I wanted a rigorous self contained book on multivariable calculus. I found someone recommending this book "Multidimensional real analysis" by Duistermaat,Kolk on mSE but couldn't find any reviews on this book. 1.Is this book self contained? 2.Are there any pre requisites for this book? Other than a course in analysis,Linear algebra(tao,kunze)
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2yes, it is self-contained, and the prerequisites are analysis I and linear algebra as you mentioned (e.g at the levels you wrote, or I think equivalently, Spivak's Calculus, and Friedberg, Insel Spence's linear algebra), and of course 'mathematical maturity'. However, be warned that Duistermaat & Kolk is not an easy text. They treat the fundamentals in a very detailed manner (hence quite long), and it's I think well-written, but it's not easy. But they have tons of problems (100+ for differentiation, and another 100+ for integration), so you should do as many as you can. – peek-a-boo May 19 '22 at 18:38