Resources

The Big Five Textbooks

  • Boyce, DiPrima, and Meade – Elementary Differential Equations and Boundary Value Problems, 12th Edition ISBN: 978-1119777694 Amazon
    • This is the most popular differential equations book. I even used it for my first course. It is not necessarily the best, but it is satisfactory.
  • Zill, Dennis G. – A First Course in Differential Equations with Modeling Applications, 11th Edition ISBN: 978-1305965720 Amazon
    • This book is similar to Boyce and DiPrima. This book includes many applications and examples. The content is good for a course or self-study.
  • Nagle, Saff, and Snider – Fundamentals of Differential Equations, 9th Edition ISBN: 978-0321977069 Amazon
    • This book is similar to Boyce and DiPrima. It has especially good sections on the Laplace Transform.
  • Edwards and Penney – Differential Equations and Boundary Value Problems: Computing and Modeling, 5th Edition ISBN: 978-0321816252 Amazon
    • This book is similar to Boyce and DiPrima. It has some computational examples but does not commit to one platform. I like the problem sets in this book.
  • Blanchard, Devaney and Hall – Differential Equations, 4th Edition ISBN: 978-1133109037 Amazon
    • This book is the last of the big 5 textbooks. I would say it is different from most other books in that it tries to approach things qualitatively and geometrically. Use this book if you are not afraid to code or do a numerical computation.

CLASSIC & SELF-STUDY REFERENCES

  • Tenenbaum and Pollard – Ordinary Differential Equations ISBN: 978-0486649405 Amazon
    • If you want the most bang for your buck, then buy this book. There are lots of examples, problems, and solutions. In the last few decades, many students have enjoyed this Dover book. The quality is good on the print version and goes as a nice pairing with another more expensive book.
  • Simmons, George F. – Differential Equations with Applications and Historical Notes, 3rd Edition ISBN: 978-1498702591 Amazon
    • The interesting thing that sets this book apart is the historical context. All around a good book on the differential equations parts though.
  • Arnold, Vladimir I. – Ordinary Differential Equations, 3rd Edition ISBN: 978-3540345633 Amazon
    • Arnold is a serious mathematician. If you are not into topology and geometry, you might pass on this book. If you are a pure mathematician then this book might be great for you.
  • Coddington, Earl A. – An Introduction to Ordinary Differential Equations ISBN: 978-0486659428 Amazon
    • This is a Dover book at the basic level. It’s a good value and the presentation is excellent.
  • Ross, Shepley L. – Introduction to Ordinary Differential Equations, 4th Edition ISBN: 978-0471098812 Amazon
    • This is an older book, before Boyce and DiPrima. It is solid however.

NONLINEAR DYNAMICS & QUALITATIVE THEORY

  • Strogatz, Steven H. – Nonlinear Dynamics and Chaos, 3rd Edition ISBN: 978-0367026509 Amazon
    • This is a very well crafted book. If you wanted to go into this field and write a book like this you would find it very difficult to do better. There are lots of interesting examples and applications that make you appreciate your differential equations knowledge more.
  • Hirsch, Smale, and Devaney – Differential Equations, Dynamical Systems, and an Introduction to Chaos, 3rd Edition ISBN: 978-0123820105 Amazon
    • This is a graduate-level course. Smale is a Fields Medalist. If you want to go from ODEs to dynamical systems then this book is a must.

APPLIED & ENGINEERING-ORIENTED TEXTS

  • Kreyszig, Erwin – Advanced Engineering Mathematics, 10th Edition ISBN: 978-0470458365 Amazon
    • This is a massive math methods book. It has sections on differential equations. You can learn a lot with this book.
  • Braun, Martin – Differential Equations and Their Applications, 4th Edition ISBN: 978-0387978949 Amazon
    • This book emphasizes applications, then the methods that are necessary to solve them.
  • Strang, Gilbert – Differential Equations and Linear Algebra ISBN: 978-0980232790 Amazon
    • Strang is a famous author from MIT. He is often considered the expert in linear algebra. This book is a good combination of differential equations and LA.

ADVANCED & GRADUATE TEXTS

  • Coddington, and Levinson – Theory of Ordinary Differential Equations ISBN: 978-0898747553 Amazon
    • This is an advanced text that is more concerns with theoretical ideas.
  • Arnol’d, Vladimir I. – Geometrical Methods in the Theory of Ordinary Differential Equations, 2nd Edition ISBN: 978-0387966496 Amazon
    • More Arnold. Crazy mathematics, but nice if you are a professional mathematician.
  • Lawrence C. Evans – Partial Differential Equations, 2nd Edition ISBN: 978-0821849743 Amazon
    • This is a graduate course in PDEs. Good for when you already mastered ODEs.
  • Farlow, Stanley J. – Partial Differential Equations for Scientists and Engineers ISBN: 978-0486676203 Amazon
  • Lebl, Jiří – Notes on Diffy Qs: Differential Equations for Engineers, 6th Edition ISBN: 978-1706230236 Amazon
    • This is a free, open-source book and not too long. Only 400 pages to show you everything.

FREE TEXTBOOKS & NOTES

YOUTUBE

INTERACTIVE & COMPUTATIONAL TOOLS

Practice and Problem Sets

If you know some good resources you think should be on this list, then contact me at jackmerrin@gmail.com