Very Good condition. Good dust jacket. Volume 2. A copy that may have a few cosmetic defects. May also contain light spine creasing or a few markings such as an owner's name, short gifter's inscription or light stamp. NOT AVAILABLE FOR SHIPMENT OUTSIDE OF THE UNITED STATES.

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Bibliographic Details

Title: Introduction to Calculus and Analysis, Vol. 2
Publisher: Interscience Publishers
Publication Date: 1965
Language: English
ISBN 10: 0471178624
ISBN 13: 9780471178620
Binding: Hardcover
Condition: Very Good
Dust Jacket Condition: Dust Jacket Included

About this title

Synopsis

The new Chapter 1 contains all the fundamental properties of linear differential forms and their integrals. These prepare the reader for the introduction to higher-order exterior differential forms added to Chapter 3. Also found now in Chapter 3 are a new proof of the implicit function theorem by successive approximations and a discus� sion of numbers of critical points and of indices of vector fields in two dimensions. Extensive additions were made to the fundamental properties of multiple integrals in Chapters 4 and 5. Here one is faced with a familiar difficulty: integrals over a manifold M, defined easily enough by subdividing M into convenient pieces, must be shown to be inde� pendent of the particular subdivision. This is resolved by the sys� tematic use of the family of Jordan measurable sets with its finite intersection property and of partitions of unity. In order to minimize topological complications, only manifolds imbedded smoothly into Euclidean space are considered. The notion of "orientation" of a manifold is studied in the detail needed for the discussion of integrals of exterior differential forms and of their additivity properties. On this basis, proofs are given for the divergence theorem and for Stokes's theorem in n dimensions. To the section on Fourier integrals in Chapter 4 there has been added a discussion of Parseval's identity and of multiple Fourier integrals.

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