MARC Record from harvard_bibliographic_metadata

LEADER: 02789nam a22004215a 4500
001 013841213-8
005 20131206202159.0
008 130125s1997 xxu| s ||0| 0|eng d
020 $a9781475726985
020 $a9781475726985
020 $a9781441928535
024 7 $a10.1007/978-1-4757-2698-5$2doi
035 $a(Springer)9781475726985
040 $aSpringer
050 4 $aQA299.6-433
072 7 $aPBK$2bicssc
072 7 $aMAT034000$2bisacsh
082 04 $a515$223
100 1 $aLang, Serge,$eauthor.
245 10 $aUndergraduate Analysis /$cby Serge Lang.
250 $aSecond Edition.
264 1 $aNew York, NY :$bSpringer New York :$bImprint: Springer,$c1997.
300 $aXV, 642 p.$bonline resource.
336 $atext$btxt$2rdacontent
337 $acomputer$bc$2rdamedia
338 $aonline resource$bcr$2rdacarrier
347 $atext file$bPDF$2rda
490 1 $aUndergraduate Texts in Mathematics,$x0172-6056
505 0 $aReview of Calculus: Sets and Mappings. Real Numbers. Limits and Continuous Functions. Differentiation. Elementary Functions. The Elementary Real Integral -- Convergence: Normed Vector Spaces. Limits. Compactness. Series. The Integral in One Variable -- Applications of the Integral: Fourier Series. Improper Integrals. The Fourier Integral -- Calculus in Vector Spaces: Function on n-Space. The Winding Number and Global Potential Functions. Derivatives in Vector Spaces. Inverse Mapping Theorem. Ordinary Differential Equations -- Multiple Integration: Multiple Integrals. Differential Forms -- Appendix -- Index.
520 $aThis 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.
650 10 $aMathematics.
650 0 $aGlobal analysis (Mathematics)
650 0 $aMathematics.
650 24 $aAnalysis.
776 08 $iPrinted edition:$z9781441928535
830 0 $aUndergraduate Texts in Mathematics.
988 $a20131119
906 $0VEN