and anthropogenic climate change, evaluating pain perception experiments using functional magnetic resonance imaging, and monitoring a nuclear test ban treaty. The book is designed to be useful as a text forgraduate level students in the physical, biological and social sciences and as a graduate level text in statistics. Some parts may also serve as an undergraduate introductory course. Theory and methodology are separated to allowpresentations on different levels. In addition to coverage of class ical methods of time series regression, ARIMA models, spectral analysis and state-space models, the text includes modern developments including categorical timeseries analysis, multivariate spectral methods, long memory series, nonlinear models, resamplin g techniques, GARCH models, stochastic volatility, wavelets and Markov chain Monte Carlo integration methods. The third edition includes anew section on testing for unit roots and the material on state-space modeling, ARMAX models, and regression with aut ocorrelated errors has been expanded. Also new to this edition is the enhanced use of the freeware statistical packageR. In particular, R code is now included in the text for nearly all of the numerical examples. Data sets and additional R scripts are now provided in one file that may be downloaded via the World Wide Web. This R supplement is asmall compressed file that can be loaded easily into R making all the data sets and scripts available to the user with one simple command. The website for the text includes the code used in each example so that the reader may simplycopy-and-paste code directly into R. Appendix R, which is new to this edition, provides a reference for the data sets an |
Note: | Springer eBooks |
Contents: | Characteristics of time series |
Time series regression and exploratory data analysis | |
ARIMA models | |
Spectral analysis and filtering | |
Additional time domain topics | |
State | |
space models | |
Statistical methods in the frequency domain | |
ISBN: | 9781441978653 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Texts in Statistics, 1431-875X |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Statistics , Mathematical statistics |
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Call number: | SPRINGER-2010-9783642139901:ONLINE Show nearby items on shelf |
Title: | Computational Physics [electronic resource] : Simulation of Classical and Quantum Systems |
Author(s): |
Philipp O. J Scherer |
Date: | 2010 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book encapsulates the coverage for a two-semester course in computational physics. The first part introduces the basic numerical methods while omitting mathematical proofs but demonstrating the algorithms by way of numerouscomputer experiments. The second part specializes in simulation of classical and quantum systems with instructive examples spanning many fields in physics, from a classical rotor to a quantum bit. All program examples are realized asJava applets ready to run in your browser an d do not require any programming skills |
Note: | Springer eBooks |
Contents: | Part I: Numerical Methods |
Error Analysis | |
Interpolation | |
Numerical Differentiation | |
Numerical Integration | |
Systems of Inhomogeneous Linear Equations | |
Roots and Minima | |
Fourier Transformation | |
Random Numbers and Monte | |
Carlo | |
Methods | |
Eigenvalue Problems | |
Data Fitting | |
Equations of Motion | |
Part II: Simulation of Classical and Quantum Systems | |
Rotational Motion | |
Simulation of Thermodynamic Systems | |
Random Walk and Brownian Motion | |
Electrostatics | |
Waves | |
Diffusion | |
Nonlinear Systems | |
Simple Quantum Systems | |
ISBN: | 9783642139901 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Chemistry, Physical organic , Chemistry , Computer science Mathematics |
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Call number: | SPRINGER-2010-9783642124303:ONLINE Show nearby items on shelf |
Title: | Scientific Computing with MATLAB and Octave [electronic resource] |
Author(s): |
Alfio Quarteroni Fausto Saleri Paola Gervasio |
Date: | 2010 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This textbook is an introduction to Scientific Computing, in which several numerical methods for the computer-based solution of certain classes of mathematical problems are illustrated. The authors show how to compute the zeros orthe integrals of con tinuous functions, solve linear systems, approximate functions using polynomials and construct accurate approximations for the solution of ordinary and partial differential equations. To make the format concrete andappealing, the programming environments Matlab and Octave are adopted as faithful companions. The book contains the solutions to several problems posed in exercises and examples, often originating from important applications. At theend of each chapter, a specific section is devoted to subjects which were not addressed in the book and contains bibliographical references for a more comprehensive treatment of the material |
Note: | Springer eBooks |
Contents: | 1. What can' t be ignored |
2. Nonlinear equations | |
3. Approximation of functions and data | |
4. Numerical differentiation and integration | |
5. Linear systems | |
6. Eigenvalues and eigenvectors | |
7. Ordinary differential equations | |
8. Numerical approximation of boundary | |
value problems | |
9. Solutions of the exercises | |
References | |
Index | |
ISBN: | 9783642124303 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Texts in Computational Science and Engineering, 1611-0994 : v2 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Chemistry , Computer science , Visualization , Engineering |
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Call number: | SPRINGER-2010-9783642044588:ONLINE Show nearby items on shelf |
Title: | Dynamics of Small Solar System Bodies and Exoplanets [electronic resource] |
Author(s): |
Jean J Souchay Rudolf Dvorak |
Date: | 2010 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book offers an up-to-date overview of current research on Dynamics of Small Solar System Bodies and Exoplanets. In course-tested extensive chapters the authors cover topics of theoretical celestial mechanics, physics anddynamics of asteroids, co mets, stability of exoplanets and numerical integration codes applied in dynamical astronomy |
Note: | Springer eBooks |
Contents: | Resonances: Models and Captures |
The Lyapounov Characteristic Exponents and Their computation | |
Asteroid Families | |
The Dynamics of the Troyan Asteroids | |
The GAIA Mission: Expected Results for Asteroid Studies | |
The Physics of Asteroids and Their Junction With Dynamics | |
Comet Dynamics | |
Dyanmical Features of the Oort Cloud Comets | |
An Introduction to Common Numerical Integration Codes Used in Dynamical Astronomy | |
Dynamic Stability of Extra | |
Solar Planets | |
ISBN: | 9783642044588 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Physics, 0075-8450 : v790 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Differentiable dynamical systems , Mathematical physics , Astrophysics |
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Call number: | SPRINGER-2010-9780857291486:ONLINE Show nearby items on shelf |
Title: | Numerical Methods for Ordinary Differential Equations [electronic resource] : Initial Value Problems |
Author(s): |
David F Griffiths Desmond J Higham |
Date: | 2010 |
Publisher: | London : Springer London |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Numerical Methods for Ordinary Differential Equations is a self-contained introduction to a fundamental field of numerical analysis and scientific computation. Written for undergraduate students with a mathematical background,this book focuses on the analysis of numerical methods without losing sight of the practical nature of the subject. It covers the topics traditionally treated in a first course, but also highlights new and emerging themes. Chapters arebroken down into `lecture' sized pieces, mot ivated and illustrated by numerous theoretical and computational examples. Over 200 exercises are provided and these are starred according to their degree of difficulty. Solutions to allexercises are available to authorized instructors. The book covers ke y foundation topics: o Taylor series methods o Runge-Kutta methods o Linear multistep methods o Convergence o Stability and a range of modern themes: o Adaptivestepsize selection o Long term dynamics o Modified equations o Geometric integration o Stochast ic differential equations The prerequisite of a basic university-level calculus class is assumed, although appropriate background resultsare also summarized in appendices. A dedicated website for the book containing extra information can be found via www. springer.com |
Note: | Springer eBooks |
Contents: | ODEsAn Introduction |
Eulers Method | |
The Taylor Series Method | |
Linear Multistep MethodsI | |
Linear Multistep MethodsII | |
Linear Multistep MethodsIII | |
Linear Multistep MethodsIV | |
Linear Multistep MethodsV | |
RungeKutta MethodI: Order Conditions | |
Runge | |
Kutta MethodsII Absolute Stability | |
Adaptive Step Size Selection | |
Long | |
Term Dynamics | |
Modified Equations | |
Geometric Integration Part IInvariants | |
Geometric Integration Part IIHamiltonian Dynamics | |
Stochastic Differential Equations | |
A Glossary and Notation | |
B Taylor Series | |
C Jacobia | |
ISBN: | 9780857291486 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Undergraduate Mathematics Series, 1615-2085 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Electronic data processing , Numerical analysis |
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Call number: | SPRINGER-2010-9780387687650:ONLINE Show nearby items on shelf |
Title: | Introduction to Probability Simulation and Gibbs Sampling with R [electronic resource] |
Author(s): |
Eric A Suess Bruce E Trumbo |
Date: | 2010 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The first seven chapters use R for probability simulation and computation, including random number generation, numerical and Monte Carlo integration, and finding limiting distributions of Markov Chains with both discrete andcontinuous states. Applica tions include coverage probabilities of binomial confidence intervals, estimation of disease prevalence from screening tests, parallel redundancy for improved reliability of systems, and various kinds ofgenetic modeling. These initial chapters can be used for a non-Bayesian course in the simulation of applied probability models and Markov Chains. Chapters 8 through 10 give a brief introduction to Bayesian estimation and illustrate theuse of Gibbs samplers to find posterior distributions and interval estim ates, including some examples in which traditional methods do not give satisfactory results. WinBUGS software is introduced with a detailed explanation of itsinterface and examples of its use for Gibbs sampling for Bayesian estimation. No previous experie nce using R is required. An appendix introduces R, and complete R code is included for almost all computational examples and problems(along with comments and explanations). Noteworthy features of the book are its intuitive approach, presenting ideas with examples from biostatistics, reliability, and other fields its large number of figures and its extraordinarilylarge number of problems (about a third of the pages), ranging from simple drill to presentation of additional topics. Hints and answers are prov ided for many of the problems. These features make the book ideal for students ofstatistics at the senior undergraduate and at the beginning graduate levels. Eric A. Suess is Chair and Professor of Statistics and Biostatistics and Bruce E. Trumbo is Profe ssor Emeritus of Statistics and Mathematics, both atCalifornia State University, East Bay. Professor Suess is experienced in applications of Bayesian methods and Gibbs sampling to epidemiology. Profes |
Note: | Springer eBooks |
Contents: | Introductory Examples: Simulation, Estimation, and Graphics |
Generating Random Numbers | |
Monte Carlo Integration and Limit Theorems | |
Sampling from Applied Probability Models | |
Screening Tests | |
Markov Chains with Two States | |
Examples of Markov Chains with Larger State Spaces | |
Introduction to Bayesian Estimation | |
Using Gibbs Samplers to Compute Bayesian Posterior Distributions | |
Using WinBUGS for Bayesian Estimation | |
Appendix: Getting Started with R | |
ISBN: | 9780387687650 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Use R : v0 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Statistics , Mathematical statistics |
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Call number: | SPRINGER-2009-9780387781655:ONLINE Show nearby items on shelf |
Title: | Monte Carlo and Quasi-Monte Carlo Sampling [electronic resource] |
Author(s): |
Christiane Lemieux |
Date: | 2009 |
Edition: | 1 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | QuasiMonte Carlo methods have become an increasingly popular alternative to Monte Carlo methods over the last two decades. Their successful implementation on practical problems, especially in finance, has motivated thedevelopment of several new resea rch areas within this field to which practitioners and researchers from various disciplines currently contribute. This book presents essential tools for using quasiMonte Carlo sampling in practice.The first part of the book focuses on issues related to Mo nte Carlo methodsuniform and non-uniform random number generation, variance reduction techniquesbut the material is presented to prepare the readers for the next step,which is to replace the random sampling inherent to Monte Carlo by quasirandom sampling. The second part of the book deals with this next step. Several aspects of quasi-Monte Carlo methods are covered, including constructions,randomizations, the use of ANOVA decompositions, and the concept of effective dimension. The third part of the book i s devoted to applications in finance and more advanced statistical tools like Markov chain Monte Carlo and sequentialMonte Carlo, with a discussion of their quasiMonte Carlo counterpart. The prerequisites for reading this book are a basic knowledge of sta tistics and enough mathematical maturity to follow through the various techniques usedthroughout the book. This text is aimed at graduate students in statistics, management science, operations research, engineering, and applied mathematics. It should also be useful to practitioners who want to learn more about MonteCarlo and quasiMonte Carlo methods and researchers interested in an up-to-date guide to these methods. Christiane Lemieux is an Associate Professor and the Associate Chair for Actuarial Science in the Department of Statistics andActuarial Science at the University of Waterloo in Canada. She is an Associate of the Society of Actuaries and was the winner of a Young Researc |
Note: | Springer eBooks |
Contents: | The Monte Carlo Method |
Sampling from Known Distributions | |
Pseudorandom Number Generators | |
Variance Reduction Techniques | |
QuasiMonte Carlo Constructions | |
Using QuasiMonte Carlo in Practice | |
Financial Applications | |
Beyond Numerical Integration | |
ISBN: | 9780387781655 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Series in Statistics, 0172-7397 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Statistics , Mathematical statistics |
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Call number: | SPRINGER-2009-9780387095042:ONLINE Show nearby items on shelf |
Title: | Mathematical Methods [electronic resource] : For Students of Physics and Related Fields |
Author(s): |
Sadri Hassani |
Date: | 2009 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Intended to follow the usual introductory physics courses, this book has the unique feature of addressing the mathematical needs of sophomores and juniors in physics, engineering and other related fields. Many original, lucid,and relevant examples fr om the physical sciences, problems at the ends of chapters, and boxes to emphasize important concepts help guide the student through the material. Beginning with reviews of vector algebra and differential andintegral calculus, the book continues with infi nite series, vector analysis, complex algebra and analysis, ordinary and partial differential equations. Discussions of numerical analysis, nonlinear dynamics and chaos, and the Diracdelta function provide an introduction to modern topics in mathematical physics. This new edition has been made more user-friendly through organization into convenient, shorter chapters. Also, it includes an entirely new section onProbability and plenty of new material on tensors and integral transforms. Some praise for the p revious edition: The book has many strengths. For example: Each chapter starts with a preamble that puts the chapters in context. Often,the author uses physical examples to motivate definitions, illustrate relationships, or culminate the development of pa rticular mathematical strands. The use of Maxwell's equations to cap the presentation of vector calculus, adiscussion that includes some tidbits about what led Maxwell to the displacement current, is a particularly enjoyable example. Historical touches li ke this are not isolated cases the book includes a large number of notes on people andideas, subtly reminding the student that science and mathematics are continuing and fascinating human activities. --Physics Today Very well written (i.e., extremely read able), very well targeted (mainly to an average student ofphysics at a point of just leaving his/her sophomore level) and very well concentrated (to an author's apparently beloved subject of PDE's w |
Note: | Springer eBooks |
Contents: | Coordinates and Calculus |
Coordinate Systems and Vectors | |
Differentiation | |
Integration: Formalism | |
Integration: Applications | |
Dirac Delta Function | |
Algebra of Vectors | |
Planar and Spatial Vectors | |
Finite | |
Dimensional Vector Spaces | |
Vectors in Relativity | |
Infinite Series | |
Infinite Series | |
Application of Common Series | |
Integrals and Series as Functions | |
Analysis of Vectors | |
Vectors and Derivatives | |
Flux and Divergence | |
Line Integral and Curl | |
Applied Vector Analysis | |
Curvilinear Vector Analysis | |
Tensor Analysis | |
Complex Analysis | |
Complex Arithmetic | |
Co | |
ISBN: | 9780387095042 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Mathematics , Mathematical physics |
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Call number: | SPRINGER-2008-9788847007529:ONLINE Show nearby items on shelf |
Title: | Partial Differential Equations in Action [electronic resource] : From Modelling to Theory |
Author(s): |
Sandro Salsa |
Date: | 2008 |
Publisher: | Milano : Springer Milan |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book is designed as an advanced undergraduate or a first-year graduate course for students from various disciplines like applied mathematics, physics, engineering. The main purpose is on the one hand to train the students toappreciate the interp lay between theory and modelling in problems arising in the applied sciences on the other hand to give them a solid theoretical background for numerical methods, such as finite elements. Accordingly, this textbookis divided into two parts. The first one h as a rather elementary character with the goal of developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. Ideas andconnections with concrete aspects are emphasized whenever possible, in or der to provide intuition and feeling for the subject. For this part, a knowledge of advanced calculus and ordinary differential equations is required. Also, therepeated use of the method of separation of variables assumes some basic results from the theor y of Fourier series, which are summarized in an appendix. The main topic of the second part is the development of Hilbert space methods forthe variational formulation and analysis of linear boundary and initial-boundary value problems\emph{. }% Given the abstract nature of these chapters, an effort has been made to provide intuition and motivation for the various conceptsand results. The understanding of these topics requires some basic knowledge of Lebesgue measure and integration, summarized in another appendix. At the end of each chapter, a number of exercises at different level of complexity isincluded. The most demanding problems are supplied with answers or hints. The exposition if flexible enough to allow substantial changes without compromising th e comprehension and to facilitate a selection of topics for a one or twosemester course |
Note: | Springer eBooks |
Contents: | Diffusion |
The Laplace Equation | |
Scalar Conservation Laws and First Order Equations | |
Waves and Vibrations | |
Elements of Functional Analysis | |
Distributions and Sobolev Spaces | |
Variational Formulation of Elliptic Problems | |
Weak Formulation of Evolution Problems | |
ISBN: | 9788847007529 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext, 0172-5939 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differential equations, partial |
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Call number: | SPRINGER-2008-9783540769675:ONLINE Show nearby items on shelf |
Title: | Jets From Young Stars III [electronic resource] : Numerical MHD and Instabilities |
Author(s): |
S Massaglia G Bodo A Mignone P Rossi |
Date: | 2008 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This volume contains the lecture notes of the Third JETSET School on Jets from Young Stars focussing on Numerical MHD and Instabilities. The introductory lectures presented here cover the basic concepts of the numerical methodsfor the integration of hydrodynamic and magnetohydrodynamic equations and of the applications of these methods to the treatment of the instabilities relevant for the physics of stellar jets. The first part of the book contains anintroduction to the finite difference and finite volume methods for computing the solutions of hyperbolic partial differential equations and a discussion of approximate Riemann solvers for both hydrodynamic and magnetohydrodynamicproblems. The second part is devoted to the discussion of some of the main instability processes that may take place in stellar jets, namely: the Kelvin-Helmholtz, the radiative shock, the pressure driven and the thermal instabilities.Graduate students and young scientists will benefit from this book by learning how to use the fundamental tools used in computational astrophysical jet research |
Note: | Springer eBooks |
Contents: | Computational Methods for Hyperbolic Equations |
Shock | |
Capturing Schemes in Computational MHD | |
The Kelvin | |
Helmholtz Instability | |
Pressure | |
Driven Instabilities in Astrophysical Jets | |
Thermal Instabilities | |
The Oscillatory Instability of Radioactive Shock Waves | |
Index | |
ISBN: | 9783540769675 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Physics, 0075-8450 : v754 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Astrophysics |
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Call number: | SPRINGER-2008-9783540683490:ONLINE Show nearby items on shelf |
Title: | Interpolation Processes [electronic resource] : Basic Theory and Applications |
Author(s): |
Giuseppe Mastroianni Gradimir V Milovanovi |
Date: | 2008 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The classical books on interpolation address numerous negative results, i.e., results on divergent interpolation processes, usually constructed over some equidistant systems of nodes. The authors present, with complete proofs,recent results on conver gent interpolation processes, for trigonometric and algebraic polynomials of one real variable, not yet published in other textbooks and monographs on approximation theory and numerical mathematics. In thisspecial, but fundamental and important field of r eal analysis the authors present the state of art. Some 500 references are cited, including many new results of the authors. Basic tools in this field (orthogonal polynomials, moduli ofsmoothness, K-functionals, etc.) as well as some selected applications in numerical integration, integral equations, moment-preserving approximation and summation of slowly convergent series are also given. Beside the basic propertiesof the classical orthogonal polynomials the book provides new results on nonclassical ortho gonal polynomials including methods for their numerical construction |
Note: | Springer eBooks |
Contents: | 1. Constructive Elements and Approaches in Approximation Theory |
1.1 Introduction to Approximation Theory | |
1.2 Basic Facts on Trigonometric Approximation | |
1.3 Chebyshev Systems and Interpolation | |
1.4 Interpolation by Algebraic Polynomials | |
2. Orthogonal Polynomials and Weighted Polynomial Approximation | |
2.1 Orthogonal Systems and Polynomials | |
2.2 Orthogonal Polynomials on the Real Line | |
2.3 Classical Orthogonal Polynomials | |
2.4 Nonclassical Orthogonal Polynomials | |
2.5 Weighted Polynomial Approximation | |
3. Trigonometric Approximation | |
3.1 Approximating Properties of Oper | |
ISBN: | 9783540683490 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Fourier analysis , Integral equations , Sequences (Mathematics) , Functions, special |
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