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SPIRES-BOOKS: FIND KEYWORD ORDINARY DIFFERENTIAL EQUATIONS *END*INIT* use /tmp/qspiwww.webspi1/11353.136 QRY 131.225.70.96 . find keyword ordinary differential equations ( in books using www Cover
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Call number:9789811031809:ONLINE Show nearby items on shelf
Title:Bifurcation in Autonomous and Nonautonomous Differential Equations with Discontinuities
Author(s): Marat Akhmet
Date:2017
Size:1 online resource (XI, 166 p. 31 illus., 26 illus. in color p.)
Contents:Introduction -- Hopf Bifurcation in Impulsive Systems -- Hopf Bifurcation in Fillopov Systems -- Nonautonomous Transcritical and Pitchfork Bifurcations in an Impulsive Bernoulli Equations -- Nonautonomous Transcritical and Pitchfork
Bifurcations in Scalar Non-solvable Impulsive Differential Equations -- Nonautonomous Transcritical and Pitchfork Bifurcations in Bernoulli Equations with Piecewise Constant Argument of Generalized Type
ISBN:9789811031809
Series:eBooks
Series:Springer eBooks
Series:Springer 2017 package
Keywords: Mathematics , Difference equations , Functional equations , Dynamics , Ergodic theory , Differential equations , Control engineering , Mathematics , Dynamical Systems and Ergodic Theory , Control , Applications of Nonlinear Dynamics and Chaos Theory , Difference and Functional Equations , Ordinary Differential Equations
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Call number:9783319517537:ONLINE Show nearby items on shelf
Title:Extended Abstracts Summer 2015 Strategic Behavior in Combinatorial Structures Quantitative Finance
Author(s):
Date:2017
Size:1 online resource (VI, 139 p. 5 illus., 3 illus. in color p.)
Contents:Part-I -- Foreword -- On the Push & Pull Protocol for Rumour Spreading -- Random Walks that Find Perfect Objects and the Lovasz Local Lemma -- Logit Dynamics with Concurrent Updates for Local Interaction Games -- Logit Dynamics with
Concurrent Updates for Local Interaction Games -- Carpooling in Social Networks -- Who to Trust for Truthful Facility Location? -- Metric and Spectral Properties of Dense Inhomogeneous Random Graphs -- On-Line List Colouring of Random
Graphs -- Approximation Algorithms for Computing Maximin Share Allocations -- An Alternate Proof of the Algorithmic Lovász Local Lemma -- Learning Game-Theoretic Equilibria via Query Protocols -- The Lower Tail: Poisson Approximation
Revisited -- Population Protocols for Majority in Arbitrary Networks -- The Asymptotic Value in Finite Stochastic Games -- Almost All 5-Regular Graphs Have a 3-Flow -- Part-II -- Foreword -- On the Short-Time Behaviour of the Implied
Volatility Skew for Spread Options and Applications -- An Alternative to CARMA Models via Iterations of Ornstein-Uhlenbeck Processes -- Euler-Poisson Schemes for Levy Processes -- On Time-Consistent Portfolios with Time-Inconsistent
Preferences -- A Generic Decomposition Formula for Pricing Vanilla Options under Stochastic Volatility Models -- A Highly Efficient Pricing Method for European-Style Options Based on Shannon Wavelets -- A New Pricing Measure in the
Barndor-Nielsen-Shephard Model for Commodity Markets
ISBN:9783319517537
Series:eBooks
Series:Springer eBooks
Series:Springer 2017 package
Keywords: Mathematics , Dynamics , Ergodic theory , Differential equations , Actuarial science , Convex geometry , Discrete geometry , Probabilities , Combinatorics , Mathematics , Combinatorics , Ordinary Differential Equations , Dynamical Systems and Ergodic Theory , Convex and Discrete Geometry , Probability Theory and Stochastic Processes , Actuarial Sciences
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Call number:9783319428604:ONLINE Show nearby items on shelf
Title:Asymptotic Representation of Relaxation Oscillations in Lasers
Author(s): Elena V Grigorieva
Date:2017
Size:1 online resource (VIII, 230 p. 73 illus p.)
Contents:1 Introduction -- 2 Spiking in Single-Mode Laser -- 3 Spiking in Lasers with Delayed Feedback -- 4 Rectangular Pulsing in Lasers with Delayed Feedback -- 5 Relaxation Oscillations in Coupled Laser Systems -- Appendixes -- References
ISBN:9783319428604
Series:eBooks
Series:Springer eBooks
Series:Springer 2017 package
Keywords: Physics , Differential equations , Fluid mechanics , Physics , Theoretical, Mathematical and Computational Physics , Ordinary Differential Equations , Optics, Lasers, Photonics, Optical Devices , Engineering Fluid Dynamics
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Call number:3527406107:ONLINE Show nearby items on shelf
Title:Numerical Solution of Ordinary Differential Equations - for Classical, Relativistic and Nano Systems
Author(s): Greenspan
Date:2006
Publisher:Wiley-VCH
Size:1 online resource (217 p.)
ISBN:9783527406104
Series:eBooks
Series:Wiley Online Library
Series:Wiley 2016 package purchase
Keywords: Physics
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Call number:1119121507:ONLINE Show nearby items on shelf
Title:Numerical Methods for Ordinary Differential Equations 3e
Author(s): Butcher
Date:2016
Size:1 online resource (539 p.)
ISBN:9781119121503
Series:eBooks
Series:Wiley Online Library
Series:Wiley 2016 package purchase
Keywords: Mathematics
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Call number:0470723351:ONLINE Show nearby items on shelf
Title:Numerical Methods for Ordinary Differential Equations 2e
Author(s): Butcher
Date:2008
Publisher:Wiley
Size:1 online resource (483 p.)
ISBN:9780470723357
Series:eBooks
Series:Wiley Online Library
Series:Wiley 2016 package purchase
Keywords: Mathematics
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Call number:0470408553:ONLINE Show nearby items on shelf
Title:General Linear Methods for Ordinary Differential Equations
Author(s): Jackiewicz
Date:2009
Publisher:Wiley
Size:1 online resource (483 p.)
ISBN:9780470408551
Series:eBooks
Series:Wiley Online Library
Series:Wiley 2016 package purchase
Keywords: Mathematics
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Call number:047004294X:ONLINE Show nearby items on shelf
Title:Numerical Solution of Ordinary Differential Equations
Author(s): Atkinson
Date:2009
Publisher:Wiley
Size:1 online resource (273 p.)
ISBN:9780470042946
Series:eBooks
Series:Wiley Online Library
Series:Wiley 2016 package purchase
Keywords: Mathematics
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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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Call number:SPRINGER-2016-9788132228127:ONLINE Show nearby items on shelf
Title:Nonlinear Ordinary Differential Equations Analytical Approximation and Numerical Methods
Author(s): Martin Hermann
Date:2016
Size:1 online resource (310 p.)
Note:10.1007/978-81-322-2812-7
Contents:A Brief Review of Elementary Analytical Methods for Solving Nonlinear ODEs -- Analytical Approximation Methods -- Further Analytical Approximation Methods and Some Applications -- Nonlinear Two-Point Boundary Value Problems -- Numerical Treatment o f Parameterized Two-Point Boundary Value Problems
ISBN:9788132228127
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Differential equations , Mathematical physics , Numerical analysis , Mathematics , Ordinary Differential Equations , Numerical Analysis , Mathematical Physics , Mathematical Applications in the Physical Sciences
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Call number:SPRINGER-2016-9783319327266:ONLINE Show nearby items on shelf
Title:Scaling of Differential Equations
Author(s): Hans Petter Langtangen
Date:2016
Size:1 online resource (138 p.)
Note:10.1007/978-3-319-32726-6
Contents:Preface -- 1 Dimensions and Units -- 2 Ordinary Differential Equations Models -- 3 Basic Partial Differential Equations Models -- Advanced Partial Differential Equations Models -- References -- Index
ISBN:9783319327266
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Simula SpringerBriefs on Computing : 2
Keywords: Mathematics , Computer simulation , Differential equations , Partial differential equations , Computer mathematics , Mathematical models , Mathematics , Ordinary Differential Equations , Partial Differential Equations , Mathematical Modeling and Industrial Mathematics , Computational Science and Engineering , Simulation and Modeling
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Call number:SPRINGER-2016-9783319324289:ONLINE Show nearby items on shelf
Title:Programming for Computations - Python A Gentle Introduction to Numerical Simulations with Python
Author(s): Svein Linge
Date:2016
Size:1 online resource (232 p.)
Note:10.1007/978-3-319-32428-9
Contents:Preface -- The first few steps -- Basic constructions -- Computing integrals -- Solving ordinary differential equations -- Solving partial differential equations -- Solving nonlinear algebraic equations -- Getting access to Python -- References -- Index
ISBN:9783319324289
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Texts in Computational Science and Engineering: 15
Keywords: Mathematics , Numerical analysis , Computer mathematics , Computer software , Mathematics , Computational Science and Engineering , Numeric Computing , Mathematical Software , Numerical Analysis
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Call number:SPRINGER-2016-9783319320854:ONLINE Show nearby items on shelf
Title:Geometry, Algebra and Applications: From Mechanics to Cryptography
Author(s):
Date:2016
Size:1 online resource (198 p.)
Note:10.1007/978-3-319-32085-4
Contents:1 W. Batat, P. M. Gadea, J. A. Oubiña, A survey on homogeneous structures on the classical hyperbolic spaces -- 2 A. Bejancu, On the (1 + 3) threading of spacetime -- 3 M. Brozos-Vázquez, E. Calviño-Louzao, E. García-Río, R. Vázquez-Lorenzo, L ocal structure of self-dual gradient Yamabe solitons -- 4 G. Calvaruso, The prescribed curvature problem in low dimension -- 5 M. Castrillón López, P. L. García, Euler-Poincare reduction by a subgroup of symmetries as an optimal control problem -- 6 M. Castrillón López, T. S. Ratiu, Morse families and Lagrangian submanifolds -- 7 R. Durán Díaz, L. Hernández Encinas, Special primes: properties and applications -- 8 F. Etayo, Rotation Minimizing vector fields and frames in Riemannian manifolds -- 9 R. Ferreiro Pérez, Local anomaly cancellation and equivariant cohomology of jet bundles -- 10 A. Fúster-Sabater, F. Montoya Vitini, Classes of nonlinear filters for stream ciphers -- 11 V. Gayoso Martínez, L. Hernández Encinas, A. Martín Muñoz,
Implementation of cryptographic algorithms for elliptic curves -- 12 R. Hernández-Amador, J. Monterde, J. Vallejo, Supermanifolds, symplectic geometry and curvature -- 13 A. Marcelo, F. Marcelo, C. Rodríguez, Prime submodules and symmetric algebra s -- 14 A. Martín del Rey, G. Rodríguez Sánchez, Application to cybersecurity of the stability theory of the systems of ordinary differential equations -- 15 I. V. Mykytyuk, On the non-triviality of the eight-form T4(w) on manifolds with a Spin(9)-stru cture -- 16 A. Peinado, Flaws in the application of Number Theory in Key Distribution Schemes for Multicast Networks -- 17 L. Pozo, E. Rosado, Einstein-Hilbert Lagrangian induced on the linear frame bundle
ISBN:9783319320854
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Springer Proceedings in Mathematics & Statistics: 161
Keywords: Mathematics , Data structures (Computer science) , Data encryption (Computer science) , Coding theory , Differential geometry , Mathematical physics , Mathematics , Mathematical Physics , Differential Geometry , Data Encryption , Data Structures , Coding and Information Theory
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Call number:SPRINGER-2016-9783319320137:ONLINE Show nearby items on shelf
Title:Trends in Differential Equations and Applications
Author(s):
Date:2016
Size:1 online resource (67 p.)
Note:10.1007/978-3-319-32013-7
Contents:1 M. J. Castro, J. M. Gallardo, A. Marquina: Approximate Osher-Solomon schemes for hyperbolic systems -- 2 G. Maicas, A.I. Muñoz, G. Galiano, A. Ben Hamza and E. Schiavi: Spectral shape analysis of the hippocampal structure for Alzheimer’s Diseas e diagnosis -- 3 P. Alonso, J.M. Peña, M.L. Serrano: Characterizations of M-banded ASSR matrices -- 4 E. Casas, K. Chrysafinos: A review of numerical analysis for the discretization of the velocity tracking problem -- 5 G. Castiñeira and J.M. Rodríguez : Asymptotic analysis of a viscous flow in a curved pipe with elastic walls -- 6 J. Mura and A. Caiazzo: A two-scale homogenization approach for the estimation of porosity in elastic media -- 7 J. M. Carnicer, Y. Khiar and J. M. Pena: A matrix approach to the Newton formula and divided differences -- 8 B. Climent-Ezquerra and F. Guillen-Gonzalez: Long-time behavior of a Cahn-Hilliard-Navier-Stokes vesicle-fluid interaction model -- 9 G. Viglialoro: Explicit blow-up time for two porous medium
problems with different reaction terms -- 10 A. Domínguez-Delgado, C. Domínguez-Torres and J. Iñesta-Vaquera: Numerical Assessment of the Energy Efficiency of an Open Joint Ventilated Facade for Typical Meteorological Months Data in Southern Spai n -- 11 E. Barrena, G. Laporte, F. A. Ortega, M. A. Pozo: Planning ecotourism routes in nature parks -- 12 M. Isabel García-Planas and M. Dolors Magret: Isometries of the Hamming space and equivalence relations of linear codes over a finite field -- 13 D aniela Giachetti, Pedro J. Martínez-Aparicio and François Murat: Advances in the study of singular semilinear elliptic problems -- 14 A. Baeza, P. Mulet, and D. Zorio: Weighted extrapolation techniques for finite difference methods on complex domains wi th Cartesian meshes -- 15 V. Domínguez and C. Turc: High order Nystrom methods for transmission problems for Helmholtz Equation -- 16 A. Algaba, N. Fuentes, C. García and M. Reyes: Algebraic inverse integrating factors for a class of generalized
nilpotent systems -- 17 R. Burger, F. Guerrero,M.C. Martı and P. Mulet: WENO schemes for multi-dimensional porous media flow without capillarity -- 18 L. Fan, P. Monk, and V. Selgas: Time dependent scattering in an acoustic waveguide via convolutio n quadrature and the Dirichlet-to-Neumann map -- 19 M. Albareda-Sambola, L. I. Martínez-Merino and A. M. Rodríguez-Chía: Location of emergency facilities with uncertainty in the demands -- 20 P. Díaz de Alba and G. Rodriguez: Regularized solution of a nonlinear problem in applied geophysics -- 21 A. Barreras and J.M. Peña: Total positivity: a new inequality and related classes of matrices -- 22 A. Ruiz and C. Muriel: Applications of C∞-symmetries in the construction of solvable structures -- 23 R. de la Rosa and M. S. Bruzón: Travelling wave solutions of a generalized variable-coefficient Gardner equation -- 24 Rodolfo Bermejo and Laura Saavedra: A second order local projection Lagrange-Galerkin method for Navier-Stokes equations at high
Reynolds numbers -- 25 F. Guillén-González and J. R. Rodrıguez-Galvan: Finite Element approximation of Hydrostatic Stokes Equations: Review and Tests
ISBN:9783319320137
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:SEMA SIMAI Springer Series: 8
Keywords: Mathematics , Differential equations , Partial differential equations , Mathematical physics , Computer mathematics , Mathematics , Partial Differential Equations , Ordinary Differential Equations , Mathematical Applications in the Physical Sciences , Computational Mathematics and Numerical Analysis
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Call number:SPRINGER-2016-9783319318424:ONLINE Show nearby items on shelf
Title:Hasse-Schmidt Derivations on Grassmann Algebras With Applications to Vertex Operators
Author(s): Letterio Gatto
Date:2016
Size:1 online resource (195 p.)
Note:10.1007/978-3-319-31842-4
Contents:Prologue -- Generic Linear Recurrence Sequences -- Algebras and Derivations -- Hasse-Schmidt Derivations on Exterior Algebras -- Schubert Derivations -- Decomposable Tensors in Exterior Powers -- Vertex Operators via Generic LRS -- Index
ISBN:9783319318424
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:IMPA Monographs : 4
Keywords: Mathematics , Matrix theory , Algebra , Operator theory , Differential equations , Mathematics , Linear and Multilinear Algebras, Matrix Theory , Ordinary Differential Equations , Operator Theory
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Call number:SPRINGER-2016-9783319314624:ONLINE Show nearby items on shelf
Title:Nonlinear Water Waves Cetraro, Italy 2013
Author(s): Adrian Constantin
Date:2016
Size:1 online resource (8 p.)
Note:10.1007/978-3-319-31462-4
Contents:Adrian Constantin: Exact travelling periodic water waves in two-dimensional irrotational flows -- Joachim Escher: Breaking Water Waves -- Robin Stanley Johnson: Asymptotic methods for weakly nonlinear and other water waves -- Gabriele Villari: A su rvival kit in phase plane analysis: some basic models and problems
ISBN:9783319314624
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes in Mathematics: 2158
Keywords: Mathematics , Differential equations , Partial differential equations , Mathematical physics , Mathematics , Mathematical Applications in the Physical Sciences , Partial Differential Equations , Ordinary Differential Equations
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Call number:SPRINGER-2016-9783319297361:ONLINE Show nearby items on shelf
Title:Differential and Difference Equations A Comparison of Methods of Solution
Author(s): Leonard C Maximon
Date:2016
Size:1 online resource (162 p.)
Note:10.1007/978-3-319-29736-1
Contents:Preface -- Introduction -- 1 Operators -- 2 Solution of homogeneous and inhomogeneous linear equations -- 3 First order homogeneous and inhomogeneous linear equations -- 4 Second-order homogeneous and inhomogeneous equations -- 5
Self-adjoint linear equations -- 6 Green’s function -- 7 Generating function, z-transforms, Laplace transforms and the solution of linear differential and difference equations -- 8 Dictionary of difference equations with polynomial
coefficients -- Appendix A: Difference operator -- Appendix B: Notation -- Appendix C: Wronskian Determinant -- Appendix D: Casoratian Determinant -- Appendix E: Cramer’s Rule -- Appendix F: Green’s function and the Superposition
principle -- Appendix G: Inverse Laplace transforms and Inverse Generating functions -- Appendix H: Hypergeometric function -- Appendix I: Confluent Hypergeometric function -- Appendix J. Solutions of the second kind -- Bibliography
ISBN:9783319297361
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Physics , Difference equations , Functional equations , Differential equations , Mathematical physics , Applied mathematics , Engineering mathematics , Physics , Mathematical Methods in Physics , Appl.Mathematics/Computational Methods of Engineering , Difference and Functional Equations , Mathematical Applications in the Physical Sciences , Ordinary Differential Equations
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Call number:SPRINGER-2016-9783319290751:ONLINE Show nearby items on shelf
Title:Divergent Series, Summability and Resurgence II Simple and Multiple Summability
Author(s): Michèle Loday-Richaud
Date:2016
Size:1 online resource (272 p.)
Note:10.1007/978-3-319-29075-1
Contents:Avant-propos -- Preface to the three volumes -- Introduction to this volume -- 1 Asymptotic Expansions in the Complex Domain -- 2 Sheaves and Čech cohomology -- 3 Linear Ordinary Differential Equations -- 4 Irregularity and Gevrey Index Theorems - - 5 Four Equivalent Approaches to k-Summability -- 6 Tangent-to-Identity Diffeomorphisms -- 7 Six Equivalent Approaches to Multisummability -- Exercises -- Solutions to Exercises -- Index -- Glossary of Notations -- References
ISBN:9783319290751
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Lecture Notes in Mathematics: 2154
Keywords: Mathematics , Difference equations , Functional equations , Dynamics , Ergodic theory , Differential equations , Sequences (Mathematics) , Mathematics , Sequences, Series, Summability , Ordinary Differential Equations , Difference and Functional Equations , Dynamical Systems and Ergodic Theory
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Call number:SPRINGER-2016-9783319290256:ONLINE Show nearby items on shelf
Title:Nonautonomous Linear Hamiltonian Systems: Oscillation, Spectral Theory and Control
Author(s): Russell Johnson
Date:2016
Edition:1st ed. 2016
Size:1 online resource (497 p.)
Note:10.1007/978-3-319-29025-6
Contents:Nonautonomous linear Hamiltonian systems -- The rotation number and the Lyapunov index for real nonautonomous linear Hamiltonian systems -- The Floquet coeffcient for nonautonomous linear Hamiltonian systems: Atkinson problems -- The Weyl functions -- Weak disconjugacy for linear Hamiltonian systems -- Nonautonomous control theory. Linear regulator problem and the Kalman-Bucy filter -- Nonautonomous control theory. A general version of the Yakubovich Frequency Theorem -- Nonautonomous control theor y. Linear-quadratic dissipative control processes -- Index -- References
ISBN:9783319290256
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Developments in Mathematics: 36
Keywords: Mathematics , Dynamics , Ergodic theory , Differential equations , System theory , Mathematics , Dynamical Systems and Ergodic Theory , Ordinary Differential Equations , Systems Theory, Control
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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-2016-9783319281063:ONLINE Show nearby items on shelf
Title:University of Toronto Mathematics Competition (2001–2015)
Author(s): Edward J Barbeau
Date:2016
Size:1 online resource (1 p.)
Note:10.1007/978-3-319-28106-3
Contents:Preface -- 1. Problems of the Contests -- 2. Algebra -- 3. Inequalities -- 4. Sequences and Series -- 5. Calculus and its Applications -- 6. Other Topics in Analysis -- 7. Linear Algebra -- 8. Geometry -- 9. Group Theory -- 10. Combinatorics and Fi nite Mathematics -- 11. Number Theory -- Appendix A: Definitions, Conventions, Notation, and Basics -- Appendix B: Top-Ranking Students -- Index.
ISBN:9783319281063
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Group theory , Differential equations , Functions of real variables , Geometry , Mathematics , Real Functions , Geometry , Group Theory and Generalizations , Ordinary Differential Equations
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Call number:SPRINGER-2016-9783319279398:ONLINE Show nearby items on shelf
Title:Mathematics in Everyday Life
Author(s): John Haigh
Date:2016
Edition:1st ed. 2016
Size:1 online resource (14 p.)
Note:10.1007/978-3-319-27939-8
Contents:Money -- Differential Equations -- Sport and Games -- Business Applications -- Social Sciences -- TV Game Shows
ISBN:9783319279398
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Differential equations , Game theory , Mathematical models , Mathematics , Mathematics, general , Ordinary Differential Equations , Game Theory, Economics, Social and Behav. Sciences , Mathematical Modeling and Industrial Mathematics
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Call number:SPRINGER-2016-9783319277608:ONLINE Show nearby items on shelf
Title:Navier–Stokes Equations An Introduction with Applications
Author(s): Grzegorz Łukaszewicz
Date:2016
Size:1 online resource (390 p.)
Note:10.1007/978-3-319-27760-8
Contents:Introduction and summary -- Equations of classical hydrodynamics -- Mathematical preliminaries -- Stationary solutions of the Navier–Stokes equations -- Stationary solutions of the Navier–Stokes equations with friction -- Stationary flows in na rrow films and the Reynolds equation -- Autonomous two-dimensional Navier–Stokes equations -- Invariant measures and statistical solutions -- Global attractors and a lubrication problem -- Exponential attractors in contact problems -- Non-autonomous Nav ier–Stokes equations and pullback attractors -- Pullback attractors and statistical solutions -- Pullback attractors and shear flows -- Trajectory attractors and feedback boundary control in contact problems.-Evolutionary systems and the Navier–Stokes equations -- Attractors for multivalued processes in contact problems -- References -- Index
ISBN:9783319277608
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Dynamics , Ergodic theory , Differential equations , Partial differential equations , Fluid mechanics , Mathematics , Partial Differential Equations , Ordinary Differential Equations , Dynamical Systems and Ergodic Theory , Engineering Fluid Dynamics
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Call number:SPRINGER-2016-9783319272658:ONLINE Show nearby items on shelf
Title:Basic Concepts in Computational Physics
Author(s): Benjamin A Stickler
Date:2016
Edition:2nd ed. 2016
Size:1 online resource (409 p.)
Note:10.1007/978-3-319-27265-8
Contents:Some Basic Remarks -- Part I Deterministic Methods -- Numerical Differentiation -- Numerical Integration -- The KEPLER Problem -- Ordinary Differential Equations – Initial Value Problems -- The Double Pendulum -- Molecular Dynamics --
Numerics of Ordinary Differential Equations - Boundary Value Problems -- The One-Dimensional Stationary Heat Equation -- The One-Dimensional Stationary SCHRÖDINGER Equation -- Partial Differential Equations -- Part II Stochastic
Methods -- Pseudo Random Number Generators -- Random Sampling Methods -- A Brief Introduction to Monte-Carlo Methods -- The ISING Model -- Some Basics of Stochastic Processes -- The Random Walk and Diffusion Theory -- MARKOV-Chain
Monte Carlo and the POTTS Model -- Data Analysis -- Stochastic Optimization -- Appendix: The Two-Body Problem -- Solving Non-Linear Equations. The NEWTON Method -- Numerical Solution of Systems of Equations -- Fast Fourier Transform --
Basics of Probability Theory -- Phase Transitions -- Fractional Integrals and Derivatives in 1D -- Least Squares Fit -- Deterministic Optimization
ISBN:9783319272658
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Physics , Chemistry, Physical and theoretical , Computer mathematics , Applied mathematics , Engineering mathematics , Physics , Numerical and Computational Physics , Appl.Mathematics/Computational Methods of Engineering , Computational Mathematics and Numerical Analysis , Theoretical and Computational Chemistry
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Call number:SPRINGER-2016-9783319271286:ONLINE Show nearby items on shelf
Title:Stochastic Integration by Parts and Functional Itô Calculus
Author(s): Vlad Bally
Date:2016
Edition:1st ed. 2016
Size:1 online resource (207 p.)
Note:10.1007/978-3-319-27128-6
ISBN:9783319271286
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Differential equations , Partial differential equations , Probabilities , Mathematics , Probability Theory and Stochastic Processes , Ordinary Differential Equations , Partial Differential Equations
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Call number:SPRINGER-2016-9783319263397:ONLINE Show nearby items on shelf
Title:Inverse Problems in Ordinary Differential Equations and Applications
Author(s): Jaume Llibre
Date:2016
Edition:1st ed. 2016
Size:1 online resource (8 p.)
Note:10.1007/978-3-319-26339-7
Contents:Preface -- 1.Differential Equations with Given Partial and First Integrals -- 2.Polynomial Vector Fields with Given Partial and First Integrals -- 3.16th Hilbert Problem for Algebraic Limit Cycles -- 4.Inverse Problem for Constrained Lagrangian Sys tems -- 5.Inverse Problem for Constrained Hamiltonian Systems -- 6.Integrability of the Constrained Rigid Body -- 7.Inverse Problem in the Vakonomic Mechanics -- Index -- Bibliography
ISBN:9783319263397
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Progress in Mathematics: 313
Keywords: Mathematics , Differential equations , Mathematics , Ordinary Differential Equations
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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-2014-9789400770942:ONLINE Show nearby items on shelf
Title:Nonlinear Dynamics and Chaotic Phenomena: An Introduction [electronic resource]
Author(s): Bhimsen K Shivamoggi
Date:2014
Edition:2nd ed. 2014
Publisher:Dordrecht : Springer Netherlands : Imprint: Springer
Size:1 online resource
Note:This book starts with a discussion of nonlinear ordinary differential equations, bifurcation theory and Hamiltonian dynamics. It then embarks on a systematic discussion of the traditional topics of modern nonlinear dynamics --integrable systems, Poin car maps, chaos, fractals and strange attractors. The Bakers transformation, the logistic map and Lorenz system are discussed in detail in view of their central place in the subject. There is a detaileddiscussion of solitons centered around the Korteweg-d eVries equation in view of its central place in integrable systems. Then, there is a discussion of the Painlev property of nonlinear differential equations which seems to provide atest of integrability. Finally, there is a detailed discussion of the appli cation of fractals and multi-fractals to fully-developed turbulence -- a problem whose understanding has been considerably enriched by the application of theconcepts and methods of modern nonlinear dynamics. On the application side, there is a special emp hasis on some aspects of fluid dynamics and plasma physics reflecting the authors involvement in these areas of physics. A fewexercises have been provided that range from simple applications to occasional considerable extension of the theory. This book ha s grown out of the authors lecture notes for an interdisciplinary graduate-level course on nonlineardynamics. The basic concepts, language and results of nonlinear dynamical systems are described in a clear and coherent way. In order to allow for an inter disciplinary readership, an informal style has been adopted and the mathematicalformalism has been kept to a minimum. This book is addressed to first-year graduate students in applied mathematics, physics, and engineering, and is useful also to any theore tically inclined researcher in the physical sciences andengineering. This second edition constitutes an extensive rewrite of the text involving refinement and enhancement of the clarity a
Contents:1 Nonlinear Ordinary Differential Equations
1.1 First
order Systems
1.1.1 Dynamical System
1.1.2 Lipschitz Condition
1.1.3 Gronwalls Lemma
1.1.4 Linear Equations
1.1.5 Autonomous Equations
1.1.6 Stability of Equilibrium Points
1.1.6.1 Liapunov and Asymptotic Stability
1.1.6.2 Liapunov Function Method
1.1.7 Center Manifold Theorem
1.2 Phase
plane Analysis
1.3 Fully Nonlinear Evolution
1.4 Non
autonomous Systems
2 Bifurcation Theory
2.1 Stability and Bifurcation
2.2 Saddle
Node, Transcritical and Pitchfork Bifurcations
2.3 Hopf Bifurcation
ISBN:9789400770942
Series:eBooks
Series:SpringerLink
Series:Fluid Mechanics and Its Applications, 0926-5112 : v103
Series:Physics and Astronomy (Springer-11651)
Keywords: Engineering , Vibration , Hydraulic engineering , Mechanical engineering
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Call number:SPRINGER-2014-9788132218357:ONLINE Show nearby items on shelf
Title:A First Course in Ordinary Differential Equations [electronic resource] : Analytical and Numerical Methods
Author(s): Martin Hermann
Masoud Saravi
Date:2014
Publisher:New Delhi : Springer India : Imprint: Springer
Size:1 online resource
Note:This book presents a modern introduction to analytical and numerical techniques for solving ordinary differential equations (ODEs). Contrary to the traditional formatthe theorem-and-proof formatthe book is focusing onanalytical and numerical methods. The book supplies a variety of problems and examples, ranging from the elementary to the advanced level, to introduce and study the mathematics of ODEs. The analytical part of the book deals withsolution techniques for scalar first-order and second-order linear ODEs, and systems of linear ODEswith a special focus on the Laplace transform, operator techniques and power series solutions. In the numerical part, theoretical andpractical aspects of Runge-Kutta methods for solving initial-value problems and sh ooting methods for linear two-point boundary-value problems are considered. The book is intended as a primary text for courses on the theory of ODEs andnumerical treatment of ODEs for advanced undergraduate and early graduate students. It is assumed that the reader has a basic grasp of elementary calculus, in particular methods of integration, and of numerical analysis. Physicists,chemists, biologists, computer scientists and engineers whose work involves solving ODEs will also find the book useful as a r eference work and tool for independent study. The book has been prepared within the framework of aGermanIranian research project on mathematical methods for ODEs, which was started in early 2012
Contents:Chapter 1. Basic Concepts of Differential Equations
Chapter 2. First
Order Differential Equations
Chapter 3. Second
Order Differential Equations
Chapter 4. Laplace Transforms
Chapter 5. System of Linear Differential Equations
Chapter 6. Power Series Solutions
Chapter 7. Numerical Methods for Initial Value Problems
Chapter 8. Shooting Methods for Linear Boundary
Appendix A. Power Series
Appendix B. Some elementary integration formulae
Appendix C. Table of Laplacetransforms.
ISBN:9788132218357
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differential Equations , Numerical analysis , Materials
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Call number:SPRINGER-2014-9783642453670:ONLINE Show nearby items on shelf
Title:Scientific Computing with MATLAB and Octave [electronic resource]
Author(s): Alfio Quarteroni
Fausto Saleri
Paola Gervasio
Date:2014
Edition:4th ed. 2014
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:This textbook is an introduction to Scientific Computing, in which several numerical methods for the computer-based solution of certain classes of mathematical problems are illustrated. The authors show how to compute the zeros,the extrema, and the i ntegrals of continuous functions, solve linear systems, approximate functions using polynomials and construct accurate approximations for the solution of ordinary and partial differential equations. To make theformat concrete and appealing, the programmin g environments Matlab and Octave are adopted as faithful companions. The book contains the solutions to several problems posed in exercises and examples, often originating from importantapplications. At the end of each chapter, a specific section is devot ed to subjects which were not addressed in the book and contains bibliographical references for a more comprehensive treatment of the material. From the review:.... This carefully written textbook, the third English edition, contains substantial new devel opments on the numerical solution of differential equations. It is typeset in a two-color design and is written in a style suited forreaders who have mathematics, natural sciences, computer sciences or economics as a background and who are interested in a well-organized introduction to the subject. Roberto Plato (Siegen), Zentralblatt MATH 1205.65002
Contents:1. What can' t be ignored
2. Nonlinear equations
3. Approximation of functions and data
4. Numerical differentiation and integration
5. Linear systems
6. Eigenvalues and eigenvectors
7. Numerical optimization
8. Ordinary differential equations
9. Numerical approximation of boundary
value problems
10. Solutions of the exercises
References
Index
ISBN:9783642453670
Series:eBooks
Series:SpringerLink
Series:Texts in Computational Science and Engineering, 1611-0994 : v2
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Chemistry , Computer science , Visualization , Engineering
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Call number:SPRINGER-2014-9783642393860: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-2014-9783319077284:ONLINE Show nearby items on shelf
Title:The Influence of Demographic Stochasticity on Population Dynamics [electronic resource] : A Mathematical Study of Noise-Induced Bistable States and Stochastic Patterns
Author(s): Tommaso Biancalani
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:The dynamics of population systems cannot be understood within the framework of ordinary differential equations, which assume that the number of interacting agents is infinite. With recent advances in ecology, biochemistry andgenetics it is becoming increasingly clear that real systems are in fact subject to a great deal of noise. Relevant examples include social insects competing for resources, molecules undergoing chemical reactions in a cell and a poolof genomes subject to evolution.When the popul ation size is small, novel macroscopic phenomena can arise, which can be analyzed using the theory of stochastic processes. This thesis is centered on two unsolved problems in populationdynamics: the symmetry breaking observed in foraging populations, and the robustness of spatial patterns. We argue that these problems can be resolved with the help of two novel concepts: noise-induced bistable states and stochasticpatterns
ISBN:9783319077284
Series:eBooks
Series:SpringerLink
Series:Springer Theses, Recognizing Outstanding Ph.D. Research, 2190-5053
Series:Physics and Astronomy (Springer-11651)
Keywords: Ecology , Distribution (Probability theory)
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Call number:SPRINGER-2014-9783319068206:ONLINE Show nearby items on shelf
Title:Dynamical Systems with Applications using MATLAB [electronic resource]
Author(s): Stephen Lynch
Date:2014
Edition:2nd ed. 2014
Publisher:Cham : Springer International Publishing : Imprint: Birkhuser
Size:1 online resource
Note:This textbook, now in its second edition, provides a broad introduction to both continuous and discrete dynamical systems, the theory of which is motivated by examples from a wide range of disciplines. It emphasizes applicationsand simulation utilizi ng MATLAB, Simulink, the Image Processing Toolbox, and the Symbolic Math Toolbox, including MuPAD. Features new to the second edition include sections on series solutions ofordinary differential equations, perturbation methods, normal forms, Grbner bas es, and chaos synchronization chapters on image processing and binary oscillator computing hundreds of newillustrations, examples, and exercises with solutions and over eighty up-to-date MATLAB program files and Simulink model files available online. T hese files were voted MATLAB Central Pick of the Week in July2013. The hands-on approach of Dynamical Systems with Applications using MATLAB, Second Edition, has minimal prerequisites, only requiring familiarity with ordinary differential equations. It w ill appeal to advanced undergraduateand graduate students, applied mathematicians, engineers, and researchers in a broad range of disciplines such as population dynamics, biology, chemistry, computing, economics, nonlinear optics, neural networks, and phy sics. Praise for the first edition Summing up, it can be said that this text allows the reader to have an easy and quick start to the huge field of dynamicalsystems theory. MATLAB/SIMULINK facilitate this approach under the aspect of learning by doing. OR News/Operations Research Spectrum The MATLAB programs are kept as simple as possible and the author's experience has shown thatthis method of teaching using MATLAB works well with computer laboratory classes of small sizes. I recommend Dynamical Syst ems with App
Contents:Preface
A Tutorial Introduction to MATLAB
Linear Discrete Dynamical Systems
Nonlinear Discrete Dynamical Systems
Complex Iterative Maps
Electromagnetic Waves and Optical Resonators
Fractals and Multifractals
The Image Processing Toolbox
Differential Equations
Planar Systems
Interacting Species
Limit Cycles
Hamiltonian Systems, Lyapunov Functions, and Stability
Bifurcation Theory
Three
Dimensional Autonomous Systems and Chaos
Poincar Maps and Nonautonomous Systems in the Plane
Local and Global Bifurcations
The Second Part of Hilbert's Sixte
ISBN:9783319068206
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differentiable dynamical systems , Differential Equations , Engineering mathematics
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Call number:SPRINGER-2014-9783319043258:ONLINE Show nearby items on shelf
Title:Scientific Computing - An Introduction using Maple and MATLAB [electronic resource]
Author(s): Walter Gander
Martin J Gander
Felix Kwok
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Scientific computing is the study of how to use computers effectively to solve problems that arise from the mathematical modeling of phenomena in science and engineering. It is based on mathematics, numerical andsymbolic/algebraic computations and vi sualization. This book serves as an introduction to both the theory and practice of scientific computing, with each chapter presenting the basic algorithms that serve as the workhorses of manyscientific codes we explain both the theory behind these algori thms and how they must be implemented in order to work reliably in finite-precision arithmetic. The book includes many programs written in Matlab and Maple Maple isoften used to derive numerical algorithms, whereas Matlab is used to implement them. The t heory is developed in such a way that students can learn by themselves as they work through the text. Each chapter contains numerous examples andproblems to help readers understand the material hands-on
Contents:Why Study Scientific Computing?
Finite Precision Arithmetic
Linear Systems of Equations
Interpolation
Nonlinear Equations
Least Squares Problems
Eigenvalue Problems
Differentiation
Quadrature
Numerical Ordinary Differential Equations
Iterative Methods for Linear Systems
Optimization
Bibliography
Index
ISBN:9783319043258
Series:eBooks
Series:SpringerLink
Series:Texts in Computational Science and Engineering, 1611-0994 : v11
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer science Mathematics , Algorithms , Computer science , Computer software , Numerical analysis
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Call number:SPRINGER-2014-9783319029498:ONLINE Show nearby items on shelf
Title:Mathematical Models and Numerical Simulation in Electromagnetism [electronic resource]
Author(s): Alfredo Bermdez
Dolores Gmez
Pilar Salgado
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:The book represents a basic support for a master course in electromagnetism oriented to numerical simulation. The main goal of the book is that the reader knows the boundary-value problems of partial differential equations thatshould be solved in ord er to perform computer simulation of electromagnetic processes. Moreover it includes a part devoted to electric circuit theory based on ordinary differential equations. The book is mainly oriented to electricengineering applications, going from the genera l to the specific, namely, from the full Maxwells equations to the particular cases of electrostatics, direct current, magnetostatics and eddy currents models. Apart from standardexercises related to analytical calculus, the book includes some others orie nted to real-life applications solved with MaxFEM free simulation software
Contents:1 The harmonic oscillator
2 The Series RLC Circuit
3 Linear electrical circuits
4 Maxwells equations in free space
5 Some solutions of Maxwells equations in free space
6 Maxwells equations in material regions
7 Electrostatics
8 Direct current
9 Magnetostatics
10 The eddy currents model
11 An introduction to nonlinear magnetics. Hysteresis
12 Electrostatics with MaxFEM
13 Direct current with MaxFEM
14 Magnetostatics with MaxFEM
15 Eddy currents with MaxFEM
16 RLC circuits with MaxFEM
A Elements of graph theory
B Vector Calculus
C Fu
ISBN:9783319029498
Series:eBooks
Series:SpringerLink
Series:UNITEXT, 2038-5714 : v74
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer science Mathematics , Magnetism , Computer engineering
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Call number:SPRINGER-2014-9783319024356:ONLINE Show nearby items on shelf
Title:Basic Concepts in Computational Physics [electronic resource]
Author(s): Benjamin A. Stickler
Ewald Schachinger
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:With the development of ever more powerful computers a new branch of physics and engineering evolved over the last few decades: Computer Simulation or Computational Physics. It serves two main purposes: - Solution of complexmathematical problems such as, differential equations, minimization/optimization, or high-dimensional sums/integrals. - Direct simulation of physical processes, as for instance, molecular dynamics or Monte-Carlo simulation ofphysical/chemical/technical processes. Consequently, the book is divided into two main parts: Deterministic methods and stochastic methods. Based on concrete problems, the first part discusses numerical differentiation and integration,and the treatment of ordinary differential equations. This is augmented by n otes on the numerics of partial differential equations. The second part discusses the generation of random numbers, summarizes the basics of stochastics whichis then followed by the introduction of various Monte-Carlo (MC) methods. Specific emphasis is on MARKOV chain MC algorithms. All this is again augmented by numerous applications from physics. The final two chapters on Data Analysisand Stochastic Optimization share the two main topics as a common denominator. The book offers a number of appendices to provide the reader with more detailed information on various topics discussed in the main part. Nevertheless, thereader should be familiar with the most important concepts of statistics and probability theory albeit two appendices have been dedicated to provide a rudimentary discussion
Contents:Some Basic Remarks
Part I Deterministic Methods: Numerical Differentiation
Numerical Integration
The KEPLER Problem
Ordinary Differential Equations Initial Value Problems
The Double Pendulum
Molecular Dynamics
Numerics of Ordinary Differential Equations
Boundary Value Problems
The One
Dimensional Stationary Heat Equation
The One
Dimensional Stationary SCHRDINGER Equation
Numerics of Partial Differential Equations
Part II Stochastic Methods
Pseudo Random Number Generators
Random Sampling Methods
A Brief Introduction to Monte
Carlo Methods
The
ISBN:9783319024356
Series:eBooks
Series:SpringerLink
Series:Physics and Astronomy (Springer-11651)
Keywords: Chemistry , Computer science Mathematics , Engineering mathematics
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Call number:SPRINGER-2014-9783319021294:ONLINE Show nearby items on shelf
Title:A Textbook on Ordinary Differential Equations [electronic resource]
Author(s): Shair Ahmad
Antonio Ambrosetti
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:The book is a primer of the theory of Ordinary Differential Equations. Each chapter is completed by a broad set of exercises the reader will also find a set of solutions of selected exercises. The book contains many interestingexamples as well (like the equations for the electric circuits, the pendium equation, the logistic equation, the Lotka-Volterra system, and many other) which introduce the reader to some interesting aspects of the theory and itsapplications. The work is mainly addressed to stud ents of Mathematics, Physics, Engineering, Statistics, Computer Sciences, with knowledge of Calculus and Linear Algebra, and contains more advanced topics for further developments,such as Laplace transform Stability theory and existence of solutions to Bo undary Value problems. The authors are preparing a complete solutions manual, containing solutions to all the exercises published in the book. The manual willbe available Summer 2014. Instructors who wish to adopt the book may request the manual by writin g directly to one of the authors
Contents:1 First order linear differential equations
2 Theory of first order differential equations
3 First order nonlinear differential equations
4 Existence and uniqueness for systems and higher order equations
5 Second Order Equations
6 Higher Order Linear Equations
7 Systems of First Order Equations
8 Qualitative analysis of 22 systems and nonlinear second order equations
9 Sturm Liouville eigenvalue theory
10 Solutions by infinite series and Bessel functions
11 Laplace transform
12 Stability Theory
13 Boundary Value problems
Appendix A. Numerical methods
ISBN:9783319021294
Series:eBooks
Series:SpringerLink
Series:UNITEXT, 2038-5714 : v73
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Differential Equations , Numerical analysis
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Call number:SPRINGER-2014-9783319020990:ONLINE Show nearby items on shelf
Title:Introduction to Partial Differential Equations [electronic resource]
Author(s): Peter J Olver
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, andelsewhere. The exposition car efully balances solution techniques, mathematical rigor, and significant applications, all illustrated by numerous examples. Extensive exercise sets appear at the end of almost every subsection, andinclude straightforward computational problems to develop and reinforce new techniques and results, details on theoretical developments and proofs, challenging projects both computational and conceptual, and supplementary material thatmotivates the student to delve further into the subject. No previous experien ce with the subject of partial differential equations or Fourier theory is assumed, the main prerequisites being undergraduate calculus, both one- andmulti-variable, ordinary differential equations, and basic linear algebra. While the classical topics of separation of variables, Fourier analysis, boundary value problems, Green's functions, and special functions continue to formthe core of an introductory course, the inclusion of nonlinear equations, shock wave dynamics, symmetry and similarity, the Maximu m Principle, financial models, dispersion and solitons, Huygens' Principle, quantum mechanical systems,and more make this text well attuned to recent developments and trends in this active field of contemporary research. Numerical approximation schemes ar e an important component of any introductory course, and the text covers the twomost basic approaches: finite differences and finite elements. Peter J. Olver is professor of mathematics at the University of Minnesota. His wide-ranging research interests a re centered on the development of symmetry-based methodsfor differential equations and their manifold applications. He is the author of over 130 papers published in major scientific research
Contents:What are Partial Differential Equations?
Linear and Nonlinear Waves
Fourier Series
Separation of Variables
Finite Differences
Generalized Functions and Greens Functions
Complex Analysis and Conformal Mapping
Fourier Transforms
Linear and Nonlinear Evolution Equations
A General Framework forLinear Partial Differential Equations
FiniteElements and Weak Solutions
Dynamics of Planar Media
Partial Differential Equations in Space .
ISBN:9783319020990
Series:eBooks
Series:SpringerLink
Series:Undergraduate Texts in Mathematics, 0172-6056
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Fourier analysis , Differential equations, partial
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Call number:SPRINGER-2014-9783319020907:ONLINE Show nearby items on shelf
Title:Reduced Order Methods for Modeling and Computational Reduction [electronic resource]
Author(s): Alfio Quarteroni
Gianluigi Rozza
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:This monograph addresses the state of the art of reduced order methods for modeling and computational reduction of complex parametrized systems, governed by ordinary and/or partial differential equations, with a special emphasison real time computing techniques and applications in computational mechanics, bioengineering and computer graphics. Several topics are covered, including: design, optimization, and control theory in real-time with applications inengineering data assimilation, geometry registr ation, and parameter estimation with special attention to real-time computing in biomedical engineering and computational physics real-time visualization of physics-based simulations incomputer science the treatment of high-dimensional problems in state s pace, physical space, or parameter space the interactions between different model reduction and dimensionality reduction approaches the development of generalerror estimation frameworks which take into account both model and discretization effects. This b ook is primarily addressed to computational scientists interested in computational reduction techniques for large scale differentialproblems
Contents:1 W. H. A. Schilders, A. Lutowska: A novel approach to model order reduction for coupled multiphysics problems
2 A. C. Ionita, A. C. Antoulas: Case study. Parametrized Reduction using Reduced
Basis and the Loewner Framework
3 M. Bebendorf, Y. Maday, B. Stamm: Comparison of some reduced representation approximations
4 H. Antil, M. Heinkenschloss, D. C. Sorensen: Application of the Discrete Empirical Interpolation Method to Reduced Order Modeling of Nonlinear and Parametric System
5 K. Urban, S. Volkwein, O. Zeeb: Greedy Sampling using Nonlinear Optimization
6 P. Benner, L. Feng:
ISBN:9783319020907
Series:eBooks
Series:SpringerLink
Series:MS&A - Modeling, Simulation and Applications, 2037-5255 : v9
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Electronic data processing , Computer science Mathematics , Engineering mathematics , Materials
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Call number:SPRINGER-2014-9783034806220:ONLINE Show nearby items on shelf
Title:Real Quaternionic Calculus Handbook [electronic resource]
Author(s): Joo Pedro Morais
Svetlin Georgiev
Wolfgang Sprig
Date:2014
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
Note:Real quaternion analysis is a multi-faceted subject. Created to describe phenomena in special relativity, electrodynamics, spin etc., it has developed into a body of material that interacts with many branches of mathematics, suchas complex analysis, harmonic analysis, differential geometry, and differential equations. It is also a ubiquitous factor in the description and elucidation of problems in mathematical physics. In the meantime real quaternion analysishas become a well established branch in ma thematics and has been greatly successful in many different directions. This book is based onconcrete examples and exercises rather than general theorems, thus making it suitable for anintroductory one- or two-semester undergraduate course on some of the major aspects of real quaternion analysis in exercises. Alternatively, it may be used for beginning graduate level courses and as a reference work. With exercises atthe end of each chapter and its straightforward writing style the book addresses readers w ho have no prior knowledge on this subject but have a basic background in graduate mathematics courses, such as real and complex analysis,ordinary differential equations, partial differential equations, and theory of distributions
Contents:1 An introduction to quaternions
2 Quaternions and spatial rotation
3 Quaternion sequences
4 Quaternion series and infinite products
5 Exponents and logarithms
6 Trigonometric functions
7 Hyperbolic functions
8 Inverse hyperbolic and trigonometric functions
9 Quaternion matrices
10 Monomials, polynomials and binomials
11 Solutions
Bibliography
Index
ISBN:9783034806220
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Matrix theory , Algebra , Functions of complex variables , Combinatorics , Geometry
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Call number:SPRINGER-2014-9781461495062:ONLINE Show nearby items on shelf
Title:Greens Functions in the Theory of Ordinary Differential Equations [electronic resource]
Author(s): Alberto Cabada
Date:2014
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:This book provides a complete and exhaustive study of the Greens functions. Professor Cabada first proves the basic properties of Green's functions and discusses the study of nonlinear boundary value problems. Classic methodsof lower and upper soluti ons are explored, with a particular focus on monotone iterative techniques that flow from them. In addition, Cabada proves the existence of positive solutions by constructing operators defined in cones. Thebook will be of interest to graduate students and researchers interested in the theoretical underpinnings of boundary value problem solutions
Contents:1. Green's Functions in the Theory of Ordinary Differential Equations
Appendix A. A Green's Function Mathematica Package
Appendix B. Expressions of Some Particular Green's Functions
ISBN:9781461495062
Series:eBooks
Series:SpringerLink
Series:SpringerBriefs in Mathematics, 2191-8198
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Operator theory , Differential Equations , Differential equations, partial
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Call number:SPRINGER-2014-9781461493235:ONLINE Show nearby items on shelf
Title:Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems [electronic resource]
Author(s): Dumitru Motreanu
Viorica Venera Motreanu
Nikolaos Papageorgiou
Date:2014
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:This book focuses on nonlinear boundary value problems and the aspects of nonlinear analysis which are necessary to their study. The authors first give a comprehensive introduction to the many different classical methods fromnonlinear analysis, varia tional principles, and Morse theory. They then provide a rigorous and detailed treatment of the relevant areas of nonlinear analysis with new applications to nonlinear boundary value problems for both ordinaryand partial differential equations. Recent res ults on the existence and multiplicity of critical points for both smooth and nonsmooth functional, developments on the degree theory of monotone type operators, nonlinear maximum andcomparison principles for p-Laplacian type operators, and new developmen ts on nonlinear Neumann problems involving non-homogeneous differential operator appears for the first time in book form. The presentation is systematic, and anextensive bibliography and a remarks section at the end of each chapter highlight the text. Thi s work will serve as an invaluable reference for researchers working in nonlinear analysis and partial differential equations as well as auseful tool for all those interested in the topics presented
Contents:Preface
Introduction
Sobolev Spaces
Nonlinear Operators
Nonsmooth Analysis
Degree Theory
Variational Principles and Critical Point Theory
Morse Theory
Bifurcation Theory
Regularity Theorems and Maximum Principles
Spectrum of Differential Operators
Ordinary Differential Equations
Nonlinear Elliptic Equations with Dirichlet Boundary Conditions
Nonlinear Elliptic Equations with Neumann Boundary Conditions
List of Symbols
References
Index
ISBN:9781461493235
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis , Operator theory , Differential Equations , Differential equations, partial , Mathematical optimization
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Call number:SPRINGER-2014-9781461488934:ONLINE Show nearby items on shelf
Title:Topological Methods in the Study of Boundary Value Problems [electronic resource]
Author(s): Pablo Amster
Date:2014
Publisher:Boston, MA : Springer US : Imprint: Springer
Size:1 online resource
Note:This textbook is devoted to the study of some simple but representative nonlinear boundary value problems by topological methods. The approach is elementary, with only a few model ordinary differential equations and applications,chosen in such a way that the student may avoid most of the technical difficulties and focus on the application of topological methods. Only basic knowledge of general analysis is needed, making the book understandable tonon-specialists. The main topics in the study of bounda ry value problems are present in this text, so readers with some experience in functional analysis or differential equations may also find some elements that complement and enrichtheir tools for solving nonlinear problems. In comparison with other texts i n the field, this one has the advantage of a concise and informal style, thus allowing graduate and undergraduate students to enjoy some of the beauties ofthis interesting branch of mathematics. Exercises and examples are included throughout the book, pro viding motivation for the reader
Contents:Introduction
Shooting type methods
The Banach Fixed Point Theorem
Schauders Theorem and applications
Topological degree: an introduction
Applications
Basic facts on metric and normed spaces
Brief review of ODEs
Hints and Solutions to Selected Exercises
ISBN:9781461488934
Series:eBooks
Series:SpringerLink
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Differential Equations , Differential equations, partial
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Call number:SPRINGER-2014-9781461488668:ONLINE Show nearby items on shelf
Title:Waves in Neural Media [electronic resource] : From Single Neurons to Neural Fields
Author(s): Paul C Bressloff
Date:2014
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Waves in Neural Media: From Single Cells to Neural Fields surveys mathematical models of traveling waves in the brain, ranging from intracellular waves in single neurons to waves of activity in large-scale brain networks. The workprovides a pedagogic al account of analytical methods for finding traveling wave solutions of the variety of nonlinear differential equations that arise in such models. These include regular and singular perturbation methods, weaklynonlinear analysis, Evans functions and wave stability, homogenization theory and averaging, and stochastic processes. Also covered in the text are exact methods of solution where applicable. Historically speaking, the propagation ofaction potentials has inspired new mathematics, particularly with regard tothe PDE theory of waves in excitable media. More recently, continuum neural field models of large-scale brain networks have generated a new set of interestingmathematical questions with regard tothe solution of nonlocal integro-differential equat ions. Advanced graduates, postdoctoral researchers and faculty working in mathematical biology, theoretical neuroscience, or applied nonlineardynamics will find this book to be a valuable resource. The main prerequisites are an introductory graduate cours e on ordinary differential equations and partial differential equations, making this an accessible and unique contributionto the field of mathematical biology.
Contents:Preface
Part I Neurons
Single Neuron Modeling
Traveling Waves in One
Dimensional Excitable Media
Wave Propagation Along Spiny Dendrites
Calcium Waves and Sparks
Part II Networks
Waves in Synaptically
Coupled Spiking Networks
Population Models and Neural Fields
Waves in Excitable Neural Fields
Neural Field Model of Binocular Rivalry Waves
Part III Development and Disease
Waves in the Developing and the Diseased Brain
Index
ISBN:9781461488668
Series:eBooks
Series:SpringerLink
Series:Lecture Notes on Mathematical Modelling in the Life Sciences, 2193-4789
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Neurosciences , Differential Equations , Physiology Mathematics , Distribution (Probability theory)
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Call number:SPRINGER-2014-9781461471325:ONLINE Show nearby items on shelf
Title:Walter Gautschi, Volume 3 [electronic resource] : Selected Works with Commentaries
Author(s): Claude Brezinski
Ahmed Sameh
Date:2014
Publisher:New York, NY : Springer New York : Imprint: Birkhuser
Size:1 online resource
Note:Walter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics. He isworld renowned for his pi oneering work in numerical analysis and constructive orthogonal polynomials, including a definitive textbook in the former, and a monograph in the latter area. This three-volume set, Walter Gautschi:Selected Works with Commentaries, is a compilation of G autschis most influential papers and includes commentaries by leading experts. The work begins with a detailed biographical section and ends with a section commemoratingWalters prematurely deceased twin brother. This title will appeal to graduate students and researchers in numerical analysis, as well as to historians of science. Selected Works with Commentaries, Vol. 1 Numerical ConditioningSpecial Functions Interpolation and Approximation Selected Works with Commentaries, Vol. 2 Orthogonal Polynomials on the Real Line Orthogonal Polynomials on the Semicircle Chebyshev Quadrature Kronrod and Other QuadraturesGauss-type Quadrature Selected Works with Commentaries, Vol. 3 Linear Difference Equations Ordinary Differential Equations Software History and B iography Miscellanea Works of Werner Gautschi
Contents:Part I Commentaries
Linear recurrence relations
Ordinary differential equations
Computer algorithms and software packages
History and biography
Miscellanea
Part II Reprints
Linear difference equations
Ordinary differential equations
Computer algorithms and software packages
History and biography
Miscellanea
Part III Werner Gautschi
Publications
Obituaries
Recording
ISBN:9781461471325
Series:eBooks
Series:SpringerLink
Series:Contemporary Mathematicians
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer science , Differential Equations , Numerical analysis
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Call number:SPRINGER-2014-9781461470496:ONLINE Show nearby items on shelf
Title:Walter Gautschi, Volume 2 [electronic resource] : Selected Works with Commentaries
Author(s): Claude Brezinski
Ahmed Sameh
Date:2014
Publisher:New York, NY : Springer New York : Imprint: Birkhuser
Size:1 online resource
Note:Walter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics. He isworld renowned for his pi oneering work in numerical analysis and constructive orthogonal polynomials, including a definitive textbook in the former, and a monograph in the latter area. This three-volume set, Walter Gautschi:Selected Works with Commentaries, is a compilation of G autschis most influential papers and includes commentaries by leading experts. The work begins with a detailed biographical section and ends with a section commemoratingWalters prematurely deceased twin brother. This title will appeal to graduate students and researchers in numerical analysis, as well as to historians of science. Selected Works with Commentaries, Vol. 1 Numerical ConditioningSpecial Functions Interpolation and Approximation Selected Works with Commentaries, Vol. 2 Orthogonal Polynomials on the Real Line Orthogonal Polynomials on the Semicircle Chebyshev Quadrature Kronrod and Other QuadraturesGauss-type Quadrature Selected Works with Commentaries, Vol. 3 Linear Difference Equations Ordinary Differential Equations Software History and B iography Miscellanea Works of Werner Gautschi
Contents:Part I Commentaries
Orthogonal polynomials on the real line
Polynomials orthogonal on the semicircle
Chebyshev quadrature
Kronrod and other quadratures
Gauss type quadrature
Part II Reprints
Orthogonal polynomials on the real line
Polynomials orthogonal on the semicircle
Chebyshev quadrature
Kronrod and other quadratures
ISBN:9781461470496
Series:eBooks
Series:SpringerLink
Series:Contemporary Mathematicians
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer science , Differential Equations , Numerical analysis
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Call number:SPRINGER-2014-9781461470342:ONLINE Show nearby items on shelf
Title:Walter Gautschi, Volume 1 [electronic resource] : Selected Works with Commentaries
Author(s): Claude Brezinski
Ahmed Sameh
Date:2014
Publisher:New York, NY : Springer New York : Imprint: Birkhuser
Size:1 online resource
Note:Walter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics. He isworld renowned for his pi oneering work in numerical analysis and constructive orthogonal polynomials, including a definitive textbook in the former, and a monograph in the latter area. This three-volume set, Walter Gautschi:Selected Works with Commentaries, is a compilation of G autschis most influential papers and includes commentaries by leading experts. The work begins with a detailed biographical section and ends with a section commemoratingWalters prematurely deceased twin brother. This title will appeal to graduate students and researchers in numerical analysis, as well as to historians of science. Selected Works with Commentaries, Vol. 1 Numerical ConditioningSpecial Functions Interpolation and Approximation Selected Works with Commentaries, Vol. 2 Orthogonal Polynomials on the Real Line Orthogonal Polynomials on the Semicircle Chebyshev Quadrature Kronrod and Other QuadraturesGauss-type Quadrature Selected Works with Commentaries, Vol. 3 Linear Difference Equations Ordinary Differential Equations Software History and B iography Miscellanea Works of Werner Gautschi
Contents:Preface
Part I Walter Gautschi
Biography of Walter Gautschi
A brief summary of my scientific work and highlights of my career
Publications
Part II Commentaries
Numerical conditioning
Special functions
Interpolation and approximation
Part III Reprints
Numerical conditioning
Special functions
Interpolation and approximation
ISBN:9781461470342
Series:eBooks
Series:SpringerLink
Series:Contemporary Mathematicians
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer science , Differential Equations , Numerical analysis
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Call number:SPRINGER-2014-9781447163985:ONLINE Show nearby items on shelf
Title:Ordinary Differential Equations [electronic resource] : Analysis, Qualitative Theory and Control
Author(s): Hartmut Logemann
Eugene P Ryan
Date:2014
Publisher:London : Springer London : Imprint: Springer
Size:1 online resource
Note:The book comprises a rigorous and self-contained treatment of initial-value problems for ordinary differential equations. It additionally develops the basics of control theory, which is a unique feature in the current textbookliterature. The followin g topics are particularly emphasised: existence, uniqueness and continuation of solutions, continuous dependence on initial data, flows, qualitative behaviour of solutions, limit sets, stability theory, invariance principles, introductory control t heory, feedback and stabilization. The last two items cover classical control theoretic material such as linear control theory and absolute stability ofnonlinear feedback systems. It also includes an introduction to the more recent concept of input-to-st ate stability. Only a basic grounding in linear algebra and analysis is assumed. Ordinary Differential Equations will be suitable forfinal year undergraduate students of mathematics and appropriate for beginning postgraduates in mathematics and in mathema tically oriented engineering and science
Contents:Introduction
Linear differential equations
Introduction to linear control theory
Nonlinear differential equations
Stability and asymptotic behaviour
Stability of feedback systems and stabilization
ISBN:9781447163985
Series:eBooks
Series:SpringerLink
Series:Springer Undergraduate Mathematics Series, 1615-2085
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differential Equations , Systems theory , Vibration
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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-2013-9789462390218:ONLINE Show nearby items on shelf
Title:Ordinary Differential Equations and Dynamical Systems [electronic resource]
Author(s): Thomas C Sideris
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:This book is a mathematically rigorous introduction to the beautiful subject of ordinary differential equations for beginning graduate or advanced undergraduate students. Students should have a solid background in analysis andlinear algebra. The pres entation emphasizes commonly used techniques without necessarily striving for completeness or for the treatment of a large number of topics. The first half of the book is devoted to the development of the basictheory: linear systems, existence and uniquen ess of solutions to the initial value problem, flows, stability, and smooth dependence of solutions upon initial conditions and parameters. Much of this theory also serves as the paradigmfor evolutionary partial differential equations. The second half of the book is devoted to geometric theory: topological conjugacy, invariant manifolds, existence and stability of periodic solutions, bifurcations, normal forms, and theexistence of transverse homoclinic points and their link to chaotic dynamics. A common t hread throughout the second part is the use of the implicit function theorem in Banach space. Chapter 5, devoted to this topic, the serves as thebridge between the two halves of the book
Note:Springer eBooks
Contents:Introduction
Linear Systems
Existence Theory
Nonautomous Linear Systems
Results from Functional Analysis
Dependence on Initial Conditions and Parameters
Linearization and Invariant Manifolds
Periodic Solutions
Center Manifolds and Bifurcation Theory
The Birkhoff Smale Homoclinic Theorem
Appendix: Results from Real Analysis
ISBN:9789462390218
Series:e-books
Series:SpringerLink (Online service)
Series:Atlantis Studies in Differential Equations, 2214-6253 : v2
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differential Equations
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