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Michael Spivak's Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus (1965, ISBN 0-8053-9021-9) is a short text treating analysis in several variables in Euclidean spaces and on differentiable manifolds. The textbook is famously used in the honors Analysis II courses at MIT, University of Chicago, and University of Toronto, and the Vector Calculus course at Auburn University, and the honors Calculus course at Autonomous University of Yucatan. The book develops the classical theorems of advanced calculus, those of Green, Gauss, and Stokes, in the language of differential forms and in the context of differentiable manifolds embedded in Euclidean space. Calculus on Manifolds aims to present the topics of vector analysis in the manner that they are seen by a working mathematician, yet simply and selectively enough to be understood by strong undergraduate students.
See also 
- "Assignments". Massachusetts Institute of Technology. Retrieved 5 January 2013. Text " Analysis II " ignored (help); Text " Mathematics " ignored (help); Text " MIT OpenCourseWare" ignored (help)
- Calculus on Manifolds at the publisher 5th ed. (1971)
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