Calculus on Manifolds

Blurb

Michael Spivak's Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus is a short text treating analysis in several variables in Euclidean spaces and on differentiable manifolds. 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.
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.