First time for me here so kindly let me know if I violate the rules - especially if this is a duplicate.

After reading the page how to become a good theoretical phycist, I started a serious revision of calculus. For exercises, Math.SE is a good place. I was attempting exercises from this user (question s/he asked and answered) and realized I couldn't solve the majority of them.

So the question is what is the level of mastery of calculus required for physics? What is(are) the best book(s) for that? I'm interested in limits, integration and infinite series for now.

Background: standard mathematics with limits, integration, infinite series, differential equations (ODEs and PDEs) and numerical analysis and optimization. Everything was fast paced because professors wanted to finish the program as fast as possible ( during 3 semesters ) so I really never got good at any of the listed above.
Note: self-study kind of books will be most helpful.

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    $\begingroup$ Hi Nt.bas, Welcome to Physics.SE. I'm not sure I'm well educated to understand this question. Perhaps, you could take a look at our set of book recommendations :-) $\endgroup$ – Waffle's Crazy Peanut Dec 26 '12 at 11:59
  • $\begingroup$ @CrazyBuddy I just read the page. But I am rather looking into the mathematics, calculus only. Not sure what part of the question is hard to understand, please let me know what i can make clearer. Thanks $\endgroup$ – nt.bas Dec 26 '12 at 12:15
  • $\begingroup$ Please don't mind me. But, You can try searching with some tags. I've got this one in response. And, this too :-) $\endgroup$ – Waffle's Crazy Peanut Dec 26 '12 at 12:22
  • $\begingroup$ @CrazyBuddy Yes, I have done that but the results weren't satisfactory. The issue I am having is to know from experienced physicists what is the right level of sophistication required. For example, should I know to solve this or this one. To sum up, the answer should tell at least a book with problem solving techniques for a great variety problems (not watered down). Thanks!!! $\endgroup$ – nt.bas Dec 26 '12 at 13:17
  • $\begingroup$ @Qmechanic : forgive me if my question is not well posed. I am interest in book on calculus good enough for physicist not for mathematicians. And not for the quantum mechanics level, just to study classical mechanics with confidence. Thanks. $\endgroup$ – nt.bas Dec 26 '12 at 17:58

The question seems to be ill-posed. From perspective I must say that mathematics knowledge requires constant improvement. I am doing a PhD now. As a student I did MSc in physics and separate MSc in mathematics. I think I have a good background to study new things, but I have to do that often. For example in quantum mechanics there is a notion of boundedness of operators, whole spectral theory, self-adjoint extension of hamiltonians. I can't imagine a person that learns these in "learn maths" mode. This should be stimulated by physical intuition and done in parallel with learning physics - the life is too short to do it in another way.

The best option is to quickly revise calculus, and then to follow a more advanced mathematical analysis course that requires mathematical thinking (topology, functional analysis, analysis on functional spaces).

It is not practical to judge one's level of familiarity with mathematics for physics by checking if one is able to solve problems. Calculus is an essential tool, which knowledge is useful, but this is just set of methods to solve standard problems. Typically one very soon encounters problems which are not solvable on paper (equation that require numerical treatment).

Level of mastery of calculus: not so big (within reason). Complex analysis (residues, analytical extensions) is important. Most interesting series are divergent, and mathematicians typically neglect "asymptotic series". The show goes on...

as for books try: simon & reed - this gives the overview of useful material, but not many people know this book by heart.

  • $\begingroup$ Thanks for the insight! is 'simon & reed' a book or a set of books? Do you have the full title. $\endgroup$ – nt.bas Dec 26 '12 at 16:29
  • $\begingroup$ "Methods of Modern Mathematical Physics" - this i s a series of 4 books. $\endgroup$ – user16611 Dec 27 '12 at 17:21

Are you currently pursuing physics related course in a university. There ought to have some basic courses to strengthen your foundation in mathematics. As a current undergraduate majoring in Physics, I can only share what I hope will be useful to you.

Mathematics is the language of physics, especially calculus. You should mastered the various techniques of integration, which appears in almost any formulation of physical theory, not to mention also differential equation and mathematical methods including special functions.

I recommend you the calculus book I am using: Thomas Calculus by George B. Thomas. It is a introductory but comprehensive book in calculus and full of examples.

  • $\begingroup$ No, I am an undergraduate engineering student but we will have nanotechnology (quantum mechanics) so the more comfortable one is with physics, the better. Also, I am learning physics for its own sake - my happiest hours are when i understand some theory in physics. :-) And I am checking out the Thomas Calculus book, there seem to be many of them. Which one to start with do you recommend? Thanks $\endgroup$ – nt.bas Dec 26 '12 at 17:55
  • $\begingroup$ Quantum mechanics surely require intensive understanding of calculus. The book I recommend is: Thomas' Calculus Global Edition 12th Edition George Thomas, Maurice Weir, Joel Hass, Frank Giordano pearsoned.co.uk/Bookshop/detail.asp?item=100000000306894 $\endgroup$ – Gosere Dec 27 '12 at 2:13
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    $\begingroup$ Quantum mechanics requires understanding of linear algebra, then analysis on Hibert spaces. Calculus is useful as well but mainly to solve problems during classes. The only really badly needed thing from calculus is "series method" and solving linear ODE of second order under different boundary conditions. $\endgroup$ – user16611 Dec 27 '12 at 17:24

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