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008 081108s1997 nyua | 001 0 eng
020 _a0387948414 (hardcover : alk. paper)
039 9 _a201402040100
_bVLOAD
_c201007251143
_dmalmash
_c200811091056
_dvenkatrajand
_c200811081339
_dNoora
_y200811081338
_zNoora
050 0 0 _aQA300
_b.L278 1997
100 1 _aLang, Serge,
_d1927-2005.
_91190
245 1 0 _aUndergraduate Analysis /
_cSerge Lang.
250 _a2nd ed.
260 _aNew York :
_bSpringer,
_c1997.
300 _axv, 642 p. :
_bill. ;
_c25 cm.
440 0 _aUndergraduate texts in mathematics
_91191
500 _aIncludes index.
505 _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 0 _aMathematical analysis.
_94699
942 _2lcc
_n0
_cBK
999 _c23229
_d23229