Mathematical methods for physicists

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1. griffzhowlNov 2024
   Learning maths is all about having the proper prerequisites (and time and effort...). The concepts all build on simpler ones in a hierarchy leading down to our basic ideas of numbers and space, so if you're missing any of those simpler ones you simply won't be able to understand anything more advanced or exotic except in a very fragmentary or superficial way.

   For differential geometry the prerequisites are linear algebra and multi-variable calculus, and the prerequisite for multi-variable calculus is single variable calculus, and the prerequisites for each of those is basic algebra, trigonometry, and elementary geometry.

   You don't need to know everything about each of these to get things at the next level, but a thorough grounding in the basics is essential in my experience. There's a reason every STEM field begins with calculus and linear algebra - they're used everywhere in anything at a higher level. Once you get through those you will find things open up for you.

   I don't know your level so it's difficult to make any concrete recommendations, but in general I find Lang's books to be clear and efficient sources. His Short Calculus covers all the 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 mathematics and has references if you want more depth on some topic, and great problems.

   I find I don't really learn anything from watching videos. They can be complementary, but most of the learning with maths comes from doing problems after reading through an introduction to the concepts

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2. elcritchSep 2019
   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.
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3. andrepdJun 2015
   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.
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4. atondwalJan 2013
   This is extrordanarily good. For a similar, but more in depth covering of the same material I reccomend

   [Osborne --- Advanced Mathematical 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 and cover concepts interesting to even practicing physicists.

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5. sidllsJan 2024
   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 (e.g. Introduction to Electricity and Magnetism, Griffiths) cover enough of the details. If you want to pursue it further than an undergraduate level study, you’ll also want a good text on differential equations that has or is supplemented by material covering, e.g., spherical harmonics and Bessel functions (among other things). I wish I could remember what I used, but it was…more years ago than I care to say when I was an grad student.
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6. andi999Mar 2022
   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?
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