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Product Identifiers
PublisherSpringer New York
ISBN-100387948414
ISBN-139780387948416
eBay Product ID (ePID)140683
Product Key Features
Number of PagesXv, 642 Pages
LanguageEnglish
Publication NameUndergraduate Analysis
SubjectMathematical Analysis
Publication Year1996
FeaturesRevised
TypeTextbook
AuthorSerge A. Lang
Subject AreaMathematics
SeriesUndergraduate Texts in Mathematics Ser.
FormatHardcover
Dimensions
Item Height0.5 in
Item Weight86.1 Oz
Item Length9.3 in
Item Width6.1 in
Additional Product Features
Edition Number2
Intended AudienceScholarly & Professional
LCCN96-026339
ReviewsSecond EditionS. LangUndergraduate Analysis"[A] fine book . . . logically self-contained . . . 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, Second Edition S. Lang Undergraduate Analysis "[A] fine book . . . logically self-contained . . . 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, Second Edition S. Lang Undergraduate Analysis "[A] fine book . . . logically self-contained . . . 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, Second Edition S. Lang Undergraduate Analysis "[A] fine book . . . logically self-contained . . . This material can be gone over quickly by the really well-prepared reader, for it is one of the booka's pedagogical strengths that the pattern of development later recapitulates this material as it deepens and generalizes it."a? AMERICAN MATHEMATICAL SOCIETY
Dewey Edition20
Number of Volumes1 vol.
IllustratedYes
Dewey Decimal515/.8
Edition DescriptionRevised edition
Table Of ContentOne Review of Calculus.- 0 Sets and Mappings.- I Real Numbers.- II Limits and Continuous Functions.- III Differentiation.- IV Elementary Functions.- V The Elementary Real Integral.- Two Convergence.- VI Normed Vector Spaces.- VII Limits.- VIII Compactness.- IX Series.- X The Integral in One Variable.- Three Applications of the Integral.- XI Approximation with Convolutions.- XII Fourier Series.- XIII Improper Integrals.- XIV The Fourier Integral.- Four Calculus in Vector Spaces.- XV Functions on n-Space.- XVI The Winding Number and Global Potential Functions.- XVII Derivatives in Vector Spaces.- XVIII Inverse Mapping Theorem.- XIX Ordinary Differential Equations.- Five Multiple Integration.- XX Multiple Integrals.- XXI Differential Forms.
SynopsisThis 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., 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. In this second edition, the author has added a new chapter on locally integrable vector fields, has rewritten many sections and expanded others. There are new sections on heat kernels in the context of Dirac families and on the completion of normed vector spaces. A proof of the fundamental lemma of Lebesgue integration is included, in addition to many interesting exercises., 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., 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.
LC Classification NumberQA299.6-433
