An Introduction to Ordinary Differential Equations

by James C. Robinson

Overview

This introduction to ordinary differential and difference equations is suited not only for mathematicians but for scientists and engineers as well. Exact solutions methods and qualitative approaches are covered, and many illustrative examples are included. Matlab is used to generate graphical representations of solutions. Numerous exercises are featured and proved solutions are available for teachers.

Product Details

ISBN-13:	9780521533911
Publisher:	Cambridge University Press
Publication date:	01/08/2004
Series:	Cambridge Texts in Applied Mathematics S
Edition description:	New Edition
Pages:	414
Product dimensions:	6.69(w) x 9.61(h) x 0.83(d)

Table of Contents

Introduction; Part I. First Order Differential Equations: 1. Radioactive decay and carbon dating; 2. Integration variables; 3. Classification of differential equations; 4. Graphical representation of solutions using MATLAB; 5. 'Trivial' differential equations; 6. Existence and uniqueness of solutions; 7. Scalar autonomous ODEs; 8. Separable equations; 9. First order linear equations and the integrating factor; 10. Two 'tricks' for nonlinear equations; Part II. Second Order Linear Equations With Constant Coefficients: 11. Second order linear equations: general theory; 12. Homogeneous 2nd order linear ODEs; 13. Oscillations; 14. Inhomogeneous 2nd order linear equations; 15. Resonance; 16. Higher order linear equations; Part III. Linear Second Order Equations With Variable Coefficients: 17. Reduction of order; 18. The variation of constants formula; 19. Cauchy-Euler equations; 20. Series solutions of second order linear equations; Part IV. Numerical Methods and Difference Equations: 21. Euler's method; 22. Difference equations; 23. Nonlinear first order difference equations; 24. The logistic map; Part V. Coupled Linear Equations: 25. Vector first order equations and higher order equations; 26. Explicit solutions of coupled linear systems; 27. Eigenvalues and eigenvectors; 28. Distinct real eigenvalues; 29. Complex eigenvalues; 30. A repeated real eigenvalue; 31. Summary of phase portraits for linear equations; Part VI. Coupled Nonlinear Equations: 32. Coupled nonlinear equations; 33. Ecological models; 34. Newtonian dynamics; 35. The 'real' pendulum; 36. Periodic orbits; 37. The Lorenz equations; 38. What next?

Editorial Reviews

'The presentation is sensitive to the needs of students, with careful algebraic steps included in most cases. Appendices on basic required mathematical techniques are also included.' Mathematical Reviews

'The book is recommended as a textbook for one-term or one-semester course.' Zentralblatt MATH

'… will be useful to anybody wanting to teach or learn elements of ordinary differential equations in the beginnings of their mathematical studies.' European Mathematical Society Newsletter

'… it is written in a friendly and informal style and covers a wide and interesting collection of topics.' Contemporary Physics

'This is an excellent book which probably would have been most welcome to older students of differential equations had it existed and which will be of great value to those currently studying the subject.' The Mathematical Gazette

From the Publisher