Differential calculus and its applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Van Nostrand
1976
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| Schriftenreihe: | The new university mathematics series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 315 S. graph. Darst. |
| ISBN: | 0442301391 |
Internformat
MARC
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| 100 | 1 | |a Field, Michael J. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Differential calculus and its applications |c Michael J. Field |
| 264 | 1 | |a New York [u.a.] |b Van Nostrand |c 1976 | |
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Datensatz im Suchindex
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| adam_text | Titel: Differential calculus and its applications
Autor: Field, Mike
Jahr: 1976
Contents Preface vii CHAPTER 0 PRELIMINARIES 0.1 Vector spaces and linear maps 1 0.2 Topological and metric spaces 6 CHAPTER 1 LINEAR ALGEBRA AND NORMED VECTOR SPACES 1.1 Normed Vector Spaces 10 1.2 Inner-product Spaces 14 1.3 Topology on Normed Vector Spaces 20 1.4 Products of Normed Vector Spaces 21 1.5 Linear and Multilinear Maps 23 1.6 Normed Spaces of Continuous Linear and Multilinear Maps 28 1.7 Some Special Spaces of Linear and Multilinear Maps 34 1.8 Equivalence of Norms 42 1.9 Complete Normed Spaces 44 1.10 Equivalence of Norms on Finite-dimensional Vector Spaces 51 1.11 Completion of a Normed Vector Space 55 1.12 Hilbert Spaces 58 1.13 Bases 65 1.14 Transpose and Adjoint of Linear Maps 73 1.15 Eigenvalues 76 1.16 Self-adjoint Maps and Quadratic Forms 80 1.17 Isometries 94 1.18 The Hahn-Banach Theorem 101 Appendix: Proof of the Hahn-Banach Theorem 105 CHAPTER 2 DIFFERENTIATION AND CALCULUS ON VECTOR SPACES 2.1 Introduction 108 2.2 o-notation 110 2.3 Differentiation of Functions on Normed Vector Spaces 111 2.4 The Composite-mapping Formula 115 2.5 Differentiable Maps into Products of Normed Vector Spaces 119 2.6 Differentiable Maps from Products and Partial Derivatives 125 2.7 The Mean-value Theorem 140
vi CONTENTS 2.8 Differentiation and Partial Differentiation 143 2.9 Higher Derivatives 151 2.10 Leibniz’Theorem and the General Composite-mapping Formula 161 2.11 Taylor’s theorem 165 2.12 Extrema 169 2.13 Curves in R 176 CHAPTER 3 THE INVERSE- AND IMPLICIT-FUNCTION THEOREMS 3.1 Topological Linear Isomorphisms 188 3.2 The Inverse-function Theorem 194 3.3 The Implicit-function Theorem 201 3.4 Change of Variables 216 CHAPTER 4 DIFFERENTIAL MANIFOLDS 4.1 Introduction 225 4.2 Charts and Atlases 226 4.3 Equivalent Atlases 236 4.4 Products of Differential Manifolds 239 4.5 Quotients of Differential Manifolds 241 4.6 Submanifolds 248 4.7 Submanifolds of R m 253 4.8 Differentiable Maps: Critical Points 262 4.9 Tangent Spaces 271 4.10 The Tangent Bundle of a Submanifold 287 4.11 Differential Equations on Manifolds 293 BIBLIOGRAPHY 308 INDEX 310
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| dewey-sort | 3515 233 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T15:38:03Z |
| institution | BVB |
| isbn | 0442301391 |
| language | English |
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| physical | VIII, 315 S. graph. Darst. |
| publishDate | 1976 |
| publishDateSearch | 1976 |
| publishDateSort | 1976 |
| publisher | Van Nostrand |
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| series2 | The new university mathematics series |
| spelling | Field, Michael J. Verfasser aut Differential calculus and its applications Michael J. Field New York [u.a.] Van Nostrand 1976 VIII, 315 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier The new university mathematics series Differentiaalrekening gtt Toepassingen gtt Differential calculus Differentialrechnung (DE-588)4012252-9 gnd rswk-swf Globale Analysis (DE-588)4021285-3 gnd rswk-swf Differentialrechnung (DE-588)4012252-9 s Globale Analysis (DE-588)4021285-3 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001282267&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Field, Michael J. Differential calculus and its applications Differentiaalrekening gtt Toepassingen gtt Differential calculus Differentialrechnung (DE-588)4012252-9 gnd Globale Analysis (DE-588)4021285-3 gnd |
| subject_GND | (DE-588)4012252-9 (DE-588)4021285-3 |
| title | Differential calculus and its applications |
| title_auth | Differential calculus and its applications |
| title_exact_search | Differential calculus and its applications |
| title_full | Differential calculus and its applications Michael J. Field |
| title_fullStr | Differential calculus and its applications Michael J. Field |
| title_full_unstemmed | Differential calculus and its applications Michael J. Field |
| title_short | Differential calculus and its applications |
| title_sort | differential calculus and its applications |
| topic | Differentiaalrekening gtt Toepassingen gtt Differential calculus Differentialrechnung (DE-588)4012252-9 gnd Globale Analysis (DE-588)4021285-3 gnd |
| topic_facet | Differentiaalrekening Toepassingen Differential calculus Differentialrechnung Globale Analysis |
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