Undergraduate Analysis

ISBN-10: 0387948414

ISBN-13: 9780387948416

Edition: 2nd 1997 (Revised)

Authors: Serge A. Lang

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Description:

This is a logically self-contained introduction to analysis, suitable for students who have had two years of calculus. The book centers around those properties that have to do with uniform convergence and uniform limits in the context of differentiation and integration. Topics discussed include the classical test for convergence of series, Fourier series, polynomial approximation, the Poisson kernel, the construction of harmonic functions on the disc, ordinary differential equation, curve integrals, derivatives in vector spaces, multiple integrals, and others. One of the author's main concerns is to achieve a balance between concrete examples and general theorems, augmented by a variety of interesting exercises.Some new material has been added in this second edition, for example: a new chapter on the global version of integration of locally integrable vector fields; a brief discussion of L1-Cauchy sequences, introducing students to the Lebesgue integral; more material on Dirac sequences and families, including a section on the heat kernel; a more systematic discussion of orders of magnitude; and a number of new exercises.
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Book details

List price: $79.95
Edition: 2nd
Copyright year: 1997
Publisher: Springer
Publication date: 6/28/2005
Binding: Hardcover
Pages: 642
Size: 6.75" wide x 9.75" long x 1.50" tall
Weight: 2.090
Language: English

Lang, Yale University, New Haven, CT.

Sets and Mappings
Real Numbers
Limits and Continuous Functions
Differentiation
Elementary Functions
The Elementary Real Integral
Normed Vector Spaces
Limits
Compactness
Series
The Integral in One Variable
Appendix: The Lebesgue Integral
Approximation with Convolutions
Fourier Series
Improper Integrals
The Fourier Integral
Calculus in Vector Spaces
The Winding Number and Global Potential Functions
Derivatives in Vector Spaces
Inverse Mapping Theorem
Ordinary Differential Equations
Multiple Integration
Differential Forms
Appendix
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