Mathematical methods for physicistsGeorge B. Arfken, Hans J. Weber, Frank E. Harris
Mathematical methods for physicists
by George B. Arfken, Hans J. Weber, Frank E. Harris · first published 1966
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Providing coverage of the mathematics necessary for advanced study in physics and engineering, this text focuses on problem-solving skills and offers a vast array of exercises, as well as clearly illustrating and proving mathematical relations.
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…Techniques: for Scientists and Engineers](http://www.amazon.com/Advanced-Mathematical-Techniques-Scien...) and for a much more indepth, but less pedagogically useful (more of a reference) [Arfken --- Mathematical Methods for Physicists, Seventh Edition: A Comprehensive Guide](http://www.amazon.com/Mathematical-Methods-Physicists-Sevent...) In addition anything by Penrose tends to target a lay audience, but quickly build up formalism…
on “Math notes to take you from one year of college calculus to grad student level” ↗I don't think it was very clear either. If you want to learn more about this I like Arfken, Mathematical Methods for Physicists as a bible of practical mathematics, or Stewart, Calculus for calculus in general.
on “Show HN: Differential Equations Explained” ↗You could try Arfken and Weber's "Mathematical Methods for Physicists". It's a common reference for Physicists. While it doesn't focus on engineering (or signal) applications, it's both fairly rigorous and succinct enough for practical use. Looks like there are pdf's online.
on “An Interactive Introduction to Fourier Transforms” ↗…basics of single variable calculus in less than 200 pages, instead of ~500 pages like many intro to calc books. Similarly his Calculus of Several Variables is ~300 pages instead of 500-700. Alternatively a mathematical methods for physicists book like the one by Riley, Hobson, and Bence might suit you. It's huge (~1300 pages), but you can pick out the chapters you want to learn from and it builds up from the basics to some quite sophisticated…
on “The Deceptively Asymmetric Unit Sphere” ↗Theoretical physicists use probably more math than other subjects. Generally the litarature to use math is called 'mathematical methods for physicists'. The book by Arfken is considered standard by many. Did you mean something like that?
on “So you want to study mathematics” ↗…in our textbook (Bishop). It's pretty dense and time consuming. However, I come from a Physics background, so the math is just different, and may in fact be easier. However, I've been referencing my Mathematical Methods for Physicists book (Boas) pretty often to brush up on some linear algebra techniques. Lastly, its been said quite a bit in these forums, but if you are just interested in implementing this stuff, definitely check…
on “Stanford Machine Learning course” ↗EM’s vector fields formulation is fairly straightforward: it’s all curls and divergence. Any 3rd (-ish) semester undergrad multivariate calculus course is likely to cover it in sufficient depth. “Mathematical Methods for Physicists” covers it in sufficient depth, for example, provided you already have a thorough understanding of the prerequisite material. Most undergrad physics degree curriculums should have E&M courses whose texts…
on “Why is Maxwell's theory so hard to understand? (2007) [pdf]” ↗