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

Differential Equations

Linear, Nonlinear, Ordinary, Partial

• Broschiertes Buch

Produktbeschreibung

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`s 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.

Produktdetails

• Verlag: CAMBRIDGE UNIVERSITY PRESS
• Seitenzahl: 556
• Erscheinungstermin: 27. Mai 2006
• Englisch
• Abmessung: 244mm x 170mm x 30mm
• Gewicht: 1086g
• ISBN-13: 9780521016872
• ISBN-10: 0521016878
• Artikelnr.: 11742148

Inhaltsangabe

Preface; Part I. Linear Equations: 1. Variable coefficient, second order, linear, ordinary differential equations; 2. Legendre functions; 3. Bessel functions; 4. Boundary value problems, Green's functions and Sturm-Liouville theory; 5. Fourier series and the Fourier transform; 6. Laplace transforms; 7. Classification, properties and complex variable methods for second order partial differential equations; Part II. Nonlinear Equations and Advanced Techniques: 8. Existence, uniqueness, continuity and comparison of solutions of ordinary differential equations; 9. Nonlinear ordinary differential equations: phase plane methods; 10. Group theoretical methods; 11. Asymptotic methods: basic ideas; 12. Asymptotic methods: differential equations; 13. Stability, instability and bifurcations; 14. Time-optimal control in the phase plane; 15. An introduction to chaotic systems; Appendix 1. Linear algebra; Appendix 2. Continuity and differentiability; Appendix 3. Power series; Appendix 4. Sequences of functions; Appendix 5. Ordinary differential equations; Appendix 6. Complex variables; Appendix 7. A short introduction to MATLAB; Bibliography; Index.

Rezensionen

'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