I'm a undergraduate student of physics and due of the new coronavirus outbreak i'm stuck at home and i like to begin my studies on ODE. And i like to know some bibliography to where a i can start my studies. To reference i studied until now about differentiation (normal and partial) and integration until line integral. I have studied too an introduction to linear algebra.
2026-04-12 11:33:13.1775993593
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From where can i start studying ODE?
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A good beginner's book from Physicists'(or applied) viewpoint is Kreyszig, Advanced Engineering Mathematics. Then, you could supplement it with books of more theoretical falvour, like Boyce-Di-prima, Differential Equations or the master book Norman Levinson's Ordinary Differential Equations
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Perhaps a little unconventional, I propose to consider Hairer-Nørsett-Wanner: "Solving ODE I: non-stiff problems". While it is a book on numerical methods for ODE, it starts with a large theory part touching all the non-exotic topics of ODE theory, and is then concerned with the production of numerical solutions. This could be a good source to get an intuition for "real life" ODE.
And for the advanced work, Arnol'd "Mathematical methods in classical mechanics" (this is probably not the easiest classic).
See What is Gian-Carlo-Rota really saying about DE courses? (For students like me), How should a DE course be re-written, if Gian-Carlo Rota is correct? on a critique by a lecturer, Gian Carlo Rota, that wrote a book and gave courses on ODE, becoming increasingly doubtful on their results.
From the very beginning!
OK, that was partly tongue-in-cheek. For someone of your level (introductory) and context (physics), I think an informal, intuitive approach is best.
To this end I'll suggest using books that don't get too hung up about free use of differentials (most of the older books satisfy this criterion; the newer ones talk about differentials only in a course on manifolds, and that in a very sluggish, clunky way) and that emphasize applications to physics -- after all that's the origin of most problems in differential equations. To enjoy this subject well, you should have more than a passing familiarity with the differential calculus, and also the integral calculus.
A book that digs dip immediately without being opaque is the Shaum's Outlines on Advanced Mathematics for Engineers and Scientists. But again, look for the older books on the internet, and enjoy. One that comes to mind is Euler's Foundations of the Differential Calculus. Don't think most of it is a rehash of calculus -- he dips into differential equations towards the end in a way that I think shows seamlessly how this is just an extension of the investigations of the calculus, albeit having blown into its own separate field today.