ODE Resources

There are many, many resources out there about ODEs. Here’s a list of some that seemed noteworthy to me. You’ll find many more if you go searching. I encourage you to start with our textbook, and then supplement with at most one or two other resources to help solidify your understanding. If you try to look at everything, you’ll just overwhelm yourself.

Some resources that cover ODEs roughly the level of our course:

• Freely available textbooks:
  • Conrad. Ordinary Differential Equations: A Systems Approach.
  • Judson. The Ordinary Differential Equations Project.
  • Lebl. Notes on Diffy Qs.
  • Trench. Elementary Differential Equations.
• Other free resources:
  • Miller and Mattuck. MIT OpenCourseWare for 18.03. (This course also has video lectures by the instructors, which some of you may find useful!)
• Textbooks you could purchase:
  • Nagle, Saff, and Snider. Fundamentals of Differential Equations. 8th edition.

Some resources that cover the linear algebra we’ll need:

• Some freely available resources:
  • Hefferon. Linear Algebra.
  • Treil. Linear Algebra Done Wrong.
• Textbooks you could purchase:
  • Axler. Linear Algebra Done Right. 3rd edition. (I highly recommend this book!)

Some resources for those who want to go deeper into ODEs:

• Gutermuth. Picard’s Existence and Uniqueness Theorem.
  • This is a nice exposition of a proof of this theorem (theorem 1.2.1 in Lebl’s Notes).
• Perko. Differential Equations and Dynamical Systems. 3rd edition.
  • Chapter 1 contains details about first order linear systems with constant coefficients.
  • Chapters 2-4 contain information about nonlinear ordinary differential equations.
• Hirsch and Smale. Differential Equations, Dynamical Systems, and Linear Algebra. 1st edition.
  • Chapters 1 through 7 contain lots of information about first order linear systems with constant coefficients.
  • Note that the 2nd edition of this book is very different from the 1st (in fact, the 2nd edition is somewhat less mathematically rigorous).
• Arnold. Ordinary Differential Equations. 3rd edition.
  • This book has lots of kinds of ordinary differential equations, including many nonlinear ones. It’s considered a classic in the subject and has lots of challenging exercises.
• Meiss. Differential Dynamical Systems.