In his first lesson (transcripted in "Tips on Physics"), Feynman talks about math for physicists in a very cool and practical way. And at the end of the section he talks something like "so the first thing to do is to learn to learn derivative, integral and algebra" (I don't know how much precise I'm being because I've read it in Portuguese). I would to know if there is some book that deals with math as Feynman did it in this lesson (respecting formalities, but teaching how to use the practical rules)? Also, someone have any recommendations for algebra book (college level)?
Answer
Higher maths for beginners is ana amzing little book on all the subjects you mentioned, written by one of the fathers of Soviet nuclear bomb, and theoretical phsyicists.
On math physics, the best introductory test is Elements of applied math physics, it has dufferential equations and complex analysis and other cool topics. Unfortunately, it may not have English version.
The comprehensive analysis text is Fundamentals Mathematical Analysis. It's a Russian textbook, but it's old school, i.e. very readable.
Another must have book is Differential Equations and Calculus Variations.
The best reference on PDEs is PDE by Bitsadze, I consult it all the time, it's very thin, and chapters are mostly self-contained.
All these books were used by Physics students, I can guarantee that.
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