Calculus on Manifolds (book): Difference between revisions
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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 space]]s and on [[differentiable manifold]]s. The textbook is famously used in the honours Analysis II courses at [[Harvard]], [[Princeton University|Princeton]] and [[MIT]]. The book develops the classical theorems of advanced calculus, those of [[Green's theorem|Green]], [[Gauss' theorem|Gauss]], and [[Stokes' theorem|Stokes]], in the language of differential forms and in the context of differentiable manifolds embedded in Euclidean space. |
[[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 space]]s and on [[differentiable manifold]]s. The textbook is famously used in the honours Analysis II courses at [[Harvard]], [[Princeton University|Princeton]] and [[MIT]]. The book develops the classical theorems of advanced calculus, those of [[Green's theorem|Green]], [[Gauss' theorem|Gauss]], and [[Stokes' theorem|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. |
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Another textbook often used in undergraduate courses to supplement Spivak's book is the text ''Analysis on Manifolds'' (1997, ISBN 9780201315967) by [[James Munkres]]. |
Another textbook often used in undergraduate courses to supplement Spivak's book is the text ''Analysis on Manifolds'' (1997, ISBN 9780201315967) by [[James Munkres]]. |
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Revision as of 02:29, 16 July 2009
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 and MIT. 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 (1997, ISBN 9780201315967) 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.
See also
- Calculus on Manifolds at the publisher 5th ed. (1971)
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