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A Course in Mathematical Analysis. Volume 2 : Metric and Topological Spaces, Functions of a Vector Variable /
The second volume of three providing a full and detailed account of undergraduate mathematical analysis.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2013.
|
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000Ia 4500 | ||
|---|---|---|---|
| 001 | EBSCO_ocn869640256 | ||
| 003 | OCoLC | ||
| 005 | 20231017213018.0 | ||
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| 016 | 7 | |a 016629183 |2 Uk | |
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| 049 | |a UAMI | ||
| 100 | 1 | |a Garling, D. J. H. | |
| 245 | 1 | 2 | |a A Course in Mathematical Analysis. |n Volume 2 : |p Metric and Topological Spaces, Functions of a Vector Variable / |c D.J.H. Garling. |
| 260 | |a Cambridge : |b Cambridge University Press, |c 2013. | ||
| 300 | |a 1 online resource (336 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Cover.pdf; Cover; A COURSE IN MATHEMATICAL ANALYSIS; Title; Copyright; Contents; Introduction; Part III Metric and topological spaces; 11 Metric spaces and normed spaces; 11.1 Metric spaces: examples; 11.2 Normed spaces; 11.3 Inner-product spaces; 11.4 Euclidean and unitary spaces; 11.5 Isometries; 11.6 *The Mazur-Ulam theorem*; 11.7 The orthogonal group bold0mu mumu OdOdOdOdOdOd; 12 Convergence, continuity and topology; 12.1 Convergence of sequences in a metric space; 12.2 Convergence and continuity of mappings; 12.3 The topology of a metric space. | |
| 505 | 8 | |a 12.4 Topological properties of metric spaces13 Topological spaces; 13.1 Topological spaces; 13.2 The product topology; 13.3 Product metrics; 13.4 Separation properties; 13.5 Countability properties; 13.6 *Examples and counterexamples*; 14 Completeness; 14.1 Completeness; 14.2 Banach spaces; 14.3 Linear operators; 14.4 *Tietze's extension theorem*; 14.5 The completion of metric and normed spaces; 14.6 The contraction mapping theorem; 14.7 *Baire's category theorem*; 15 Compactness; 15.1 Compact topological spaces; 15.2 Sequentially compact topological spaces; 15.3 Totally bounded metric spaces. | |
| 505 | 8 | |a 15.4 Compact metric spaces15.5 Compact subsets of C(K); 15.6 *The Hausdorff metric*; 15.7 Locally compact topological spaces; 15.8 Local uniform convergence; 15.9 Finite-dimensional normed spaces; 16 Connectedness; 16.1 Connectedness; 16.2 Paths and tracks; 16.3 Path-connectedness; 16.4 *Hilbert's path*; 16.5 *More space-filling paths*; 16.6 Rectifiable paths; Part IV Functions of a vector variable; 17 Differentiating functions of a vector variable; 17.1 Differentiating functions of a vector variable; 17.2 The mean-value inequality; 17.3 Partial and directional derivatives. | |
| 505 | 8 | |a 17.4 The inverse mapping theorem17.5 The implicit function theorem; 17.6 Higher derivatives; 18 Integrating functions of several variables; 18.1 Elementary vector-valued integrals; 18.2 Integrating functions of several variables; 18.3 Integrating vector-valued functions; 18.4 Repeated integration; 18.5 Jordan content; 18.6 Linear change of variables; 18.7 Integrating functions on Euclidean space; 18.8 Change of variables; 18.9 Differentiation under the integral sign; 19 Differential manifolds in Euclidean space; 19.1 Differential manifolds in Euclidean space; 19.2 Tangent vectors. | |
| 505 | 8 | |a 19.3 One-dimensional differential manifolds19.4 Lagrange multipliers; 19.5 Smooth partitions of unity; 19.6 Integration over hypersurfaces; 19.7 The divergence theorem; 19.8 Harmonic functions; 19.9 Curl; B Linear algebra; B.1 Finite-dimensional vector spaces; B.2 Linear mappings and matrices; B.3 Determinants; B.4 Cramer's rule; B.5 The trace; C Exterior algebras and the cross product; C.1 Exterior algebras; C.2 The cross product; D Tychonoff's theorem; Index; Contents for Volume I; Contents for Volume III. | |
| 520 | |a The second volume of three providing a full and detailed account of undergraduate mathematical analysis. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Mathematical analysis. | |
| 650 | 6 | |a Analyse mathématique. | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a Mathematical analysis. |2 fast |0 (OCoLC)fst01012068 | |
| 776 | 0 | 8 | |i Print version: |a Garling, D.J.H. |t Course in Mathematical Analysis. |d Cambridge : Cambridge University Press, 2013 |z 9781107345805 |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=545672 |z Texto completo |
| 938 | |a Askews and Holts Library Services |b ASKH |n AH26050201 | ||
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL1139728 | ||
| 938 | |a EBSCOhost |b EBSC |n 545672 | ||
| 994 | |a 92 |b IZTAP | ||