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Frequently Asked Questions
Abstract This is a solution manual of selected exercise problems from Calculus on manifolds: A modern approach to classical theorems of advanced calculus, by Michael Spivak. If you would like to correct any typos/errors, please send email to [email protected] Contents
Is Munkres's analysis on manifolds better than calculus?At more than twice the length of Calculus on Manifolds, Munkres's work presents a more careful and detailed treatment of the subject matter at a leisurely pace. Nevertheless, Munkres acknowledges the influence of Spivak's earlier text in the preface of Analysis on Manifolds.
Is Spivak's book a good introduction to integration?Spivak's book gives a decent intro to differentiation on R^n and Fubini's theorem for integration. However, the development of forms and integration of forms is unintuitive formal manipulation at best.
Is calculus on manifolds a prerequisite for differential geometry?Spivak's five-volume textbook A Comprehensive Introduction to Differential Geometry states in its preface that Calculus on Manifolds serves as a prerequisite for a course based on this text. In fact, several of the concepts introduced in Calculus on Manifolds reappear in the first volume of this classic work in more sophisticated settings.
