Hubbard Vector Calculus Djvu Download
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This book covers calculus in two and three variables. It is suitable for a one-semester course, normally known as “Vector Calculus”, “Multivariable Calculus”, or simply “Calculus III”. The prerequisites are the standard courses in single-variable calculus (a.k.a. Calculus I and II). I have tried to be somewhat rigorous about proving.
Vector Calculus Pdf
Michael Spivak (b. 1940) is an American differential geometer and expositor of mathematics. In addition to this current volume (1965), he is also well known for his introductory but rigorous textbook Calculus (1967, 4th ed. 2008) and five-volume magnum opus A Comprehensive Introduction to Differential Geometry (1979, 3rd ed. 1999).
Within a brief 146 pages, Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus gives a rigorous account of multivariable calculus. The first three chapters examine functions in Euclidean space and the generalization of differential and integral calculus to functions f: Rn→Rm. The final two chapters develop the modern machinery of differential forms and the exterior calculus to state and prove a sweeping generalization of the theorems of vector calculus, the generalized Stokes' theorem for manifolds-with-boundary. The classical theorems of Cauchy-Green, Ostrogradsky-Gauss, and Kelvin-Stokes alluded to in the subtitle are restated and proved as immediate corollaries thereof.
This volume is aimed at the student who has completed at least one year of one-variable calculus and a term of linear algebra and who has, in the author's words, a certain 'rapport with abstract mathematics.' By presenting the contents of a third-term calculus course as seen by a modern mathematician, Spivak introduces the student to some of the language and concepts of differential geometry, allowing this text to serve as a prelude to his grand treatise on the subject.
Within a brief 146 pages, Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus gives a rigorous account of multivariable calculus. The first three chapters examine functions in Euclidean space and the generalization of differential and integral calculus to functions f: Rn→Rm. The final two chapters develop the modern machinery of differential forms and the exterior calculus to state and prove a sweeping generalization of the theorems of vector calculus, the generalized Stokes' theorem for manifolds-with-boundary. The classical theorems of Cauchy-Green, Ostrogradsky-Gauss, and Kelvin-Stokes alluded to in the subtitle are restated and proved as immediate corollaries thereof.
This volume is aimed at the student who has completed at least one year of one-variable calculus and a term of linear algebra and who has, in the author's words, a certain 'rapport with abstract mathematics.' By presenting the contents of a third-term calculus course as seen by a modern mathematician, Spivak introduces the student to some of the language and concepts of differential geometry, allowing this text to serve as a prelude to his grand treatise on the subject.