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.
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge :
Cambridge University Press,
2013.
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| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | The second volume of three providing a full and detailed account of undergraduate mathematical analysis. |
| Beschreibung: | 1 online resource (336 pages) |
| ISBN: | 9781107342057 1107342058 9781107345805 1107345804 9781107352926 1107352924 9781107032033 1107032032 9781139424509 1139424505 |
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| 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) | ||
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| 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. |0 http://id.loc.gov/authorities/subjects/sh85082116 | |
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| 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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| adam_text | |
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| author | Garling, D. J. H. |
| author_GND | http://id.loc.gov/authorities/names/n85306701 |
| author_facet | Garling, D. J. H. |
| author_role | |
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| building | Verbundindex |
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| callnumber-first | Q - Science |
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| callnumber-raw | QA300 .B68 2013 |
| callnumber-search | QA300 .B68 2013 |
| callnumber-sort | QA 3300 B68 42013 |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | 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. 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. 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. 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. 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. |
| ctrlnum | (OCoLC)869640256 |
| dewey-full | 515 |
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| dewey-ones | 515 - Analysis |
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| dewey-search | 515 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| indexdate | 2024-11-27T13:25:46Z |
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| spelling | Garling, D. J. H. http://id.loc.gov/authorities/names/n85306701 A Course in Mathematical Analysis. Volume 2 : Metric and Topological Spaces, Functions of a Vector Variable / D.J.H. Garling. Cambridge : Cambridge University Press, 2013. 1 online resource (336 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Print version record. 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. 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. 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. 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. 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. The second volume of three providing a full and detailed account of undergraduate mathematical analysis. Mathematical analysis. http://id.loc.gov/authorities/subjects/sh85082116 Analyse mathématique. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Mathematical analysis fast Print version: Garling, D.J.H. Course in Mathematical Analysis. Cambridge : Cambridge University Press, 2013 9781107345805 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=545672 Volltext |
| spellingShingle | Garling, D. J. H. A Course in Mathematical Analysis. 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. 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. 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. 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. 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. Mathematical analysis. http://id.loc.gov/authorities/subjects/sh85082116 Analyse mathématique. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Mathematical analysis fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85082116 |
| title | A Course in Mathematical Analysis. |
| title_auth | A Course in Mathematical Analysis. |
| title_exact_search | A Course in Mathematical Analysis. |
| title_full | A Course in Mathematical Analysis. Volume 2 : Metric and Topological Spaces, Functions of a Vector Variable / D.J.H. Garling. |
| title_fullStr | A Course in Mathematical Analysis. Volume 2 : Metric and Topological Spaces, Functions of a Vector Variable / D.J.H. Garling. |
| title_full_unstemmed | A Course in Mathematical Analysis. Volume 2 : Metric and Topological Spaces, Functions of a Vector Variable / D.J.H. Garling. |
| title_short | A Course in Mathematical Analysis. |
| title_sort | course in mathematical analysis metric and topological spaces functions of a vector variable |
| topic | Mathematical analysis. http://id.loc.gov/authorities/subjects/sh85082116 Analyse mathématique. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Mathematical analysis fast |
| topic_facet | Mathematical analysis. Analyse mathématique. MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. Mathematical analysis |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=545672 |
| work_keys_str_mv | AT garlingdjh acourseinmathematicalanalysisvolume2 AT garlingdjh courseinmathematicalanalysisvolume2 |