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Differential Equations and Linear Algebra.Fundamentals of Differential Equations bound with IDE CD.Differential Equations with Boundary-Value Problems.Differential Equations and Boundary Value Problems.A First Course in Differential Equations with Modeling Applications.Can't see how you can work with PDEs if you don't have undergrad familiarity with ODEs as many problems are solved by converting a PDE to an ODE. I'm curious if you have a gap in PDEs also. And even has a lot of non rigorous proofs.
This is why you can't teach a young gymnast a double back when they start.Ī good, cheap book for self study is Tenanbaum and Pollard. The human brain is not a computer, it learns from imitation and repetition. It's actually more efficient and you will learn more and deeper by learning the content first in terms of problem solving manipulation and later in terms of all the fancy stuff. And it's not just about how books are constructed and how people typically learn. Then after that, go grab some fancy book with all the grad school emphasis on proofs and Sobolev spaces and the like.īecause 90%+ of those books assume exposure to diffyQs first (in the way that "real analysis" typically assumes "calculus" exposure first). But one emphasizing manipulation and problem solving and applications. Not one with all the fancy connections to other fields of math that you know. Work through a standard undergrad text on DiffyQs first. It is very classical, but it really does cover all the essential theory. It sounds like you have a strong geometry/topology background, so maybe this disqualifies this text for you.įor a more classical treatment of ODEs, in particular the treatment of ODEs as linear operators (Sturm-Liouville theory), I might go for Coddington's Theory of Ordinary Differential Equations. There are some tools missing, in particular from geometry/topology, that could make the presentation a bit cleaner. Some flaws: The book really only presupposes mastery of analysis. However, I think the emphasis of this text on geometry, and on using some more modern results, makes the book a decent choice. I would not call this a standard introduction to ODE - it does not cover some of the absolute basics. The focus of this book is on qualitative behavior - existence of fixed points, limit cycles, blow-up solutions, etc. I occasionally use a book called Differential Equations and Dynamical Systems, by Lawrence Perko. There are way too many approaches to ODEs to have any one book cover them all.
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