An Introduction to Ordinary Differential Equations
An Introduction to Ordinary Differential Equations
AUD$103.59
exc GSTThis 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 [email protected]
- 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
'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
Product details
April 2004Paperback
9780521533911
414 pages
244 × 170 × 21 mm
0.83kg
147 b/w illus. 120 exercises
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?
