An Introduction to Ordinary Differential Equations
$105.00 (X)
- Author: James C. Robinson, University of Warwick
- Date Published: February 2004
- availability: Available
- format: Paperback
- isbn: 9780521533911
$
105.00
(X)
Paperback
-
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.
Read more- 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
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
See more 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: February 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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