Introduction to Calculus and Analysis, Volume Two

Courant, Richard, John, Fritz

ISBN 10: 0471178624 / ISBN 13: 9780471178620

Published by John Wiley & Sons Inc., 1974

About this Item

First edition, first printing, 954 pp., hardcover, minor (mostly internal) library markings else text clean & binding tight (lacks dust jacket). - If you are reading this, this item is actually (physically) in our stock and ready for shipment once ordered. We are not bookjackers. Buyer is responsible for any additional duties, taxes, or fees required by recipient's country. Seller Inventory # ZB1324475

Bibliographic Details

Title: Introduction to Calculus and Analysis, ...

Publisher: John Wiley & Sons Inc.

Publication Date: 1974

Binding: Hardcover

Condition: Very Good

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.