Differential Equations: Linear, Nonlinear, Ordinary, Partial

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A. C. KingCambridge University Press, 5/8/2003EAN 9780521016872, ISBN10: 0521016878Paperback, 556 pages, 24.4 x 17 x 3.2 cmLanguage: EnglishFinding and interpreting the solutions o f 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.PrefacePart I. Linear Equations1. Variable coefficient, second order, linear, ordinary differential equations2. Legendre functions3. Bessel functions4. Boundary value problems, Green's functions and Sturm–Liouville theory5. Fourier series and the Fourier transform6. Laplace transforms7. Classification, properties and complex variable methods for second order partial differential equationsPart II. Nonlinear Equations and Advanced Techniques8. Existence, uniqueness, continuity and comparison of solutions of ordinary differential equations9. Nonlinear ordinary differential equationsphase plane methods10. Group theoretical methods11. Asymptotic methodsbasic ideas12. Asymptotic methodsdifferential equations13. Stability, instability and bifurcations14. Time-optimal control in the phase plane15. An introduction to chaotic systemsAppendix 1. Linear algebraAppendix 2. Continuity and differentiabilityAppendix 3. Power seriesAppendix 4. Sequences of functionsAppendix 5. Ordinary differential equationsAppendix 6. Complex variablesAppendix 7. A short introduction to MATLABBibliographyIndex.'This is a useful book, providing an excellent introduction to postgraduate studies in applied mathematics. It is very well produced and one is grateful to the publishers for having produced a useful book which, at its paperback price, is reasonable these days ... I have no hesitation in giving this book my full recommendation.' The Mathematical Gazette Show more