Calculus on Manifolds (book)

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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 honours Analysis II courses at Harvard, Princeton, MIT, UNAM, The University of Toronto, as well as other leading universities. 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" presents 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.

Another textbook often used in undergraduate courses to supplement Spivak's book is the text "Analysis on Manifolds" by James Munkres.

The cover of "Calculus on Manifolds" features a copy of the original publication of Stokes' Theorem as it was written in a letter by Lord Kelvin to Sir George Stokes.