Level of calculus required for physics 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.
 A: 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.
A: 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.
