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Catalogue Information
Field name	Details
Dewey Class	515
Title	Undergraduate Analysis ([EBook]) / by Serge Lang.
Author	Lang, Serge. , 1927-2005
Other name(s)	SpringerLink (Online service)
Edition statement	Second Edition.
Publication	New York, NY : Springer , 1997.
Physical Details	XV, 642 pages, 23 illus. : online resource.
Series	Undergraduate texts in mathematics 0172-6056
ISBN	9781475726985
Summary Note	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.:
Contents note	One 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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4757-2698-5
Links to Related Works	Subject References: Analysis . Analysis (Mathematics) . Mathematical analysis . Mathematics . Authors: Lang, Serge. 1927-2005 . Lang, Serge, 1927-2005. . Corporate Authors: SpringerLink (Online service) . Series: Undergraduate texts in mathematics . Classification: 515 .

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Undergraduate Analysis

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