Introduction to Calculus and Analysis: Volume II: 002 - Rilegato

Courant, Richard; John, Fritz

Rilegato

ISBN 10: 0387971521 ISBN 13: 9780387971520

Casa editrice: Springer Verlag, 1990

Riassunto

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.

Su questo libro

Product Description

Book by Courant Richard John Fritz

Dettagli dell?edizione

• Editore: Springer Verlag
• Data di pubblicazione: 1990
• ISBN 10: 0387971521
• ISBN 13: 9780387971520
• Rilegatura: Copertina rigida
• Lingua: Inglese
• Numero di pagine: 979