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Does anyone know of any good textbooks which contain a lot of exercises and solutions? A lot have exercises, and that's useful but I really would prefer having solutions if I'm going to be doing 100+questions. I'm not too worried about the contents of the textbook as such (in terms of how the theory is explained) as I have lecture notes and an understanding of it anyway. I'm just looking to spend a lot of time going through all the questions.

I'm looking for anything related to:

Something covering Stoke's Theorem/Divergence/surface integrals/line integrals and related

Basic complex analysis such as Cauchy's Theorem, Cauchy’s formulae, Taylor’s and Liouville’s Theorem, differentiation, etc

Multivariable differentiation (more general than between finite Euclidean vector spaces, i.e functions between (infinite) normed vector spaces and also manifolds (introductory) Implicit/inverse function theorems/Lagrange multiplier

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The Schaum's Outline series has books full of endless worked examples of computations in all of these areas. It's not so big on proofs, so you won't get any practice doing the kinds of problems you'll find in Spivak's Calculus on Manifolds, but for pure computational stuff, they're the goods.

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  • $\begingroup$ Ahh yes, good suggestions! $\endgroup$ – Displayname Feb 16 at 0:50

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