>>11346669For multivariable Calculus you could use Spivak’s Calculus on Manifolds, it sucks cock in spite of how great Spivak’s other books are; Munkres’, Analysis on Manifolds, requires explicit knowledge of introductory Real Analysis and abstract Linear Algebra; CH Edwards, Advanced Calculus of Several Variables, somewhat easy compared to the first two but is rigorous, theorems are all stated correctly, gives you a crash course in basic Lin Alg and does not require learning Analysis first; Loomis and Sternberg, Advanced Calculus, very abstract introduces calculus on Normed Linear Spaces, heavily dependent on exercises to the point where many proofs in other advanced calc books are shifted there, lucid interesting discussion of vector space theory throughout the book, archaic formatting and style of teaching, I would recommend using it as a reference text with something else as your main resource. Zorich Mathematical Analysis Vol I-II most closely resembles L&S and Tao’s books in scope and detail and is much more readable than Spivak’s Calc on Manifolds but Zorich writes for physics students and with an inelegant approach to his statement of certain proofs. Edwards is the smoothest transition I think w/Rudin accompanying it.
