This refreshing, introductory textbook covers both standard techniques for solving ordinary differential equations, as well as introducing students to qualitative methods such as phase-plane analysis. The presentation is concise, informal yet rigorous; it can be used either for 1-term or 1-semester courses. Topics such as Euler's method, difference equations, the dynamics of the logistic map, and the Lorenz equations, demonstrate the vitality of the subject, and provide pointers to further study. The author also encourages a graphical approach to the equations and their solutions, and to that end the book is profusely illustrated. The files to produce the figures using MATLAB are all provided in an accompanying website. Numerous worked examples provide motivation for and illustration of key ideas and show how to make the transition from theory to practice. Exercises are also provided to test and extend understanding: solutions for these are available for teachers.
- Ideal for undergraduate mathematics students
- Solutions to exercises available to lecturers from solutions@cambridge.org
- Full of illustrations, worked examples, exercises and accompanying MATLAB code
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Reviews & endorsements
'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
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Product details
- Date Published: January 2004
- format: Paperback
- isbn: 9780521533911
- length: 414 pages
- dimensions: 244 x 170 x 21 mm
- weight: 0.83kg
- contains: 147 b/w illus. 120 exercises
- availability: Available
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?
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An Introduction to Ordinary Differential Equations

James C. Robinson
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Instructors have used or reviewed this title for the following courses
- Ordinary Differential Equations
Author
James C. Robinson, University of Warwick