[Math] Undergraduate ODE textbook following Rota

ca.classical-analysis-and-odesdifferential equationssoft-questiontextbook-recommendation

I imagine many people are familiar with the extremely entertaining article "Ten Lessons I Wish I Had Learned Before I Started Teaching Differential Equations" by Gian-Carlo Rota. (If you're not, do yourself a favor and follow the link I provided.)

I, a number theorist, have been told that I am to teach an undergraduate ODE class one year from now. (Nevermind that my familiarity with ODEs is, to put it mildly, minimal.) In a good faith effort to serve my students as well as possible, I am asking the following question.

Has any ODE textbook been written which addresses and assuages the issues brought forth in Rota's article?

Is there any way for me to teach ODEs next year and not, having read Rota's article, feel dirty about it?

Best Answer

There are a number of textbooks which are not as guilty:

  • M.W. Hirsch, S. Smale, R. Devaney, Differential Equations, Dynamical Systems, and an Introduction to Chaos
  • G. Teschl, Ordinary Differential Equations and Dynamical Systems

The last one is also freely available here. As the titles say, both take a rather geometric path and give many examples from various sciences.

The first one waits until the final chapter to give the classical existence and uniqueness theorems.

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