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Call number: | 9783319516585:ONLINE Show nearby items on shelf |
Title: | Inverse Problems for Partial Differential Equations |
Author(s): |
Victor Isakov |
Date: | 2017 |
Edition: | 3rd ed. 2017 |
Size: | 1 online resource (XV, 406 p. 4 illus p.) |
Contents: | Inverse Problems -- Ill-Posed Problems and Regularization -- Uniqueness and Stability in the Cauchy Problem -- Elliptic Equations: Single Boundary Measurements -- Elliptic Equations: Many Boundary Measurements -- Scattering Problems |
and Stationary Waves -- Integral Geometry and Tomography -- Hyperbolic Problems -- Inverse Parabolic Problems -- Some Numerical Methods -- Appendix: Functional Spaces | |
ISBN: | 9783319516585 |
Series: | eBooks |
Series: | Springer eBooks |
Series: | Springer 2017 package |
Keywords: | Mathematics , Remote sensing , Partial differential equations , Computer mathematics , Physics , Mathematics , Partial Differential Equations , Computational Mathematics and Numerical Analysis , Theoretical, Mathematical and Computational Physics , Remote Sensing/Photogrammetry |
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Call number: | 9783319470795:ONLINE Show nearby items on shelf |
Title: | Recent Trends in Operator Theory and Partial Differential Equations The Roland Duduchava Anniversary Volume |
Author(s): | |
Date: | 2017 |
Size: | 1 online resource (XVIII, 300 p. 24 illus., 22 illus. in color p.) |
Contents: | Roland Duduchava -- The Duduchava-Roch formula -- Convolution Type Operators with Symmetry in Bessel Potential Spaces -- On Symmetries of the Feinberg-Zee Random Hopping Matrix -- Inequalities of Babuška-Aziz and Friedrichs-Velte for |
differential forms -- High Frequency Oscillations of first Eigenmodes in Axisymmetric shells as the thickness tends to zero -- Kernels of Wiener-Hopf plus Hankel operators with matching generating functions -- Spline Galerkin methods | |
for the double layer potential equations on contours with corners -- C*-algebras of Bergman Type Operators with Piecewise Continuous Coefficients over Bounded Polygonal Domains -- Solvability and Lyapunov stability of a two-component | |
system of generalized Poisson-Nernst-Planck equations -- A local uniqueness result for a quasi-linear heat transmission problem in a periodic two-phase dilute composite -- The method of potential operators for anisotropic Helmholtz | |
operators on domains with smooth unbounded boundaries -- Gabor Analysis for Schrödinger Equations and Propagation of Singularities -- Commutative algebras of Toeplitz operators on a Siegel domain associated with the nilpotent group of | |
its biholomorphisms | |
ISBN: | 9783319470795 |
Series: | eBooks |
Series: | Springer eBooks |
Series: | Springer 2017 package |
Keywords: | Mathematics , Integral equations , Operator theory , Partial differential equations , Numerical analysis , Mathematics , Operator Theory , Partial Differential Equations , Integral Equations , Numerical Analysis |
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Call number: | 9783319008318:ONLINE Show nearby items on shelf |
Title: | Analytic Inequalities and Their Applications in PDEs |
Author(s): |
Yuming Qin |
Date: | 2017 |
Size: | 1 online resource (XIII, 564 p p.) |
Contents: | Preface -- 1 Integral Inequalities -- 2 Differential and Difference Inequalities -- 3 Global Attractors for Evolutionary Differential Equations -- 4 Global Existence and Uniqueness for Evolutionary PDEs -- 5 Asymptotic Behavior for |
Evolutionary PDEs.-6 Blow-up of Solutions to Evolutionary PDEs -- 7 Appendix: Basic Inequalities. | |
ISBN: | 9783319008318 |
Series: | eBooks |
Series: | Springer eBooks |
Series: | Springer 2017 package |
Keywords: | Mathematics , Operator theory , Partial differential equations , Mathematical physics , Mathematics , Partial Differential Equations , Classical Mechanics , Operator Theory , Mathematical Physics |
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Call number: | 9781608075355:ONLINE Show nearby items on shelf |
Title: | Microstrip lines and slotlines |
Author(s): |
Ramesh Garg I. J. Bahl Maurizio Bozzi |
Date: | 2013 |
Edition: | Third edition. |
Publisher: | Artech House |
Size: | 1 online resource (589 p.) |
Contents: | Chapter 1 Microstrip Lines I - Quasi-Static Analyses, Dispersion Models, and Measurements -- Planar Transmission Structures -- Microstrip Field Configuration -- Methods of Microstrip Analysis Quasi-Static Analyses of a Microstrip -- Modified Conformal Transformation Method -- Finite Difference Method -- Integral Equation Meth od -- Variational Method in the Fourier Transform Domain -- Segmentation and Boundary Element Method -- Microstrip Dispersion Models -- Coupled TEM Mode and TM Mode Model -- An Empirical Relation -- Dielectric-Loaded Ridged Waveguide Model -- Empirical F ormulae for Broad Frequency Range -- Planar Waveguide Model -- Microstrip Transitions -- Coaxial-to-Microstrip Transition -- Waveguide-to-Microstrip Transition -- Microstrip Measurements -- Substrate Dielectric Constant -- Characteristic Impendance -- Pha se Velocity or Effective Dielectric Constant -- Attenuation Constant -- Fabrication -- Printed Circuit Technologies -- Hybrid Microwave Integrated Circuits -- Monolithic Integrated Circuit Technologies |
Chapter 2 Microstrip Lines II -- Fullwave Analyses, Design Considerations, and Applications -- Methods of Fullwave Analysis -- Analysis of an Open Microstrip -- Integral Equation Method in the Space Domain -- Galerkin.s Method in the Spectral Domain -- Analysis of an Enclosed Microstrip -- Integral Equation Methods -- Finite Difference Method -- Design Considerations -- Microstrip Losses -- Power Handling Capability -- Effect of Tolerances -- Effect of Dielectric Anisotropy -- Frequency Range of Ope ration -- Lumped Element Model of Microstrip Interconnect -- Other Types of Microstrip Lines -- Suspended and Inverted Microstrip Lines -- Multilayered Dielectric Microstrip -- Thin Film Microstrip -- Valley Microstrip Lines -- Buried Microstrip Line -- S uperconducting Microstrip Circuits -- Microstrip Applications -- Lumped Elements -- Passive Components -- Active Components -- Packages and Assemblies | |
Chapter 3 Microstrip Discontinuities I -- Quasi-Static Analysis and Characterization -- Discontinui ty Capacitance Evaluation -- Matrix Inversion Method -- Variational Method -- Galerkins Method in the Fourier Transform Domain -- Use of Line Sources with Charge Reversal -- Discontinuity Inductance Evaluation -- Characterization of Various Discontinuitie s -- Open Ends -- Gaps in a Microstrip -- T-Junctions -- Cross Junctions -- RF Short and Via Hole -- Compensated Microstrip Discontinuities | |
Chapter 4 Microstrip Discontinuities II: Fullwave Analysis and Measurements -- Planar Waveguide Analysis -- Discontinuity Characterization -- Compensation of Discontinuity Reactances -- Radiation and Parasitic Coupling -- Fullwave Analysis of Discon tinuities . Galerkins Method in the Spectral Domain -- Integral Equation Solution in the Space Domain -- Time Domain Methods for Microstrip Discontinuity -- Discontinuity Measurements -- Linear Resonator Method -- Ring Resonator Method -- Scattering Param eters Measurement Method | |
Chapter 5 Slotlines -- Slotline Analysis -- Approximate Analysis -- Transverse Resonance Method . Galerkins Method in the Spectral Domain -- Design Considerations -- Closed-Form Expressions -- Effect of Metal Thickness -- Effec t of Tolerances -- Losses in Slotline -- Slotline Discontinuities -- Short End Discontinuty -- Open End Discontinuity -- Variants of Slotline -- Coupled Microstrip-Slotline -- Conductor-Backed Slotline -- Conductor-Backed Slotline with Superstrate -- Slot lines with Double-Layered Dielectric -- Slotline Transitions -- Coaxial-to-Slotline Transition -- Microstrip-to-Slotline Cross-Junction Transition -- Slotline Applications -- Circuits Using T-Junctions -- Circuits Using Wideband 180 Phase Shift -- Hybrid /de Ronde.s Branchline Couplers | |
Chapter 6 Defected Ground Structure (DGS) -- Basic Structure of DGS -- Unit Cell and Periodic DGS -- Advantages and Disadvantages of DGS -- DGS Characteristics -- Stop-Band Properties -- Slow-Wave Propagation -- Realization of Transmission Lines wit h High Characteristic Impedance -- Modeling of DGS -- Full-Wave Modeling -- Equivalent Circuit Models -- Applications of DGS -- DGS-Based Filters -- Other DGS-Based Passive Components -- DGS-Based Active Circuits -- DGS-Based Antennas | |
Chapter 7 Coplan ar Lines: Coplanar Waveguide and Coplanar Strips -- Quasi-Static Conformal Mapping Analysis of CPW -- Quasi-Static Conformal Mapping Analysis of CPS -- Fullwave Analysis -- Design Considerations -- Design Equations -- Dispersion -- Effect of Metallization Thickness -- Losses in Coplanar Lines -- Dielectric Loss -- Conductor Loss -- Radiation and Surface Wave Losses -- Effect of Tolerances -- Comparison with Microstrip Line and Slotline -- Transitions -- Coax-to-CPW Transitions -- Microstrip-to-CPS Transit ions -- Microstrip-to-CPW Transition -- CPW-to-CPS Transitions -- CPS-to-Slotline Transitions -- Slotline-to-CPW Transitions -- Discontinuities in Coplanar Lines -- CAD Models for Discontinuities in Coplanar Waveguide Circuits -- CAD Models for Discontinu ities in Coplanar Strips Circuits -- Coplanar Line Circuits -- Circuits with Series and Shunt Reactances in CPW -- Circuits Using Slotline-CPW Junctions | |
Chapter 8 Coupled Microstrip Lines -- General Analysis of Coupled Lines -- Methods of Analysis -- Coupled Mode Approach -- Even- and Odd-Mode Approach -- Characteristics of Coupled Microstrip Lines -- Quasi-Static Analysis -- Fullwave Analysis -- Di spersion Models -- Measurements on Coupled Microstrip Lines -- Impedance Measurements -- Phase Constant Measurements -- Design Considerations for Coupled Microstrip Lines -- Design Equations -- Effect of Fabrication Tolerances -- Coupled Microstrip Lines with Dielectric Overlays -- Effect of Dielectric Anisotropy -- Slot-Coupled Microstrip Lines -- Coupled Multiconductor Microstrip Lines -- Discontinuities in Coupled Microstrip Lines -- Network Model -- Open-End Discontinuity | |
Chapter 9 Substrate Integrated Waveguide (SIW) -- Operation Principle -- Analysis Techniques of SIW . Equivalent Rectangular Waveguide -- Full-wave Modeling of SIW Interconnects -- Full-wave Modeling of SIW Components -- Equivalent Circuits Models o f SIW Discontinuities -- Design Considerations -- Mechanisms of Loss -- Guided.wave and Leaky-wave Regions of Operation -- Band-gap Effects in SIW Structures -- SIW Design Rules -- Substrate Integrated Folded Waveguide (SIFW) -- Half-Mode Substrate Integr ated Waveguide (HMSIW) -- Substrate Integrated Slab Waveguide (SISW) -- Substrate Integrated Ridge Waveguide (SIRW) -- Transitions Between SIW and Planar Transmission Lines -- Microstrip-to-SIW Transitions -- CPW-to-SIW Transitions -- SIW Components and A ntennas -- Passive Components -- Active Circuits -- Antennas -- System-on-Substrate (SoS) -- Fabrication Technologies and Materials -- Fabrication by PCB and LTCC Technologies -- Integration of SIW on Silicon -- Use of Novel Substrate Materials -- Solutio ns for High Frequency Operation of SIW | |
ISBN: | 9781608075355 |
Series: | eBooks |
Series: | Artech eBooks |
Keywords: | Strip transmission lines. , Microwave transmission lines. , Microwave integrated circuits. |
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Location: | ONLINE |
Call number: | 047140165X:ONLINE Show nearby items on shelf |
Title: | Integral Equations |
Author(s): |
Hochstadt |
Date: | 1973 |
Publisher: | Wiley |
Size: | 1 online resource (283 p.) |
ISBN: | 9780471401650 |
Series: | eBooks |
Series: | Wiley Online Library |
Series: | Wiley 2016 package purchase |
Keywords: | Mathematics |
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Call number: | 0470487674:ONLINE Show nearby items on shelf |
Title: | Time and Frequency Domain Solutions of EM Problems Using Integral Equations and a Hybrid Methodology |
Author(s): |
Jung |
Date: | 2010 |
Publisher: | Wiley-IEEE Press |
Size: | 1 online resource (482 p.) |
ISBN: | 9780470487679 |
Series: | eBooks |
Series: | Wiley Online Library |
Series: | Wiley 2016 package purchase |
Keywords: | Electrical & Electronics Engineering |
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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-2016-9783319321448:ONLINE Show nearby items on shelf |
Title: | From Particle Systems to Partial Differential Equations III Particle Systems and PDEs III, Braga, Portugal, December 2014 |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (3 p.) |
Note: | 10.1007/978-3-319-32144-8 |
Contents: | Convergence of Diffusion-Drift Many Particle Systems in Probability under a Sobolev Norm -- Global asymptotic stability of a general nonautonomous Cohen-Grossberg model with unbounded ampliﬁcation functions -- Modelling of systems with a dispersed phase: “measuring” small sets in the presence of elliptic operators -- From market data to agent-based models and stochastic differential equations -- Entropy dissipation estimates for the Landau equation: General cross sections -- Phase transitions and coarse-graining for a system of particles in the continuum -- Sub–shock formation in reacting gas mixtures -- The gradient ﬂow approach to hydrodynamic limits for the simple exclusion process -- The gradient ﬂow approach to hydrodynamic limits f or the simple exclusion process -- Hydrodynamic limit of quantum random walks -- Derivation of the Boltzmann equation: hard spheres, short-range potentials and beyond -- Duality relations for the periodic ASEP conditioned on a low current -- |
Asymptotics for FBSDES with Jumps and Connections with Partial Integral Differential Equations -- The Boltzmann Equation over RD: Dispersion vs Dissipation | |
ISBN: | 9783319321448 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Springer Proceedings in Mathematics & Statistics: 162 |
Keywords: | Mathematics , Functional analysis , Partial differential equations , Applied mathematics , Engineering mathematics , Probabilities , Physics , Mathematics , Functional Analysis , Partial Differential Equations , Applications of Mathematics , Probability Theory and Stochastic Processes , Numerical and Computational Physics |
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Call number: | SPRINGER-2016-9783319301303:ONLINE Show nearby items on shelf |
Title: | Adaptive Discontinuous Galerkin Methods for Non-linear Reactive Flows |
Author(s): |
Murat Uzunca |
Date: | 2016 |
Size: | 1 online resource (10 p.) |
Note: | 10.1007/978-3-319-30130-3 |
Contents: | 1 INTRODUCTION -- 1.1 Geological and computational background -- 1.2 Outline -- 2 DISCONTINUOUS GALERKIN METHODS -- 2.1 Preliminaries -- 2.2 Construction of IPG Methods -- 2.3 Computation Tools for Integral Terms -- 2.4 Effect of Penalty Parameter -- 2.5 Problems with Convection -- 3 ELLIPTIC PROBLEMS WITH ADAPTIVITY -- 3.1 Model Elliptic Problem -- 3.2 Adaptivity -- 3.3 Solution of Linearized Systems -- 3.4 Comparison with Galerkin Least Squares FEM (GLSFEM) -- 3.5 Numerical Examples -- 4 PARABOLI C PROBLEMS WITH TIME-SPACE ADAPTIVITY -- 4.1 Preliminaries and Model Equation -- 4.2 Semi-Discrete and Fully Discrete Formulations -- 4.3 Time-Space Adaptivity for Non-Stationary Problems -- 4.4 Solution of Fully Discrete System -- 4.5 Numerical Examples. -REFERENCES. |
ISBN: | 9783319301303 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Geophysics , Partial differential equations , Numerical analysis , Mathematics , Numerical Analysis , Partial Differential Equations , Geophysics/Geodesy |
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Call number: | SPRINGER-2016-9783319299778:ONLINE Show nearby items on shelf |
Title: | The Callias Index Formula Revisited |
Author(s): |
Fritz Gesztesy |
Date: | 2016 |
Size: | 1 online resource (192 p.) |
Note: | 10.1007/978-3-319-29977-8 |
Contents: | Introduction.-Notational Conventions -- Functional Analytic -- On Schatten–von Neumann Classes and Trace Class -- Pointwise Estimates for Integral Kernels -- Dirac-Type -- Derivation of the Trace Formula – The Trace Class Result -- Derivation o f the Trace Formula – Diagonal Estimates -- The Case n = 3 -- The Index Theorem and Some Consequences -- Perturbation Theory for the Helmholtz Equation -- The Proof of Theorem 10.2: The Smooth Case -- The Proof of Theorem 10.2: The General Case -- A Par ticular Class of Non-Fredholm Operators L and Their Generalized Witten Index -- A: Construction of the Euclidean Dirac Algebra -- B: A Counterexample to [22, Lemma 5] -- References -- Index |
ISBN: | 9783319299778 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Mathematics: 2157 |
Keywords: | Mathematics , Functional analysis , Operator theory , Partial differential equations , Mathematics , Partial Differential Equations , Operator Theory , Functional Analysis |
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Call number: | SPRINGER-2016-9783319296685:ONLINE Show nearby items on shelf |
Title: | A Concise Course on the Theory of Classical Liquids Basics and Selected Topics |
Author(s): |
Andrés Santos |
Date: | 2016 |
Size: | 1 online resource (94 p.) |
Note: | 10.1007/978-3-319-29668-5 |
Contents: | Foreword -- Preface -- Summary of Thermodynamic Potentials -- Summary of Equilibrium Statistical Ensembles -- Density Expansion of the Equation of State -- Spatial Correlation Functions and Thermodynamic Routes -- One-Dimensional |
Systems. Exact Solution for Nearest-Neighbor Interactions -- Density Expansion of the Radial Distribution Function. Approximate Integral Equations -- Exact Solution of the Percus–Yevick Approximation for Hard Spheres ... and Beyond -- | |
Index -- References | |
ISBN: | 9783319296685 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Physics: 923 |
Keywords: | Physics , Physical chemistry , Fluids , Thermodynamics , Amorphous substances , Complex fluids , Statistical physics , Dynamical systems , Physics , Soft and Granular Matter, Complex Fluids and Microfluidics , Statistical Physics, Dynamical Systems and Complexity , Physical Chemistry , Thermodynamics , Fluid- and Aerodynamics |
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Call number: | SPRINGER-2016-9783319290003:ONLINE Show nearby items on shelf |
Title: | Divergent Series, Summability and Resurgence III Resurgent Methods and the First Painlevé Equation |
Author(s): |
Eric Delabaere |
Date: | 2016 |
Size: | 1 online resource (14 p.) |
Note: | 10.1007/978-3-319-29000-3 |
Contents: | Avant-Propos -- Preface to the three volumes -- Preface to this volume -- Some elements about ordinary differential equations -- The first Painlevé equation -- Tritruncated solutions for the first Painlevé equation -- A step beyond Borel-Laplace summability -- Transseries and formal integral for the first Painlevé equation -- Truncated solutions for the first Painlevé equation -- Supplements to resurgence theory -- Resurgent structure for the first Painlevé equation -- Index |
ISBN: | 9783319290003 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Mathematics: 2155 |
Keywords: | Mathematics , Functions of complex variables , Differential equations , Sequences (Mathematics) , Special functions , Mathematics , Sequences, Series, Summability , Ordinary Differential Equations , Functions of a Complex Variable , Special Functions |
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Call number: | SPRINGER-2016-9783319287393:ONLINE Show nearby items on shelf |
Title: | Nonlocal Diffusion and Applications |
Author(s): |
Claudia Bucur |
Date: | 2016 |
Size: | 1 online resource (23 p.) |
Note: | 10.1007/978-3-319-28739-3 |
Contents: | Introduction -- 1 A probabilistic motivation.-1.1 The random walk with arbitrarily long jumps -- 1.2 A payoff model.-2 An introduction to the fractional Laplacian.-2.1 Preliminary notions -- 2.2 Fractional Sobolev Inequality and Generalized Coarea F ormula -- 2.3 Maximum Principle and Harnack Inequality -- 2.4 An s-harmonic function -- 2.5 All functions are locally s-harmonic up to a small error -- 2.6 A function with constant fractional Laplacian on the ball -- 3 Extension problems -- 3.1 Water wave model -- 3.2 Crystal dislocation -- 3.3 An approach to the extension problem via the Fourier transform -- 4 Nonlocal phase transitions -- 4.1 The fractional Allen-Cahn equation -- 4.2 A nonlocal version of a conjecture by De Giorgi -- 5 Nonlocal minimal surfaces -- 5.1 Graphs and s-minimal surfaces -- 5.2 Non-existence of singular cones in dimension 2 5.3 Boundary regularity -- 6 A nonlocal nonlinear stationary Schrödinger type equation -- 6.1 From the nonlocal Uncertainty Principle to a |
fractional weighted inequality -- Alternative proofs of some results -- A.1 Another proof of Theorem A.2 Another proof of Lemma 2.3 -- References | |
ISBN: | 9783319287393 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes of the Unione Matematica Italiana: 20 |
Keywords: | Mathematics , Functional analysis , Integral transforms , Operational calculus , Partial differential equations , Calculus of variations , Mathematics , Partial Differential Equations , Calculus of Variations and Optimal Control Optimization , Integral Transforms, Operational Calculus , Functional Analysis |
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Call number: | SPRINGER-2016-9783319284439:ONLINE Show nearby items on shelf |
Title: | Computational Analysis AMAT, Ankara, May 2015 Selected Contributions |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (396 p.) |
Note: | 10.1007/978-3-319-28443-9 |
Contents: | Bivariate Left Fractional Pseudo-Polynomial Monotone Approximation (Anastassiou, G.A.) -- Bivariate Right Fractional Polynomial Monotone Approximation (Anastassiou, G.A.) -- Uniform Approximation with Rates by Multivariate Generalized Discrete Singu lar Operators (Anastassiou, G.A. & Kester, M.) -- Summation Process by Max-Product Operators (Gökçer, T.Y. & Duman, O.) -- Fixed Point in a Non-Metrizable Space (Tallafha, A. & Alhihi, S.A.) -- Second Hankel Determinant for New Subclass Defined by a Lin ear Operator (Amer, A.A.) -- Some Asymptotics for Extremal Polynomials (Alpan, G., Goncharov, A. & Hatinoglu, B.) -- Some Differential Subordinations Using Ruscheweyh Derivative and a Multiplier Transformation (Lupas, A.A.) -- Some Results on the Bivariat e Laguerre Polynomials (Özarslan, M.A. & Kürt, C.) -- Inner Product Spaces and Quadratic Functional Equations (Park, C., Park, W.-G. & Rassias, T.M.) -- Fuzzy Partial Metric Spaces (Amer, F.J.) -- Bounded and Unbounded Fundamental Solutions |
in MAC Models (Neygebauer, I.) -- Schurer Generalization of q-Hybrid Summation Integral Type Operators (Vural, İ., Altın, B. & Yüksel, I.) -- Approximation by q-Baskakov-Durrmeyer Type Operators of Two Variables (Yüksel, İ., Dinlemez, Ü. & Alt ın, B.) -- Blow up of Solutions of Second Order Semilinear Parabolic Equations Under Robin Boundary Conditions (Kalantarova, J. & Polat, M.) -- Functional Inequalities in Fuzzy Normed Spaces (Lee, J.R., Saadati, R. & Shin, D.Y.) -- Principal Vectors of M atrix-valued Difference Operators (Aygar, Y. & Olgun, M.) -- Some Extensions of Preinvexity for Stochastic Processes (Okur Bekar, N., Günay Akdemir, H. & İşcan, İ.) -- On One Boundary-Value Problem with Two Nonlocal Conditions for a Parabolic Equation (Danilkina, O.) -- Neighborhoods of Analytic Functions Associated with Fractional Derivative (Altıntaş, O) -- Spectrums of Solvable Pantograph Type Delay Differential Operators for First Order (Ismailov, Z.I. & Ipek, P.) -- Non-Commutative Geometry | |
and Applications to Physical Systems (Zaim, S.) -- The (s,t)-Generalized Jacobsthal Matrix Sequences (Uygun, Ş. & Uslu, K.) -- Domain Decomposition Approximation Approach for an Elliptic Partial Differential Equation (Buttar, T.N. & Sajid, N.) -- V oronovskaja Type Approximation Theorem for q-Szasz-Schurer Operators (Vedi, T. & Özarslan, M.A.) -- Approximation to Derivatives of Functions by Linear Operators Acting on Weighted Spaces by Power Series Method (Taş, E. & Yurdakadim, T.) -- Generalized Iterated Fractional Representation Formulae and Inequalities (Anastassiou, G.A.). | |
ISBN: | 9783319284439 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Springer Proceedings in Mathematics & Statistics: 155 |
Keywords: | Mathematics , Approximation theory , Potential theory (Mathematics) , Number theory , Mathematics , Number Theory , Potential Theory , Approximations and Expansions |
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Call number: | SPRINGER-2016-9783319266459:ONLINE Show nearby items on shelf |
Title: | Retarded Potentials and Time Domain Boundary Integral Equations A Road Map |
Author(s): |
Francisco-Javier Sayas |
Date: | 2016 |
Size: | 1 online resource (2 p.) |
Note: | 10.1007/978-3-319-26645-9 |
Contents: | The retarted layer potentials -- From time domain to Laplace domain -- From Laplace domain to time domain -- Convulution Quadrature -- The Discrete layer potentials -- A General Class of Second Order Differential Equations.- Time domain analysis of the single layer potential.- Time domain analysis of the double layer potential.- Full discretization revisited -- Patterns, Extensions, and Conclusions -- Appendices |
ISBN: | 9783319266459 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Springer Series in Computational Mathematics: 50 |
Keywords: | Mathematics , Integral equations , Partial differential equations , Computer mathematics , Mathematics , Integral Equations , Partial Differential Equations , Computational Mathematics and Numerical Analysis |
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Call number: | SPRINGER-2016-9783319263090:ONLINE Show nearby items on shelf |
Title: | Boundary Integral Equation Methods and Numerical Solutions Thin Plates on an Elastic Foundation |
Author(s): |
Christian Constanda |
Date: | 2016 |
Edition: | 1st ed. 2016 |
Size: | 1 online resource (196 p.) |
Note: | 10.1007/978-3-319-26309-0 |
Contents: | Preface -- 1. The Mathematical Model -- 2. The Layer Potentials -- 3. Existence of Solutions -- 4. Software Development -- 5. Computational Examples -- References -- Index |
ISBN: | 9783319263090 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Developments in Mathematics: 35 |
Keywords: | Mathematics , Functions of complex variables , Integral equations , Partial differential equations , Mathematics , Integral Equations , Partial Differential Equations , Functions of a Complex Variable |
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Call number: | SPRINGER-2016-9783319255897:ONLINE Show nearby items on shelf |
Title: | Stochastic Analysis for Finance with Simulations |
Author(s): |
Geon Ho Choe |
Date: | 2016 |
Size: | 1 online resource (107 p.) |
Note: | 10.1007/978-3-319-25589-7 |
Contents: | Preface -- Acknowledgements -- List of Figures -- List of Tables -- List of Simulations -- Fundamental Concepts -- Financial Derivatives -- The Lebesgue Integral -- Basic Probability Theory -- Conditional Expectation -- Stochastic Processes -- Brown ian Motion -- Girsanov's Theorem -- The Reflection Principle of Brownian Motion -- The Ito Integral -- The Ito Formula -- Stochastic Differential Equations -- The Feynmann-Kac Theorem -- The Binomial Tree Method for Option Pricing -- The Black-Scholes-Mer ton Differential Equation -- The Martingale Method -- Pricing of Vanilla Options -- Pricing of Exotic Options -- American Options -- The Capital Asset Pricing Model -- Dynamic Programming -- Bond Pricing -- Interest Rate Models -- Numeraires -- Numerical Estimation of Volatility -- Time Series -- Random Numbers -- The Monte Carlo Method for Option Pricing -- Numerical Solution of the Black-Scholes-Merton Equation -- Numerical Solution of Stochastic Differential Equations. Appendices -- |
Solutions for Selected Problems -- Glossary -- References -- Index. | |
ISBN: | 9783319255897 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Economics, Mathematical , Mathematics , Mathematics, general , Quantitative Finance |
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Call number: | SPRINGER-2016-9783319239538:ONLINE Show nearby items on shelf |
Title: | Dynamics of a Quantum Spin Liquid |
Author(s): |
Johannes Knolle |
Date: | 2016 |
Size: | 1 online resource (4 p.) |
Note: | 10.1007/978-3-319-23953-8 |
Contents: | Introduction -- Kitaev's Honeycomb Lattice Model -- Dynamic Spin Correlations - Mapping to a Quantum Quench -- Results for the Structure Error -- Non-Abelian Phase and the Effect of Disorder -- Raman Scattering -- Conclusion and |
Outlook -- Appendix A: Pfaffians from Path Integrals -- Appendix B: X-Ray Edge and Singular Integral Equations -- Appendix C: Exact Diagonalization of Four Dimers -- Appendix D: Calculation of Matrix Elements | |
ISBN: | 9783319239538 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Physics , Quantum field theory , String theory , Superconductivity , Superconductors , Magnetism , Magnetic materials , Physics , Strongly Correlated Systems, Superconductivity , Magnetism, Magnetic Materials , Quantum Field Theories, String Theory |
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Call number: | SPRINGER-2016-9783319229669:ONLINE Show nearby items on shelf |
Title: | Concepts in Quantum Field Theory A Practitioner's Toolkit |
Author(s): |
Victor Ilisie |
Date: | 2016 |
Size: | 1 online resource (190 p.) |
Note: | 10.1007/978-3-319-22966-9 |
Contents: | 1 Vectors, tensors, manifolds and Special Relativity -- 2 Lagrangians, Hamiltonians and Noether's Theorem -- 3 Relativistic kinematics and phase space -- 4 Angular Distributions -- 5 Dirac algebra -- 6 Dimensional regularization. |
Ultraviolet and infrared divergences -- 7 QED renormalization -- 8 One-loop two and three-point functions -- 9 Massive spin one and renormalizable gauges -- 10 Symmetries and effective vertices -- 11 Effective field theory -- 12 | |
Optical theorem -- A Master integral -- B Renormalization group equations -- C Feynman rules for derivative couplings | |
ISBN: | 9783319229669 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Physics , Quantum field theory , String theory , Elementary particles (Physics) , Physics , Elementary Particles, Quantum Field Theory , Quantum Field Theories, String Theory |
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Call number: | SPRINGER-2016-9783319210155:ONLINE Show nearby items on shelf |
Title: | Integral Operators in Non-Standard Function Spaces Volume 1: Variable Exponent Lebesgue and Amalgam Spaces |
Author(s): |
Vakhtang Kokilashvili |
Date: | 2016 |
Size: | 1 online resource (567 p.) |
Note: | 10.1007/978-3-319-21015-5 |
Contents: | Preface -- I: Variable Exponent Lebesgue and Amalgam spaces -- 1 Hardy Type Operators -- 2 Oscillating weights -- 3 Kernel Integral Operators -- 4 Two-Weight Estimates -- 5 One-sided Operators -- 6 Two-weight Inequalities for Fractional Maximal Fun ctions -- 7 Hypersingular Integrals -- 8 Description of the Range of Potentials 213 -- 9 More on Compactness -- 10 Applications to Singular Integral Equations -- II: Hölder Spaces of Variable Order -- 11 Variable Order Hölder Spaces -- III: Variable Exp onent Morrey-Campanato and Herz Spaces -- 12 Morrey Type Spaces Constant Exponents -- 13 Morrey Type Spaces Variable Exponents -- Bibliography -- Symbol Index -- Subject Index |
ISBN: | 9783319210155 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Operator Theory: Advances and Applications: 248 |
Keywords: | Mathematics , Functional analysis , Operator theory , Mathematics , Operator Theory , Functional Analysis |
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Call number: | SPRINGER-2016-9783034809641:ONLINE Show nearby items on shelf |
Title: | Application of Holomorphic Functions in Two and Higher Dimensions |
Author(s): |
Klaus Gürlebeck |
Date: | 2016 |
Size: | 1 online resource (3 p.) |
Note: | 10.1007/978-3-0348-0964-1 |
Contents: | 1.Basic Properties of Holomorphic Functions -- 2.Conformal and Quasi-conformal Mappings -- 3.Function Theoretic Function spaces -- 4.Operator Calculus -- 5.Decompositions -- 6.Some First Order Systems of Partial Differential Equations -- 7.Boundary Value Problems of Second Order Partial Differential Equations -- 8.Some Initial-boundary Value Problems -- 9.Riemann-Hilbert Problems -- 10.Initial Boundary Value Problems on the Sphere -- 11.Fourier Transforms -- Bibliography -- Index |
ISBN: | 9783034809641 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Functional analysis , Functions of complex variables , Integral transforms , Operational calculus , Partial differential equations , Mathematics , Integral Transforms, Operational Calculus , Functions of a Complex Variable , Partial Differential Equations , Functional Analysis |
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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-2014-9788876424991:ONLINE Show nearby items on shelf |
Title: | Introduction to Stochastic Analysis and Malliavin Calculus [electronic resource] |
Author(s): |
Giuseppe Prato |
Date: | 2014 |
Publisher: | Pisa : Scuola Normale Superiore |
Size: | 1 online resource |
Contents: | Introduction, Gaussian measures in Hilbert spaces, Gaussian random variables, The Malliavin derivative, Brownian Motion, Markov property of Brownian motion, Itos integral, Itos formula, Stochastic differential equations, Relationship between stocha stic and parabolic equations, Formulae of FeynmanKac and Girsanov, Malliavin calculus, Asymptotic behaviour of transition semigroups, The Dynkin Theorem, Conditional expectation, Martingales, Fixed points depending on parameters, E A basic ergodic theorem |
ISBN: | 9788876424991 |
Series: | eBooks |
Series: | Springerlink |
Series: | Publications of the Scuola Normale Superiore : v13 |
Keywords: | Mathematics , Functional analysis , Distribution (Probability theory) |
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Call number: | SPRINGER-2014-9788132218951:ONLINE Show nearby items on shelf |
Title: | Periodic Solutions of First-Order Functional Differential Equations in Population Dynamics [electronic resource] |
Author(s): |
Seshadev Padhi John R Graef P. D. N Srinivasu |
Date: | 2014 |
Publisher: | New Delhi : Springer India : Imprint: Springer |
Size: | 1 online resource |
Note: | This book provides cutting-edge results on the existence of multiple positive periodic solutions of first-order functional differential equations. It demonstrates how the Leggett-Williams fixed-point theorem can be applied tostudy the existence of tw o or three positive periodic solutions of functional differential equations with real-world applications, particularly with regard to the Lasota-Wazewska model, the Hematopoiesis model, the Nicholsons Blowfliesmodel, and some models with Allee effects. Ma ny interesting sufficient conditions are given for the dynamics that include nonlinear characteristics exhibited by population models. The last chapter provides results related to the globalappeal of solutions to the models considered in the earlier chapt ers. The techniques used in this book can be easily understood by anyone with a basic knowledge of analysis. This book offers a valuable reference guide for students andresearchers in the field of differential equations with applications to biology, ecolo gy, and the environment |
Contents: | Chapter 1. Introduction |
Chapter 2. Positive Periodic Solutions of Nonlinear Functional Differential Equations with Parameter | |
Chapter 3. Multiple Periodic Solutions of a System of Functional Differential Equations | |
Chapter 4. Multiple Periodic Solutions of Nonlinear Functional Differential Equations | |
Chapter 5. Asymptotic Behavior of Periodic Solutions of Differential Equations of First Order | |
Bibliography | |
ISBN: | 9788132218951 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Integral equations , Differential Equations |
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Call number: | SPRINGER-2014-9788132218869:ONLINE Show nearby items on shelf |
Title: | Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations [electronic resource] |
Author(s): |
Jzef Bana Mohammad Mursaleen |
Date: | 2014 |
Publisher: | New Delhi : Springer India : Imprint: Springer |
Size: | 1 online resource |
Note: | This book deals with the study of sequence spaces, matrix transformations, measures of noncompactness and their various applications. The notion of measure of noncompactness is one of the most useful ones available and has manyapplications. Thebookdi scusses some of the existence results for various types of differential and integral equations with the help of measures of noncompactness in particular, the Hausdorff measure of noncompactness has beenapplied to obtain necessary and sufficient conditions for matrix operators between BK spaces to be compact operators. Thebookconsists of eight self-contained chapters. Chapter 1 discussesthe theory of FK spaces andChapter2various duals of sequence spaces, which are used to characterize the matrix classes be tween these sequence spaces (FK and BK spaces) in Chapters 3 and 4. Chapter 5 studies the notion of a measure of noncompactness and its properties.The techniques associated with measures of noncompactness are applied to characterize the compact matrix ope rators in Chapters 6. In Chapters 7 and 8, some of the existence results are discussed for various types of differential andintegral equations, which are obtained with the help of argumentations based on compactness conditions |
Contents: | Chapter 1. Introduction to FK spaces |
Chapter 2. Matrix Transformations | |
Chapter 3. Some new sequence spaces of non | |
absolute type | |
Chapter 4. Some non | |
classical sequence spaces | |
Chapter 5. Measures of noncompactness | |
Chapter 6. Application to compact matrix operators | |
Chapter 7. Applications to infinite systems of differential equations | |
Chapter 8. Applications to integral equations | |
ISBN: | 9788132218869 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Integral equations , Operator theory , Differential Equations , Differential equations, partial , Sequences (Mathematics) |
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Call number: | SPRINGER-2014-9783642545931:ONLINE Show nearby items on shelf |
Title: | Neural Fields [electronic resource] : Theory and Applications |
Author(s): |
Stephen Coombes Peter beim Graben Roland Potthast James Wright |
Date: | 2014 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | With this book, the editors present the first comprehensive collection in neural field studies, authored by leading scientists in the field - among them are two of the founding-fathers of neural field theory. Up to now, researchresults in the field h ave been disseminated across a number of distinct journals from mathematics, computational neuroscience, biophysics, cognitive science and others. Starting with a tutorial for novices in neural field studies, thebook comprises chapters on emergent pattern s, their phase transitions and evolution, on stochastic approaches, cortical development, cognition, robotics and computation, large-scale numerical simulations, the coupling of neural fieldsto the electroencephalogram and phase transitions in anesthesia. The intended readership are students and scientists in applied mathematics, theoretical physics, theoretical biology, and computational neuroscience. Neural field theoryand its applications have a long-standing tradition in the mathematical and computati onal neurosciences. Beginning almost 50 years ago with seminal work by Griffiths and culminating in the 1970ties with the models of Wilson and Cowan,Nunez and Amari, this important research area experienced a renaissance during the 1990ties by the groups of Ermentrout, Bressloff, Haken, and Wright. Since then, much progress has been made in both, the development of mathematical andnumerical techniques, and in physiological refinement and understanding. In contrast to large-scale neural network models desc ribed by huge connectivity matrices that are computationally expensive in numerical simulations, neural fieldmodels described by connectivity kernels allow for analytical treatment by means of functional analysis methods. Thus, a number of rigorous result s on the existence of bump and wave solutions or on inverse kernel construction problemsare nowadays available. Moreover, neural fields provide an important interface for the coupling of continuous neur |
Contents: | Preface |
1.Tutorial on Neural Field Theory. S. Coombes, P. beim Graben and R. Potthast | |
Part I Theory of Neural Fields | |
2.A Personal Account of the Development of the Field Theory of Large | |
Scale Brain Activity from 1945 Onward. J. Cowan | |
3.HeavisideWorld: Excitation and Self | |
Organization of Neural Fields. Shun | |
ichi Amari | |
4.Spatiotemporal Pattern Formation in Neural Fields with Linear Adaptation. G.B. Ermentrout, S.E. Folias and Z.P. Kilpatrick | |
5.PDE Methods for Two | |
Dimensional Neural Fields. C.R. Laing | |
6.Numerical Simulation Scheme of One | |
and Two Dimensional Neural Fields Inv | |
ISBN: | 9783642545931 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Functional analysis , Integral equations , Consciousness |
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Call number: | SPRINGER-2014-9783642541247:ONLINE Show nearby items on shelf |
Title: | Mathematics for Physicists and Engineers [electronic resource] : Fundamentals and Interactive Study Guide |
Author(s): |
Klaus Weltner Sebastian John Wolfgang J Weber Peter Schuster Jean Grosjean |
Date: | 2014 |
Edition: | 2nd ed. 2014 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | This textbook offers an accessible and highly approved approach which is characterized by the combination of the textbook with a detailed study guide available online at our repository extras.springer.com. This study guide dividesthe whole learning t ask into small units which the student is very likely to master successfully. Thus he or she is asked to read and study a limited section of the textbook and to return to the study guide afterwards. Working with thestudy guide his or her learning results are controlled, monitored and deepened by graded questions, exercises, repetitions and finally by problems and applications of the content studied. Since the degree of difficulties is slowlyrising the students gain confidence and experience their own prog ress in mathematical competence thus fostering motivation. Furthermore in case of learning difficulties he or she is given supplementary explanations and in case ofindividual needs supplementary exercises and applications. So the sequence of the studies i s individualized according to the individual performance and needs and can be regarded as full tutorial course. The study guide satisfies twoobjectives simultaneously: firstly it enables students to make effective use of the textbook and secondly it offer s advice on the improvement of study skills. Empirical studies have shown that the student's competence for using writteninformation has improved significantly by using this study guide. The new edition includes a new chapter on Fourier integrals and Four ier transforms, numerous sections had been updated, 30 new problems with solutions had been added.The interactive study guide has seen a substantial update |
Contents: | From the Contents: Vector Algebra I: Scalars and Vectors |
Vector Algebra II: Scalar and Vector Products | |
Functions | |
Exponential, Logarithmic and Hyperbolic Functions | |
Differential Calculus | |
Integral Calculus | |
Applications of Integration | |
Taylor Series and Power Series | |
Complex Numbers | |
Differential Equations | |
Laplace Transforms | |
Functions of Several Variables Partial Differentiation and Total Differentiation | |
Multiple Integrals Coordinate Systems | |
Transformation of Coordinates Matrices | |
Sets of Linear Equations Determinanats | |
Eigenvalues and Eigenvectors of R | |
ISBN: | 9783642541247 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Chemistry , Mathematical physics , Engineering mathematics |
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Call number: | SPRINGER-2014-9783642393860:ONLINE Show nearby items on shelf |
Title: | The Concept of Stability in Numerical Mathematics [electronic resource] |
Author(s): |
Wolfgang Hackbusch |
Date: | 2014 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | In this book, the author compares the meaning of stability in different subfields of numerical mathematics. Concept of Stability in numerical mathematics opens by examining the stability of finite algorithms. A more precisedefinition of stability hol ds for quadrature and interpolation methods, which the following chapters focus on. The discussion then progresses to the numerical treatment of ordinary differential equations (ODEs). While one-step methodsfor ODEs are always stable, this is not the case for hyperbolic or parabolic differential equations, which are investigated next. The final chapters discuss stability for discretisations of elliptic differential equations and integralequations. In comparison among the subfields we discuss the practical importance of stability and the possible conflict between higher consistency order and stability. |
Contents: | Preface |
Introduction | |
Stability of Finite Algorithms | |
Quadrature | |
Interpolation | |
Ordinary Differential Equations | |
Instationary Partial Difference Equations | |
Stability for Discretisations of Elliptic Problems | |
Stability for Discretisations of Integral Equations | |
Index | |
ISBN: | 9783642393860 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Series in Computational Mathematics, 0179-3632 : v45 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Integral equations , Differential equations, partial , Numerical analysis |
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Call number: | SPRINGER-2014-9783319061542:ONLINE Show nearby items on shelf |
Title: | Renormalization Group Analysis of Equilibrium and Non-equilibrium Charged Systems [electronic resource] |
Author(s): |
Evgeny Barkhudarov |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | This thesis has two parts, each based on an application of the renormalization-group (RG). The first part is an analysis of the d-dimensional Coulomb gas. The goal was to determine if the Wilson RG could provide input intoparticle-in-cell simulations in plasma physics, which are the main family of simulation methods used in this field. The role of the RG was to identify the effect of coarse-graining on the coupling constants as a function of thecut-offs. The RG calculation reproduced established resu lts, but in a more concise form, and showed the effect of the cut-offs on the Debye screening length. The main part of the thesis is the application of the dynamic RG toturbulence in magnetohydrodynamics. After transformation to Elsasser variables, which is a symmetrisation of the original equations, the solution is presented as a functional integral, which includes stirring forces, their conjugatesand functional Jacobian. The coarse-graining of the functional integral is represented as a diagrammatic exp ansion, followed by rescaling, and casting the results into differential equations for the analysis of RG trajectories.Detailed comparisons are made with the Navier-Stokes limit and with previous calculations for MHD |
Contents: | Part I Renormalization Group |
Historical Overview | |
Wilson | |
Kadanoff Renormalization Group | |
Part II Equilibrium Statistical Mechanics | |
Coulomb Gas | |
D | |
dimensional Coulomb Gas | |
Renormalization Group Analysis | |
Part III Non | |
equilibrium Statistical Mechanics | |
Randomly Stirred Magnetohydrodynamics | |
Turbulent Flows | |
Recursion Relations and Fixed Point Analysis | |
ISBN: | 9783319061542 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Theses, Recognizing Outstanding Ph.D. Research, 2190-5053 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Mathematical physics , Quantum theory |
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Call number: | SPRINGER-2014-9783319040813:ONLINE Show nearby items on shelf |
Title: | Free-Electron Lasers in the Ultraviolet and X-Ray Regime [electronic resource] : Physical Principles, Experimental Results, Technical Realization |
Author(s): |
Peter Schmser Martin Dohlus Jrg Rossbach Christopher Behrens |
Date: | 2014 |
Edition: | 2nd ed. 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | The main goal of the book is to provide a systematic and didactic approach to the physics and technology of free-electron lasers. Numerous figures are used for illustrating the underlying ideas and concepts, and links to otherfields of physics are pr ovided. After an introduction to undulator radiation and the low-gain FEL, the one-dimensional theory of the high-gain FEL is developed in a systematic way. Particular emphasis is put on explaining andjustifying the various assumptions and approximations that are needed to obtain the differential and integral equations governing the FEL dynamics. Analytical and numerical solutions are presented and important FEL parameters aredefined, such as gain length, FEL bandwidth and saturation power. One of the mos t important features of a high-gain FEL, the formation of microbunches, is studied at length. The increase of gain length due to beam energy spread, spacecharge forces, and three-dimensional effects such as betatron oscillations and optical diffraction is analyzed. The mechanism of Self-Amplified Spontaneous Emission is described theoretically and illustrated with numerous experimentalresults. Various methods of FEL seeding by coherent external radiation are introduced, together with experimental results. The worlds first soft X-ray FEL, the user facility FLASH at DESY, is described in some detail to give animpression of the complexity of such an accelerator-based light source. The last chapter is devoted to the new hard X-ray FELs which generate extremel y intense radiation in the Angstrm regime. The appendices contain supplementarymaterial and more involved calculations. |
Contents: | Introduction |
Undulator Radiation | |
Low | |
Gain FEL Theory | |
One | |
Dimensional Theory of the High | |
Gain FEL | |
Applications of the High | |
Gain FEL Equations | |
Energy Spread, Space Chargeand 3D Effects | |
Self | |
Amplified Spontaneous Emission and FEL Seeding | |
The EUV and Soft X | |
Ray FEL in Hamburg | |
X | |
Ray Free | |
Electron Lasers: Technical Realization and Experimental Results | |
Appendices | |
A. Hamiltonian Formalism | |
B. Supplements to Chapter 4 | |
C. Gaussian Modes of Laser Beams | |
D. Eigenmode Approach | |
E. Statistical Methods and Tools | |
F. Conventions and Frequently used Symbols | |
Index | |
ISBN: | 9783319040813 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Tracts in Modern Physics, 0081-3869 : v258 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Particle acceleration |
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Call number: | SPRINGER-2014-9783319002125:ONLINE Show nearby items on shelf |
Title: | Lectures on Complex Integration [electronic resource] |
Author(s): |
A. O Gogolin Elena G Tsitsishvili Andreas Komnik |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | The theory of complex functions is a strikingly beautiful and powerful area of mathematics. Some particularly fascinating examples are seemingly complicated integrals which are effortlessly computed after reshaping them intointegrals along contours, as well as apparently difficult differential and integral equations, which can be elegantly solved using similar methods. To use them is sometimes routine but in many cases it borders on an art. The goal ofthe book is to introduce the reader to this beaut iful area of mathematics and to teach him or her how to use these methods to solve a variety of problems ranging from computation of integrals to solving difficult integral equations.This is done with a help of numerous examples and problems with detailed solutions |
Contents: | Basics |
Hypergeometric series with applications | |
Integral equations | |
Orthogonal polynomials | |
Solutions to the problems | |
ISBN: | 9783319002125 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Undergraduate Lecture Notes in Physics, 2192-4791 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Functions of complex variables |
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Title: | Variable Lebesgue Spaces and Hyperbolic Systems [electronic resource] |
Author(s): |
David Cruz-Uribe Alberto Fiorenza Michael Ruzhansky Jens Wirth Sergey Tikhonov |
Date: | 2014 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | This book targets graduate students and researchers who want to learn about Lebesgue spaces and solutions to hyperbolic equations. It is divided into two parts. Part 1 provides an introduction to the theory of variable Lebesguespaces: Banach function spaces like the classical Lebesgue spaces but with the constant exponent replaced by an exponent function. These spaces arise naturally from the study of partial differential equations and variational integralswith non-standard growth conditions. They ha ve applications to electrorheological fluids in physics and to image reconstruction. After an introduction that sketches history and motivation, the authors develop the function spaceproperties of variable Lebesgue spaces proofs are modeled on the classic al theory. Subsequently, the Hardy-Littlewood maximal operator is discussed. In the last chapter, other operators from harmonic analysis are considered, such asconvolution operators and singular integrals. The text is mostly self-contained, with only some more technical proofs and background material omitted. Part 2 gives an overview of the asymptotic properties of solutions to hyperbolicequations and systems with time-dependent coefficients. First, an overview of known results is given for general scalar hyperbolic equations of higher order with constant coefficients. Then strongly hyperbolic systems withtime-dependent coefficients are considered. A feature of the described approach is that oscillations in coefficients are allowed. Propagators for the Ca uchy problems are constructed as oscillatory integrals by working in appropriatetime-frequency symbol classes. A number of examples is considered and the sharpness of results is discussed. An exemplary treatment of dissipative terms shows how effective lo wer order terms can change asymptotic properties and thuscomplements the exposition |
Contents: | Part I: Introduction to the Variable Lebesgue Spaces |
Introduction and motivation | |
Properties of variable Lebesgue spaces | |
The Hardy | |
Littlewood maximal operator | |
Extrapolation in variable Lebesgue spaces | |
Part II:Asymptotic Behaviour of Solutions to Hyperbolic Equations and Systems | |
Equations with constant coefficients | |
Some interesting model cases | |
Time | |
dependent hyperbolic systems | |
Effective lower order perturbations | |
Examples and counter | |
examples | |
Related topics | |
ISBN: | 9783034808408 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Advanced Courses in Mathematics - CRM Barcelona, 2297-0304 : v27 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Integral equations , Differential equations, partial , Functions, special |
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Call number: | SPRINGER-2014-9783034808163:ONLINE Show nearby items on shelf |
Title: | Operator Theory, Operator Algebras and Applications [electronic resource] |
Author(s): |
M. Amlia Bastos Amarino Lebre Stefan Samko Ilya M Spitkovsky |
Date: | 2014 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | This book consists of research papers that cover the scientific areas of the International Workshop on Operator Theory, Operator Algebras and Applications, held in Lisbon in September 2012. The volume particularly focuses on (i)operator theory and ha rmonic analysis (singular integral operators with shifts pseudodifferential operators, factorization of almost periodic matrix functions inequalities Cauchy type integrals maximal and singular operators ongeneralized Orlicz-Morrey spaces the Riesz potenti al operator modification of Hadamard fractional integro-differentiation), (ii) operator algebras (invertibility in groupoid C*-algebras inner endomorphisms of some semi group,crossed products C*-algebras generated by mappings which have finite orbits Foln er sequences in operator algebras arithmetic aspect of C*_r SL(2) C*-algebras of singular integral operators algebras of operator sequences) and (iii)mathematical physics (operator approach to diffraction from polygonal-conical screens Poisson geometry of difference Lax operators) |
Contents: | Flner Sequences in Operator Theory and Operator Algebras |
On the Factorization of Some Block Triangular Almost Periodic Matrix Functions | |
A C | |
algebra of Singular Integral Operators with Shifts Similar to Affine Mappings | |
On Cauchy Type Integrals Related to the Cimmino System of Partial Differential Equations | |
Singular Integral Operators with Linear Fractional Shifts on the Unit Circle | |
Diffraction from Polygonal | |
Conical Screens, An Operator Approach | |
Boundedness of the Maximal and Singular Operators on Generalized Orlicz | |
Morrey Spaces | |
On a Question by Markus Seidel | |
Inver | |
ISBN: | 9783034808163 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Operator Theory: Advances and Applications, 0255-0156 : v242 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Operator theory , Differential equations, partial |
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Call number: | SPRINGER-2014-9783034806480:ONLINE Show nearby items on shelf |
Title: | Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation [electronic resource] : 22nd International Workshop in Operator Theory and its Applications, Sevilla, July 2011 |
Author(s): |
Manuel Cepedello Boiso Hkan Hedenmalm Marinus A Kaashoek Alfonso Montes Rodrguez Sergei Treil |
Date: | 2014 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | This book contains a collection of research articles and surveys on recent developments on operator theory as well as its applications covered in the IWOTA 2011 conference held at Sevilla University in the summer of 2011. Thetopics includespectral th eory, differential operators, integral operators, composition operators, Toeplitz operators, andmore.The book also presents a largenumber of techniques in operator theory |
Contents: | Israel Gohberg Memorial Session |
Research work of Israel Gohberg | |
Some new refined Hardy type inequalities with breaking points p=2 or p=3 | |
Non | |
negative self | |
adjoint extensions in rigged Hilbert space | |
Matrices with bidiagonal decomposition, accurate computations and corner cutting algorithms | |
Boundary | |
value problems for higher | |
order elliptic equations in non | |
smooth domains | |
Additive maps preserving the inner local spectral radius | |
and more | |
ISBN: | 9783034806480 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Operator Theory: Advances and Applications, 0255-0156 : v236 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Operator theory , Differential Equations , Systems theory |
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Call number: | SPRINGER-2014-9781461495932:ONLINE Show nearby items on shelf |
Title: | Linear Integral Equations [electronic resource] |
Author(s): |
Rainer Kress |
Date: | 2014 |
Edition: | 3rd ed. 2014 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | This book combines theory, applications, and numerical methods, and covers each of these fields with the same weight. In order to make the book accessible to mathematicians, physicists, and engineers alike, the author has made itas self-contained as possible, requiring only a solid foundation in differential and integral calculus. The functional analysis which is necessary for an adequate treatment of the theory and the numerical solution of integral equationsis developed within the book itself. Prob lems are included at the end of each chapter. For this third edition in order to make the introduction to the basic functional analytic tools more complete the HahnBanach extensiontheorem and the Banach open mapping theorem are now included in the text. The treatment of boundary value problems in potential theory has been extended by a more complete discussion of integral equations of the first kind in theclassical Holder space setting and of both integral equations of the first and second kind in the co ntemporary Sobolev space setting. In the numerical solution part of the book, the author included a new collocation method fortwo-dimensional hypersingular boundary integral equations and a collocation method for the three-dimensional Lippmann-Schwinger e quation. The final chapter of the book on inverse boundary value problems for the Laplace equation hasbeen largely rewritten with special attention to the trilogy of decomposition, iterative and sampling methods Reviews of earlier editions: This book is an excellent introductory text for students, scientists, and engineers whowant to learn the basic theory of linear integral equations and their numerical solution. (Math. Reviews, 2000) This is a good introductory text book on linear integral equations. It contains almost all the topics necessary fora student. The presentation of the subject matter is lucid, clear and in the proper modern framework without being too abstract. (ZbM |
Contents: | Normed Spaces |
Bounded and Compact Operators | |
Riesz Theory | |
Dual Systems and Fredholm Alternative | |
Regularization in Dual Systems | |
Potential Theory | |
Singular Integral Equations | |
Sobolev Spaces | |
The Heat Equation | |
Operator Approximations | |
Degenerate Kernel Approximation | |
Quadrature Methods | |
Projection Methods | |
Iterative Solution and Stability | |
Equations of the First Kind | |
Tikhonov Regularization | |
Regularization by Discretization | |
Inverse Boundary Value Problems | |
References | |
Index | |
ISBN: | 9781461495932 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Applied Mathematical Sciences, 0066-5452 : v82 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Numerical analysis |
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Call number: | SPRINGER-2014-9781461495871:ONLINE Show nearby items on shelf |
Title: | Introduction to Stochastic Integration [electronic resource] |
Author(s): |
K.L Chung R.J Williams |
Date: | 2014 |
Edition: | 2nd ed. 2014 |
Publisher: | New York, NY : Springer New York : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | A highly readable introduction to stochastic integration and stochastic differential equations, this book combines developments of the basic theory with applications. It is written in a style suitable for the text of a graduatecourse in stochastic ca lculus, following a course in probability. Using the modern approach, the stochastic integral is defined for predictable integrands and local martingales then Its change of variable formula is developedfor continuous martingales. Applications include a c haracterization of Brownian motion, Hermite polynomials of martingales, the FeynmanKac functional and theSchrdinger equation. For Brownian motion, the topics of local time,reflected Brownian motion, and time change are discussed. New to the second editio n are a discussion of the CameronMartinGirsanov transformation and a final chapter which provides an introduction to stochastic differentialequations, as well as many exercises for classroom use. This book will be a valuable resource to all mathematician s, statisticians, economists, and engineers employing the modern tools of stochastic analysis. The text also provesthat stochastic integration has made an important impact on mathematical progress over the last decades and that stochastic calculus has be come one of the most powerful tools in modern probability theory. Journal of the AmericanStatistical Association An attractive textwritten in [a] lean and precise styleeminently readable. Especially pleasant are the care and attention devoted to details A very fine book. Mathematical Reviews |
Contents: | 1 Preliminaries |
2 Definition of the Stochastic Integral | |
3 Extension of the Predictable Integrands | |
4 Quadratic Variation Process | |
5 The Ito Formula | |
6 Applications of the Ito Formula | |
7 Local Time and Tanaka's Formula | |
8 Reflected Brownian Motions | |
9 Generalization Ito Formula, Change of Time and Measure | |
10 Stochastic Differential Equations | |
References | |
Index | |
ISBN: | 9781461495871 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Modern Birkhuser Classics, 2197-1803 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Distribution (Probability theory) |
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Call number: | SPRINGER-2014-9781447164340:ONLINE Show nearby items on shelf |
Title: | Mathematical Methods for Elastic Plates [electronic resource] |
Author(s): |
Christian Constanda |
Date: | 2014 |
Publisher: | London : Springer London : Imprint: Springer |
Size: | 1 online resource |
Note: | Mathematical models of deformation of elastic plates are used by applied mathematicians and engineers in connection with a wide range of practical applications, from microchip production to the construction of skyscrapers andaircraft. This book emplo ys two important analytic techniques to solve the fundamental boundary value problems for the theory of plates with transverse shear deformation, which offers a more complete picture of the physical process ofbending than Kirchhoffs classical one. The fi rst method transfers the ellipticity of the governing system to the boundary, leading to singular integral equations on the contour of the domain. These equations, established on thebasis of the properties of suitable layer potentials, are then solved in spaces of smooth (Hlder continuous and Hlder continuously differentiable) functions. The second technique rewrites the differential system in terms ofcomplex variables and fully integrates it, expressing the solution as a combination of complex analytic potentials. The last chapter develops a generalized Fourier series method closely connected with the structure of the system,which can be used to compute approximate solutions. The numerical results generated as an illustration for the interior Dirichlet problem are accompanied by remarks regarding the efficiency and accuracy of the procedure. Thepresentation of the material is detailed and self-contained, making Mathematical Methods for Elastic Plates accessible to researchers and graduate students wit h a basic knowledge of advanced calculus |
Contents: | Singular Kernels |
Potentials and Boundary Integral Equations | |
Bending of Elastic Plates | |
The Layer Potentials | |
The Newtonian Potential | |
Existence of Regular Solutions | |
Complex Variable Treatment | |
Generalized Fourier Series | |
ISBN: | 9781447164340 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Integral equations , Materials |
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Call number: | SPRINGER-2014-9781447163954:ONLINE Show nearby items on shelf |
Title: | An Introduction to Laplace Transforms and Fourier Series [electronic resource] |
Author(s): |
Phil Dyke |
Date: | 2014 |
Edition: | 2nd ed. 2014 |
Publisher: | London : Springer London : Imprint: Springer |
Size: | 1 online resource |
Note: | Laplace transforms continue to be a very important tool for the engineer, physicist and applied mathematician. They are also now useful to financial, economic and biological modellers as these disciplines become more quantitative.Any problem that has underlying linearity and with solution based on initial values can be expressed as an appropriate differential equation and hence be solved using Laplace transforms. In this book, there is a strong emphasis onapplication with the necessary mathematical g rounding. There are plenty of worked examples with all solutions provided. This enlarged new edition includes generalised Fourier series and a completely new chapter on wavelets. Onlyknowledge of elementary trigonometry and calculus are required as prereq uisites. An Introduction to Laplace Transforms and Fourier Series will be useful for second and third year undergraduate students in engineering, physics ormathematics, as well as for graduates in any discipline such as financial mathematics, econometrics and biological modelling requiring techniques for solving initial value problems |
Contents: | The Laplace Transform |
Further Properties of the Laplace Transform | |
Convolution and the Solution of Ordinary Differential Equations | |
Fourier Series | |
Partial Differential Equations | |
Fourier Transforms | |
Wavelets and Signal Processing | |
Complex Variables and Laplace Transforms | |
ISBN: | 9781447163954 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Undergraduate Mathematics Series, 1615-2085 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Fourier analysis , Functions of complex variables , Integral Transforms , Mathematical physics , Engineering mathematics |
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Call number: | SPRINGER-2014-9781447153610:ONLINE Show nearby items on shelf |
Title: | Probability Theory [electronic resource] : A Comprehensive Course |
Author(s): |
Achim Klenke |
Date: | 2014 |
Edition: | 2nd ed. 2014 |
Publisher: | London : Springer London : Imprint: Springer |
Size: | 1 online resource |
Note: | This second edition of the popular textbook contains a comprehensive course in modern probability theory. Overall, probabilistic concepts play an increasingly important role in mathematics, physics, biology, financial engineeringand computer science. They help us in understanding magnetism, amorphous media, genetic diversity and the perils of random developments at financial markets, and they guide us in constructing more efficient algorithms. To addressthese concepts, the title covers a wide variet y of topics, many of which are not usually found in introductory textbooks, such as: limit theorems for sums of random variables martingales percolation Markov chains andelectrical networks construction of stochastic processes Poisson point process and infinite divisibility large deviation principles and statistical physics Brownian motion stochastic integral and stochasticdifferential equations. The theory is developed rigorously and in a self-contained way, with the chapters on measure theory interlaced with the probabilistic chapters in order to display the power of the abstract concepts inprobability theory. This second edition has been carefully extended and includes many new features. It contains updated figures (over 50), computer simulat ions and some difficult proofs have been made more accessible. A wealth ofexamples and more than 270 exercises as well as biographic details of key mathematicians support and enliven the presentation. It will be of use to students and researchers in mathe matics and statistics in physics, computer science,economics and biology |
Contents: | Basic Measure Theory |
Independence | |
Generating Functions | |
The Integral | |
Moments and Laws of Large Numbers | |
Convergence Theorems | |
Lp | |
Spaces and the RadonNikodym Theorem | |
Conditional Expectations | |
Martingales | |
Optional Sampling Theorems | |
Martingale Convergence Theorems and Their Applications | |
Backwards Martingales and Exchangeability | |
Convergence of Measures | |
Probability Measures on Product Spaces | |
Characteristic Functions and the Central Limit Theorem | |
Infinitely Divisible Distributions | |
Markov Chains | |
Convergence of Markov Chains | |
Markov Chains and Electr | |
ISBN: | 9781447153610 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Universitext, 0172-5939 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Functional analysis , Distribution (Probability theory) |
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Call number: | SPRINGER-2013-9789491216862:ONLINE Show nearby items on shelf |
Title: | Single Variable Differential and Integral Calculus [electronic resource] : Mathematical Analysis |
Author(s): |
Elimhan Mahmudov |
Date: | 2013 |
Publisher: | Paris : Atlantis Press : Imprint: Atlantis Press |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The book Single variable Differential and Integral Calculus is an interesting text book for students of mathematics and physics programs, and a reference book for graduate students in any engineering field. This book isunique in the field of mathemat ical analysis in content and in style. It aims to define, compare and discuss topics in single variable differential and integral calculus, as well as giving application examples in important businessfields. Some elementary concepts such as the power of a set, cardinality, measure theory, measurable functions are introduced. It also covers real and complex numbers, vector spaces, topological properties of sets, series and sequencesof functions (including complex-valued functions and functions of a complex variable), polynomials and interpolation and extrema of functions. Although analysis is based on the single variable models and applications, theorems andexamples are all set to be converted to multi variable extensions. For example, Newton, Riemann, Sti eltjes and Lebesque integrals are studied together and compared |
Note: | Springer eBooks |
Contents: | Introduction to Numbers and Set Theory |
Sequences and Series | |
Limits and Continuity of Functions | |
Differential Calculus | |
Some Basic Properties of Differentiable Functions | |
Polynomials and Interpolations | |
Applications of Differential Calculus to Limit Calculations and Extremum Problems | |
The Indefinite Integral | |
The Definite Integral | |
Applications of the Definite Integral | |
ISBN: | 9789491216862 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Differential Equations |
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Title: | Non-Equilibrium Thermodynamics in Multiphase Flows [electronic resource] |
Author(s): |
Roberto Mauri |
Date: | 2013 |
Publisher: | Dordrecht : Springer Netherlands : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Non-equilibrium thermodynamics is a general framework that allows the macroscopic description of irreversible processes. This book introduces non-equilibrium thermodynamics and its applications to the rheology of multiphaseflows. The subject is relev ant to graduate students in chemical and mechanical engineering, physics and material science. This book is divided into two parts. The first part presents the theory of non-equilibrium thermodynamics,reviewing its essential features and showing, when pos sible, some applications. The second part of this book deals with how the general theory can be applied to model multiphase flows and, in particular, how to determine theirconstitutive relations. Each chapter contains problems at the end, the solutions of which are given at the end of the book. No prior knowledge of statistical mechanics is required the necessary prerequisites are elements of transportphenomena and on thermodynamics. The style of the book is mathematical, but nonetheless it remains very r eadable and anchored in the physical world rather than becoming too abstract. Though it is up-to-date and includes recentimportant developments, there is a lot of classical material in the book, albeit presented with unprecedented clarity and coherence. T he first six chapters are actually a very good introduction to the theory underlying many phenomenain soft matter physics, beyond the focus on flow and transport of the later chapters of the book. Prof Richard A.L. Jones FRS, Pro-Vice-Chancellor for Resea rch and Innovation, University of Sheffield |
Note: | Springer eBooks |
Contents: | From the Contents: Microscopic reversibility |
The Langevin equation | |
The Fokker | |
Planck equation | |
Stochastic differential calculus | |
The path integral | |
Balance equations | |
The constitutive relations | |
Multiphase Flows | |
Effective constitutive relations | |
Multiple scale analysis | |
ISBN: | 9789400754614 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Soft and Biological Matter, 2213-1736 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Chemistry, Physical organic , Polymers , Thermodynamics , Hydraulic engineering |
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Title: | Lp-Theory for Incompressible Newtonian Flows [electronic resource] : Energy Preserving Boundary Conditions, Weakly Singular Domains |
Author(s): |
Matthias Khne |
Date: | 2013 |
Publisher: | Wiesbaden : Springer Fachmedien Wiesbaden : Imprint: Springer Spektrum |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This thesis is devoted to the study of the basic equations of fluid dynamics. First Matthias Khne focuses on the derivation of a class of boundary conditions, which is based on energy estimates, and, thus, leads to physicallyrelevant conditions. The derived class thereby contains many prominent artificial boundary conditions, which have proved to be suitable for direct numerical simulations involving artificial boundaries. The second part is devoted to thedevelopment of a complete Lp-theory for the r esulting initial boundary value problems in bounded smooth domains, i.e. the Navier-Stokes equations complemented by one of the derived energy preserving boundary conditions. Finally, thethird part of this thesis focuses on the corresponding theory for bo unded, non-smooth domains, where the boundary of the domain is allowed to contain a finite number of edges, provided the smooth components of the boundary that meet atsuch an edge are locally orthogonal. Contents Navier-Stokes Equations Energy Preservin g Boundary Condition Weakly Singular Domain Maximal Lp-Regularity TargetGroups Scientists, lecturers and graduate students in the fields of mathematical fluid dynamics and partial differential equations as well as experts in applied analysis. The autho r Matthias Khne earned a doctorateof Mathematics under the supervision of Prof. Dr. Dieter Bothe at the Department of Mathematics at TU Darmstadt, where his research was supported by the cluster of excellence ''Center of Smart Interfaces'' and the interna tionalresearch training group ''Mathematical Fluid Dynamics'' |
Note: | Springer eBooks |
Contents: | Navier |
Stokes Equations | |
Energy Preserving Boundary Condition | |
Weakly Singular Domain | |
Maximal Lp | |
Regularity | |
ISBN: | 9783658010522 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Integral equations |
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Call number: | SPRINGER-2013-9783642331497:ONLINE Show nearby items on shelf |
Title: | Stochastic Calculus with Infinitesimals [electronic resource] |
Author(s): |
Frederik Herzberg |
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: | Stochastic analysis is not only a thriving area of pure mathematics with intriguing connections to partial differential equations and differential geometry. It also has numerous applications in the natural and social sciences(for instance in financia l mathematics or theoretical quantum mechanics) and therefore appears in physics and economics curricula as well. However, existing approaches to stochastic analysis either presuppose various concepts frommeasure theory and functional analysis or lack ful l mathematical rigour. This short book proposes to solve the dilemma: By adopting E. Nelson's radically elementary theory of continuous-time stochastic processes, it is based on ademonstrably consistent use of infinitesimals and thus permits a radically s implified, yet perfectly rigorous approach to stochastic calculus and its fascinating applications, some of which (notably the Black-Scholes theory of optionpricing and the Feynman path integral) are also discussed in the book |
Note: | Springer eBooks |
Contents: | 1 Infinitesimal calculus, consistently and accessibly |
2 Radically elementary probability theory | |
3 Radically elementary stochastic integrals | |
4 The radically elementary Girsanov theorem and the diffusion invariance principle | |
5 Excursion to nancial economics: A radically elementary approach to the fundamental theorems of asset pricing | |
6 Excursion to financial engineering: Volatility invariance in the Black | |
Scholes model | |
7 A radically elementary theory of It diffusions and associated partial differential equations | |
8 Excursion to mathematical physics: A radically elementary d | |
ISBN: | 9783642331497 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2067 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Logic, Symbolic and mathematical , Distribution (Probability theory) |
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Call number: | SPRINGER-2013-9783642326660:ONLINE Show nearby items on shelf |
Title: | Multi-Layer Potentials and Boundary Problems [electronic resource] : for Higher-Order Elliptic Systems in Lipschitz Domains |
Author(s): |
Irina Mitrea Marius Mitrea |
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: | Many phenomena in engineering and mathematical physics can be modeled by means of boundary value problems for a certain elliptic differential operator in a given domain. When the differential operator under discussion is ofsecond order a variety of t ools are available for dealing with such problems, including boundary integral methods, variational methods, harmonic measure techniques, and methods based on classical harmonic analysis. When thedifferential operator is of higher-order (as is the case, e .g., with anisotropic plate bending when one deals with a fourth order operator) only a few options could be successfully implemented. In the 1970s Alberto Caldern, one ofthe founders of the modern theory of Singular Integral Operators, advocated the use of layer potentials for the treatment of higher-order elliptic boundary value problems. The present monograph represents the first systematic treatmentbased on this approach. This research monograph lays, for the first time, the mathematical foundation ai med at solving boundary value problems for higher-order elliptic operators in non-smooth domains using the layer potential methodand addresses a comprehensive range of topics, dealing with elliptic boundary value problems in non-smooth domains including l ayer potentials, jump relations, non-tangential maximal function estimates, multi-traces and extensions,boundary value problems with data in WhitneyLebesque spaces, WhitneyBesov spaces, WhitneySobolev- based Lebesgue spaces, WhitneyTriebelLizorkin spaces, WhitneySobolev-based Hardy spaces, WhitneyBMO and WhitneyVMOspaces |
Note: | Springer eBooks |
Contents: | 1 Introduction |
2 Smoothness scales and Calden | |
Zygmund theory in the scalar | |
valued case | |
3 Function spaces of Whitney arrays | |
4 The double multi | |
layer potential operator | |
5 The single multi | |
layer potential operator | |
6 Functional analytic properties of multi | |
layer potentials and boundary value problems | |
ISBN: | 9783642326660 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2063 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Fourier analysis , Integral equations , Differential equations, partial , Potential theory (Mathematics) |
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Call number: | SPRINGER-2013-9783642307096:ONLINE Show nearby items on shelf |
Title: | Variational, Topological, and Partial Order Methods with Their Applications [electronic resource] |
Author(s): |
Zhitao Zhang |
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: | Nonlinear functional analysis is an important branch of contemporary mathematics. It's related to topology, ordinary differential equations, partial differential equations, groups, dynamical systems, differential geometry,measure theory, and more. In this book, the author presents some new and interesting results on fundamental methods in nonlinear functional analysis, namely variational, topological and partial order methods, which have been usedextensively to solve existence of solutions for ellipt ic equations, wave equations, Schrdinger equations, Hamiltonian systems etc., and are also used to study the existence of multiple solutions and properties of solutions. This bookis useful for researchers and graduate students in the field of nonlinear fu nctional analysis. Chapter 1 contains preliminaries. In Chapter 2, three kinds of operators are introduced: increasing operators, decreasing operators, andmixed monotone operators. In Chapter 3, the minimax methods are presented and in Chapter 4, the auth or uses bifurcation and critical point theory to study structures of the solutions of elliptic equations. Chapter 5 is concerned with aclass of MongeAmpre equations. In Chapter 6, the superlinear system of Hammerstein integral equations and applications i s studied. Chapter 7 is devoted to the DancerFucik spectrum. In Chapter 8, some results on sign-changingsolutions are introduced. In Chapter 9, a local minimizer problem of a functional in differential topology is studied. Chapter 10 focuses on a class of nonlocal Kirchhoff elliptic problems via different methods. In Chapter 11, thefocus is on free boundary problems, Schrdinger systems from BoseEinstein condensate and competing systems with many species |
Note: | Springer eBooks |
Contents: | 1 Preliminaries |
Sobolev spaces and embedding theorems | |
Critical point | |
Cone and partial order | |
Brouwer Degree | |
Compact map and Leray | |
Schauder Degree | |
Fredholm operators | |
Fixed point index | |
Banach's Contract Theorem, Implicit Functions Theorem | |
Krein | |
Rutman theorem | |
Bifurcation theory | |
Rearrangements of sets and functions | |
Genus and Category | |
Maximum principles and symmetry of solution | |
Comparison theorems | |
2 Cone and Partial Order Methods | |
Increasing operators | |
Decreasing operators | |
Mixed monotone operators | |
Applications of mixed monotone operators | |
Fur | |
ISBN: | 9783642307096 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Developments in Mathematics, 1389-2177 : v29 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis |
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Call number: | SPRINGER-2013-9783642272639:ONLINE Show nearby items on shelf |
Title: | Vito Volterra [electronic resource] |
Author(s): |
Angelo Guerraggio Giovanni Paoloni |
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: | Vito Volterra (1860-1940) was one of the most famous representatives of Italian science in his day. Angelo Guerragio and Giovanni Paolini analyze Volterras most important contributions to mathematics and their applications, aswell as his outstanding organizational achievements in scientific policy. Volterra was one of the founding fathers of functional analysis and the author of fundamental contributions in the field of integral equations, elasticity theoryand population dynamics (Lotka-Volterra mode l). He delivered keynote lectures on the occasion of the International Congresses of Mathematicians held in Paris (1900), Rome (1908), Strasbourg (1920) and Bologna (1928). He becameinvolved in the scientific development in united Italy and was appointed senator of the kingdom in 1905. One of his numerous non-mathematical activities was founding the National Research Council (Consiglio Nazionale delle Ricerche,CNR). During the First World War he was active in military research. After the war he took a c lear stand against fascism, which was the starting point for his exclusion. In 1926 he resigned as president of the world famous AccademiaNazionale dei Lincei and was later on excluded from the academy. In 1931 he was one of the few university lecturers w ho denied to swear an oath of allegiance to the fascistic regime. In 1938 he suffered from the impact of the raciallaws. The authors draw a comprehensive picture of Vito Volterra, both as a great mathematician and an organizer of science |
Note: | Springer eBooks |
Contents: | I. Chronicles of Italian life |
II. Professor in Pisa | |
III. The cats of Torino | |
IV. Rome, public appointments, the politician | |
V. Days of firing from a dirigible | |
VI. From war to peace: Italys National Research Council | |
VII. The end of freedom | |
VIII. After the cats, fish | |
IX. Time runs out | |
Appendix I: Significant dates in Italian history 1849 | |
1945 | |
Appendix II: Significant dates in the life of Vito Volterra 1860 | |
1940 | |
Index of Names | |
ISBN: | 9783642272639 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics |
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Call number: | SPRINGER-2013-9783319012551:ONLINE Show nearby items on shelf |
Title: | Constant-Sign Solutions of Systems of Integral Equations [electronic resource] |
Author(s): |
Ravi P Agarwal Donal ORegan Patricia J. Y Wong |
Date: | 2013 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This monograph provides a complete and self-contained account of the theory, methods, and applications of constant-sign solutions of integral equations. In particular, the focus is on different systems of Volterra and Fredholmequations. The presentat ion is systematic and the material is broken down into several concise chapters. An introductory chapter covers the basic preliminaries. Throughout the book many examples are included to illustrate the theory.The book contains a wealth of results that are both deep and interesting. This unique book will be welcomed by mathematicians working on integral equations, spectral theory, and on applications of fixed point theory and boundary valueproblems. |
Note: | Springer eBooks |
Contents: | Introduction and Preliminaries |
System of Fredholm Integral Equations: Existence of a Constant | |
Sign Solution | |
System of Fredholm Integral Equations: Eigenvalues | |
System of Fredholm Integral Equations: Triple Constant | |
Sign Solutions | |
System of Fredholm Integral Equations: Existence of a Constant | |
Sign Lp Solution | |
System of Fredholm Integral Equations: Semipositone and Singular Case | |
Systems of Fredholm and Volterra Integral Equations: Integrable Singularities | |
Systems of Higher Order Boundary Value Problems: Integrable Singularities | |
System of Volterra Integral Equations: Integr | |
ISBN: | 9783319012551 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Integral equations , Differential Equations |
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Call number: | SPRINGER-2013-9783319011950:ONLINE Show nearby items on shelf |
Title: | Mathematical Physics [electronic resource] : A Modern Introduction to Its Foundations |
Author(s): |
Sadri Hassani |
Date: | 2013 |
Edition: | 2nd ed. 2013 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The goal of this book is to expose the reader to the indispensable role that mathematics---often very abstract---plays in modern physics. Starting with the notion of vector spaces, the first half of the book develops topics asdiverse as algebras, cla ssical orthogonal polynomials, Fourier analysis, complex analysis, differential and integral equations, operator theory, and multi-dimensional Green's functions. The second half of the book introduces groups,manifolds, Lie groups and their representations , Clifford algebras and their representations, and fiber bundles and their applications to differential geometry and gauge theories. This second edition is a substantial revision of thefirst one with a complete rewriting of many chapters and the addition of new ones, including chapters on algebras, representation of Clifford algebras and spinors, fiber bundles, and gauge theories. The spirit of the first edition,namely the balance between rigor and physical application, has been maintained, as is the abun dance of historical notes and worked out examples that demonstrate the unreasonable effectiveness of mathematics in modern physics.Einstein has famously said, The most incomprehensible thing about nature is that it is comprehensible. What he had in mind w as reiterated in another one of his famous quotes concerning the question of how ... mathematics, beingafter all a product of human thought, is so admirably appropriate to the objects of reality. It is a question that comes to everyone's mind when encoun tering the highly abstract mathematics required for a deep understanding of modernphysics. It is the experience that Eugene Wigner so profoundly described as the unreasonable effectiveness of mathematics in the natural sciences. |
Note: | Springer eBooks |
Contents: | Mathematical Preliminaries |
I Finite | |
Dimensional Vector Spaces | |
1 Vectors and Linear Maps | |
2 Algebras | |
3 Operator Algebra | |
4 Matrices | |
5 Spectral Decomposition | |
II Infinite | |
Dimensional Vector Spaces | |
6 Hilbert Spaces | |
7 Classical Orthogonal Polynomials | |
8 Fourier Analysis | |
III Complex Analysis | |
9 Complex Calculus | |
10 Calculus of Residues | |
11 Advanced Topics | |
IV Differential Equations | |
12 Separation of Variables in Spherical Coordinates | |
13 Second | |
Order Linear Differential Equations | |
14 Complex Analysis of SOLDEs | |
15 Integral Transforms and Differential Equ | |
ISBN: | 9783319011950 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Mathematics , Mathematical physics |
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Call number: | SPRINGER-2013-9783034806367:ONLINE Show nearby items on shelf |
Title: | Introduction to Mathematical Analysis [electronic resource] |
Author(s): |
Igor Kriz Ale Pultr |
Date: | 2013 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The book begins at an undergraduate student level, assuming only basic knowledge of calculus in one variable. It rigorously treats topics such as multivariable differential calculus, theLebesgue integral, vector calculus anddifferential equations. Af ter having created a solid foundation of topology and linear algebra, the text later expands into more advanced topics such as complex analysis, differential forms, calculus of variations, differentialgeometry and even functional analysis. Overall, this t ext provides a unique and well-rounded introduction to the highly developed and multi-faceted subject of mathematical analysis as understood by mathematicians today |
Note: | Springer eBooks |
Contents: | Preface |
Introduction | |
Part 1. A Rigorous Approach to Advanced Calculus | |
1. Preliminaries | |
2. Metric and Topological Spaces I | |
3. Multivariable Differential Calculus | |
4. Integration I: Multivariable Riemann Integral and Basic Ideas toward the Lebesgue Integral | |
5. Integration II: Measurable Functions, Measure and the Techniques of Lebesgue Integration | |
6. Systems of Ordinary Differential Equations | |
7. System of Linear Differential Equations | |
8. Line Integrals and Green's Theorem | |
Part 2. Analysis and Geometry | |
9. An Introduction to Complex Analysis | |
10. Metric and Top | |
ISBN: | 9783034806367 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Matrix theory , Functions of complex variables , Differential Equations , Sequences (Mathematics) |
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