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001 | vtls000001673 | ||
003 | VRT | ||
005 | 20250102224908.0 | ||
008 | 081108s1997 nyua | 001 0 eng | ||
020 | _a0387948414 (hardcover : alk. paper) | ||
039 | 9 |
_a201402040100 _bVLOAD _c201007251143 _dmalmash _c200811091056 _dvenkatrajand _c200811081339 _dNoora _y200811081338 _zNoora |
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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 |
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942 |
_2lcc _n0 _cBK |
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999 |
_c23229 _d23229 |