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More copies of this ISBNOther titles in the Undergraduate Texts in Mathematics series:
Undergraduate Analysis 2ND Editionby Serge Lang
Synopses & ReviewsPublisher Comments:This is a logically selfcontained 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 L1Cauchy 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 selfcontained 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 wellprepared 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 ContentsChapter 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
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