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25 Remote Warehouse Mathematics- Analysis General

Undergraduate Analysis 2ND Edition

by

Undergraduate Analysis 2ND Edition Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

This logically self-contained introduction to analysis centers around those properties that have to do with uniform convergence and uniform limits in the context of differentiation and integration. From the reviews: "This material can be gone over quickly by the really well-prepared reader, for it is one of the book's pedagogical strengths that the pattern of development later recapitulates this material as it deepens and generalizes it." --AMERICAN MATHEMATICAL SOCIETY

Table of Contents

Chapter 0: Sets and MappingsChapter 1: Real NumbersChapter 2: Limits and Continuous FunctionsChapter 3: DifferentiationChapter 4: Elementary FunctionsChapter 5: The Elementary Real IntegralChapter 6: Normed Vector SpacesChapter 7: LimitsChapter 8: CompactnessChapter 9: SeriesChapter 10: The Integral in One VariableAppendix: The Lebesgue IntegralChapter 11: Approximation with ConvolutionsChapter 12: Fourier SeriesChapter 13, Improper IntegralsChapter 14: The Fourier IntegralChapter 15: Calculus in Vector SpacesChapter 16: The Winding Number and Global Potential FunctionsChapter 17: Derivatives in Vector SpacesChapter 18: Inverse Mapping TheoremChapter 19: Ordinary Differential EquationsChapter 20: Multiple IntegrationChapter 22: Differential FormsAppendix

Product Details

ISBN:
9780387948416
Author:
Lang, S.
Author:
Lang, Serge A.
Author:
Lang, S.
Publisher:
Springer
Location:
New York, NY
Subject:
Calculus
Subject:
Mathematical Analysis
Subject:
Analysis
Subject:
Differentialrechnung
Subject:
Integralrechnung
Subject:
General
Subject:
Mathematics-Analysis General
Subject:
Mathematics
Subject:
The Arts
Subject:
mathematics and statistics
Subject:
Global analysis (Mathematics)
Copyright:
Edition Number:
2
Edition Description:
1997. Corr. 4th
Series:
Undergraduate Texts in Mathematics
Series Volume:
39
Publication Date:
December 1996
Binding:
HARDCOVER
Language:
English
Illustrations:
Y
Pages:
657
Dimensions:
235 x 155 mm 2440 gr

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Related Subjects

Education » General
Science and Mathematics » Mathematics » Advanced
Science and Mathematics » Mathematics » Algebra » General
Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » Real Analysis
Science and Mathematics » Physics » General

Undergraduate Analysis 2ND Edition New Hardcover
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$87.75 In Stock
Product details 657 pages Springer-Verlag - English 9780387948416 Reviews:
"Synopsis" by , This logically self-contained introduction to analysis centers around those properties that have to do with uniform convergence and uniform limits in the context of differentiation and integration. From the reviews: "This material can be gone over quickly by the really well-prepared reader, for it is one of the book's pedagogical strengths that the pattern of development later recapitulates this material as it deepens and generalizes it." --AMERICAN MATHEMATICAL SOCIETY
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