Is there any text that I can use as a short reference for the standard techniques for solving basic ODEs? I currently have been using Boyce and diPrima as my ODEs text, and it is far too wordy for my taste. I'm also not too interested in expositions of applications of physics or phase plane analysis, as I have other books for that. Basically, I'm looking for something short that can quickly remind me how to use techniques like integrating factors, series solutions, etc. which I keep on forgetting.
Concise ODEs reference?
3 Answers
You might try "Differential equations: based on Schaum's outline of theory and problems of differential equations", second edition, by Richard Bronson http://books.google.ca/books?id=ZDe07OpdGMAC
I really learned a lot from Speigel's Applied Differential Equations. It gives a lot of techniques to solve ODEs, including:
- Series
- Taylor Series.
- Picard's Iteration.
- Frobenius's Method.
- Operational Method.
- Laplace's Transform.
- Integrating Factors.
- ...and many more.
Although it may seem it focuses only on the applications, Spiegel gives a great deal of theory before actually applying it.
Micheal E.Taylor has just published Introduction to Differential Equations,an introductory differential equations text with the AMS which is designed specifically for the purpose of being clear and concise. It's advertised here. I haven't seen it yet,but from the Preface and my familiarity with Taylor's other texts, it may be exactly what you're looking for.