An Introduction to Ordinary Differential Equations
1st Edition
Published on 30. April 2006
978-0-511-16243-5 (ISBN)
Description
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.
Reviews / Votes
'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 GazetteMore details
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Cambridge University Press
Target group
College/higher education
Illustrations
Worked examples or Exercises; 7 Halftones, unspecified; 140 Line drawings, unspecified
File size
4,82 MB
ISBN-13
978-0-511-16243-5 (9780511162435)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
James C. Robinson
An Introduction to Ordinary Differential Equations
Book
01/2004
Cambridge University Press
€116.10
Shipment within 15-20 days
James C. Robinson
An Introduction to Ordinary Differential Equations
Book
01/2004
Cambridge University Press
€86.66
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Content
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?
