Differential equations

Linear, nonlinear, ordinary, partial

A.C. King J. Billingham, S.R. Otto

552 pages, parution le 26/05/2003

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Résumé

Finding and interpreting the solutions of differential equations is a central and essential part of applied mathematics. This book aims to enable the reader to develop the required skills needed for a thorough understanding of the subject. The authors focus on the business of constructing solutions analytically, and interpreting their meaning, using rigorous analysis where needed.

MATLAB is used extensively to illustrate the material. There are many worked examples based on interesting and unusual real world problems. A large selection of exercises is provided, including several lengthier projects, some of which involve the use of MATLAB. The coverage is broad, ranging from basic second-order ODEs and PDEs, through to techniques for nonlinear differential equations, chaos, asymptotics and control theory.

This broad coverage, the authors' clear presentation and the fact that the book has been thoroughly class-tested will increase its attraction to undergraduates at each stage of their studies.

Linear Equations
- Variable coefficient, second-order, linear ordinary differential equations
- Legendre functions
- Bessel functions
- Boundary value problems, Green's functions and Sturm-Liouville theory
- Fourier series and the Fourier transform
- Laplace transforms
- Classification Properties and Complex Variable Methods for Second Order Partial Differential equations

Nonlinear Equations and Advanced Techniques
- Existence, uniqueness, continuity and comparison of solutions of ordinary differential equations
- Nonlinear ordinary differential equations
- Group theoretical methods
- Asymptotic methods: basic ideas
- Asymptotic methods: differential equations
- Stability, instability and bifurcations
- Time-optimal control in the phase plane
- An introduction to chaotic systems

Appendices
Bibliography
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	A.C. King J. Billingham, S.R. Otto
Parution	26/05/2003
Nb. de pages	552
Format	17,3 x 24,7
Couverture	Broché
Poids	1095g
Intérieur	Noir et Blanc
EAN13	9780521016872
ISBN13	978-0-521-01687-2