A Course in Mathematical Analysis.: Volume 2 : Metric and Topological Spaces, Functions of a Vector Variable
(eBook)
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Published:
Cambridge : Cambridge University Press, 2013.
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eBook
ISBN:
9781107342057, 1107342058, 9781107345805, 1107345804, 9781107352926, 1107352924, 9781107032033, 1107032032, 9781139424509, 1139424505
Physical Desc:
1 online resource (336 pages)
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Ebsco (CCU)
Description
The second volume of three providing a full and detailed account of undergraduate mathematical analysis.
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APA Citation (style guide)
Garling, D. J. H. (2013). A Course in Mathematical Analysis. Cambridge, Cambridge University Press.
Chicago / Turabian - Author Date Citation (style guide)Garling, D. J. H. 2013. A Course in Mathematical Analysis. Cambridge, Cambridge University Press.
Chicago / Turabian - Humanities Citation (style guide)Garling, D. J. H, A Course in Mathematical Analysis. Cambridge, Cambridge University Press, 2013.
MLA Citation (style guide)Garling, D. J. H. A Course in Mathematical Analysis. Cambridge, Cambridge University Press, 2013.
Note! Citation formats are based on standards as of July 2022. Citations contain only title, author, edition, publisher, and year published. Citations should be used as a guideline and should be double checked for accuracy.
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Language:
English
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Description
The second volume of three providing a full and detailed account of undergraduate mathematical analysis.
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Grouped Work ID:
22d4b17c-e7ac-c81b-9b07-ff5bd0c9b14b
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Last File Modification Time | Apr 05, 2024 09:35:02 PM |
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Last Grouped Work Modification Time | Apr 05, 2024 09:12:39 PM |
MARC Record
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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. | ||
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 | |
776 | 0 | 8 | |i Print version:|a Garling, D.J.H.|t Course in Mathematical Analysis.|d Cambridge : Cambridge University Press, 2013|z 9781107345805 |
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