Functions of several variables:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Springer
1977
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Undergraduate texts in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 411 S. Ill. u. graph. Darst. |
| ISBN: | 0387902066 3540902066 |
Internformat
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| 245 | 1 | 0 | |a Functions of several variables |c Wendell Fleming |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York |b Springer |c 1977 | |
| 300 | |a XI, 411 S. |b Ill. u. graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Undergraduate texts in mathematics | |
| 650 | 4 | |a Cálculo diferencial | |
| 650 | 4 | |a Cálculo integral | |
| 650 | 4 | |a Funciones | |
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| 650 | 0 | 7 | |a Funktion |0 (DE-588)4195664-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mehrere Variable |0 (DE-588)4277015-4 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804116419483271168 |
|---|---|
| adam_text | Contents
Chapter 1
Euclidean spaces 1
1.1 The real number system 2
1.2 Euclidean E 5
1.3 Elementary geometry of E 10
1.4 Basic topological notions in E 14
*1.5 Convex sets 19
Chapter 2
Elementary topology of E 28
2.1 Functions 28
2.2 Limits and continuity of transformations 31
2.3 Sequences in E 37
2.4 Bolzano Weierstrass theorem 43
2.5 Relative neighborhoods, continuous transformations 47
2.6 Topological spaces 50
2.7 Connectedness 56
2.8 Compactness 60
2.9 Metric spaces 62
2.10 Spaces of continuous functions 67
*2.11 Noneuclidean norms on E 70
Chapter 3
Differentiation of real valued functions 76
3.1 Directional and partial derivatives 76
3.2 Linear functions 79
ix
Contents
3.3 Differentiable functions 82
3.4 Functions of class C 1 89
3.5 Relative extrema 99
*3.6 Convex and concave functions 107
Chapter 4
Vector valued functions of several variables 119
4.1 Linear transformations 119
4.2 Affine transformations 125
4.3 Differentiable transformations 128
4.4 Composition 134
4.5 The inverse function theorem 140
4.6 The implicit function theorem 147
4.7 Manifolds 153
4.8 The multiplier rule 161
Chapter 5
Integration 167
5.1 Intervals 168
5.2 Measure 170
5.3 Integrals over E 181
5.4 Integrals over bounded sets 186
5.5 Iterated integrals 190
5.6 Integrals of continuous functions 200
5.7 Change of measure under affine transformations 206
5.8 Transformation of integrals 209
5.9 Coordinate systems in E 216
5.10 Measurable sets and functions; further properties 222
5.11 Integrals: general definition, convergence theorems 227
5.12 Differentiation under the integral sign 237
5.13 // spaces 240
Chapter 6
Curves and line integrals 245
6.1 Derivatives 245
6.2 Curves in E 247
6.3 Differential 1 forms 253
6.4 Line integrals 258
*6.5 Gradient method 265
*6.6 Integrating factors; thermal systems 268
Chapter 7
Exterior algebra and differential calculus 275
7.1 Covectors and differential forms of degree 2 276
7.2 Alternating multilinear functions 283
x
Contents
7.3 Multicovectors 287
7.4 Differential forms 291
7.5 Multivectors 295
7.6 Induced linear transformations 306
7.7 Transformation law for differential forms 309
7.8 The adjoint and codifferential 311
*7.9 Special results for n = 3 316
*7.10 Integrating factors (continued) 318
Chapter 8
Integration on manifolds 321
8.1 Regular transformations 322
8.2 Coordinate systems on manifolds 329
8.3 Measure and integration on manifolds 334
8.4 The divergence theorem 340
*8.5 Fluid flow 350
8.6 Orientations 353
8.7 Integrals of r forms 356
8.8 Stokes s formula 362
8.9 Regular transformations on submanifolds 367
8.10 Closed and exact differential forms 369
8.11 Motion of a particle 375
8.12 Motion of several particles 380
Appendix 1
Axioms for a vector space 383
Appendix 2
Mean value theorem; Taylor s theorem 385
Appendix 3
Review of Riemann integration 386
Appendix 4
Monotone functions 388
References 389
Answers to problems 391
Index 405
xi
|
| any_adam_object | 1 |
| author | Fleming, Wendell Helms 1928- |
| author_GND | (DE-588)115373217 |
| author_facet | Fleming, Wendell Helms 1928- |
| author_role | aut |
| author_sort | Fleming, Wendell Helms 1928- |
| author_variant | w h f wh whf |
| building | Verbundindex |
| bvnumber | BV001975100 |
| classification_rvk | SK 400 SK 780 |
| classification_tum | MAT 263f |
| ctrlnum | (OCoLC)318330910 (DE-599)BVBBV001975100 |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV001975100 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:38:13Z |
| institution | BVB |
| isbn | 0387902066 3540902066 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001288227 |
| oclc_num | 318330910 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-384 DE-703 DE-355 DE-BY-UBR DE-20 DE-824 DE-19 DE-BY-UBM DE-29T DE-706 DE-634 DE-83 DE-188 |
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| physical | XI, 411 S. Ill. u. graph. Darst. |
| psigel | TUB-nveb |
| publishDate | 1977 |
| publishDateSearch | 1977 |
| publishDateSort | 1977 |
| publisher | Springer |
| record_format | marc |
| series2 | Undergraduate texts in mathematics |
| spelling | Fleming, Wendell Helms 1928- Verfasser (DE-588)115373217 aut Functions of several variables Wendell Fleming 2. ed. New York Springer 1977 XI, 411 S. Ill. u. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Cálculo diferencial Cálculo integral Funciones Reelle Funktion (DE-588)4048918-8 gnd rswk-swf Infinitesimalrechnung (DE-588)4072798-1 gnd rswk-swf Funktion Mathematik (DE-588)4071510-3 gnd rswk-swf Funktion (DE-588)4195664-3 gnd rswk-swf Mehrere Variable (DE-588)4277015-4 gnd rswk-swf Mehrere reelle Variable (DE-588)4202599-0 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Infinitesimalrechnung (DE-588)4072798-1 s Mehrere Variable (DE-588)4277015-4 s DE-604 Funktion Mathematik (DE-588)4071510-3 s Analysis (DE-588)4001865-9 s Funktion (DE-588)4195664-3 s 1\p DE-604 Reelle Funktion (DE-588)4048918-8 s 2\p DE-604 Mehrere reelle Variable (DE-588)4202599-0 s 3\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001288227&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Fleming, Wendell Helms 1928- Functions of several variables Cálculo diferencial Cálculo integral Funciones Reelle Funktion (DE-588)4048918-8 gnd Infinitesimalrechnung (DE-588)4072798-1 gnd Funktion Mathematik (DE-588)4071510-3 gnd Funktion (DE-588)4195664-3 gnd Mehrere Variable (DE-588)4277015-4 gnd Mehrere reelle Variable (DE-588)4202599-0 gnd Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4048918-8 (DE-588)4072798-1 (DE-588)4071510-3 (DE-588)4195664-3 (DE-588)4277015-4 (DE-588)4202599-0 (DE-588)4001865-9 |
| title | Functions of several variables |
| title_auth | Functions of several variables |
| title_exact_search | Functions of several variables |
| title_full | Functions of several variables Wendell Fleming |
| title_fullStr | Functions of several variables Wendell Fleming |
| title_full_unstemmed | Functions of several variables Wendell Fleming |
| title_short | Functions of several variables |
| title_sort | functions of several variables |
| topic | Cálculo diferencial Cálculo integral Funciones Reelle Funktion (DE-588)4048918-8 gnd Infinitesimalrechnung (DE-588)4072798-1 gnd Funktion Mathematik (DE-588)4071510-3 gnd Funktion (DE-588)4195664-3 gnd Mehrere Variable (DE-588)4277015-4 gnd Mehrere reelle Variable (DE-588)4202599-0 gnd Analysis (DE-588)4001865-9 gnd |
| topic_facet | Cálculo diferencial Cálculo integral Funciones Reelle Funktion Infinitesimalrechnung Funktion Mathematik Funktion Mehrere Variable Mehrere reelle Variable Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001288227&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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