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Loomis L.H., Sternberg S. Advanced Calculus
Jones & Bartlett Publishers, 1989. - 592 pages.

As Spivak's "Calculus on Manifolds", this book is labeled with a very modest title. It should be something as "All you wanted to know about analysis on manifolds but were afraid to ask". This book is a must-reading for the analyst. It covers everything from the most basic vector space concepts up to the fundamental theorems of classical mechanics, running through multivariate calculus, exterior calculus, integration of forms, and many topics more, always keeping a very mode and rigorous style. The undergraduate may find it a little difficult, but the effort is worth it. For the graduate student and the working mathematician it is an almost-daily reference.
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