A course in advanced calculus:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | Undetermined |
| Veröffentlicht: |
New York [u.a.]
North Holland
1983
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 388 S. graph. Darst. |
| ISBN: | 0444006389 |
Internformat
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| 100 | 1 | |a Borden, Robert S. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a A course in advanced calculus |c Robert S. Borden |
| 264 | 1 | |a New York [u.a.] |b North Holland |c 1983 | |
| 300 | |a XII, 388 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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Datensatz im Suchindex
| _version_ | 1804117794182135808 |
|---|---|
| adam_text | CONTENTS
Preface xi
CHAPTER 1 SETS AND STRUCTURES 1
1.1 Sets 1
1.2 Algebraic Structures 12
1.3 Morphisms 16
1.4 Order Structures 18
Problems 24
CHAPTER 2 LIMIT AND CONTINUITY IN En 30
2.1 Limit of a Function 30
2.2 Sequences in E 34
2.3 Limit Superior and Limit Inferior of a Function 39
Problems 41
CHAPTER 3 INEQUALITIES 48
3.1 Some Basic Inequalities 48
Problems 55
CHAPTER 4 LINEAR SPACES 58
4.1 Linear and Affine Mappings 58
4.2 Continuity of Linear Maps 64
4.3 Determinants 67
4.4 The Grassmann Algebra 72
Problems 74
CHAPTER 5 FORMS IN En 78
5.1 Orientation of Parallelotopes 78
5.2 1 Forms in E 84
viii CONTENTS
5.3 Some Applications of 1 Forms 87
5.4 O Forms in E 90
5.5 2 Formsin£ 93
5.6 An Application in £3 96
5.7 A Substantial Example 99
5.8 k Fortas in E 102
5.9 Another Example 104
Problems 107
CHAPTER 6 TOPOLOGY 112
6.1 The Open Set Topology 113
6.2 Continuity and Limit 118
6.3 Metrics and Norms 122
6.4 Product Topologies 125
6.5 Compactness 126
6.6 Dense Sets, Connected Sets, Separability, and Category 136
6.7 Some Properties of Continuous Maps 140
6.8 Normal Spaces and the Tietze Extension Theorem 143
6.9 The Cantor Ternary Set 146
Problems 149
CHAPTER 7 INNER PRODUCT SPACES 155
7.1 Real Inner Products 155
7.2 Orthogonality and Orthonormal Sets 157
7.3 An Example: The Space L2(0,2m) 167
7.4 Fourier Series and Convergence 172
7.5 The Gram Schmidt Process 173
7.6 Approximation by Projection 176
7.7 Complex Inner Product Spaces 179
7.8 The Gram Determinant and Measures of /c Parallelotopes 181
7.9 Vector Products in £3 186
Problems 188
CHAPTER 8 MEASURE AND INTEGRATION 197
8.1 Measure 199
8.2 Measure Spaces and a Darboux Integral 208
8.3 The Measure Space (£ ,91t,/i) and Lebesgue Measure 211
8.4 The Lebesgue Integral in E 212
8.5 Signed Measures 216
8.6 AffineMapson(£ ,c)Tl,fi) 218
8.7 Integration by Pullbacks; the Affine Case 221
8.8 A Nonmeasurable Set in £ 223
8.9 The Riemann Stieltjes Integral in £ 224
8.10 Fubini s Theorem 235
8.11 Approximate Continuity 239
Problems 242
CONTENTS ix
CHAPTER 9 DIFFERENTIABLE MAPPINGS 249
9.1 The Derivative of a Map 249
9.2 Taylor s Formula 258
9.3 The Inverse Function Theorem 262
9.4 The Implicit Function Theorem 268
9.5 Lagrange Multipliers 276
9.6 Some Particular Parametric Maps 278
9.7 A Fixed Point Theorem 284
Problems 287
CHAPTER 10 SEQUENCES AND SERIES 295
10.1 Convergence of Sequences of Functions 295
10.2 Series of Functions and Convergence 300
10.3 Power Series 310
10.4 Arithmetic with Series 315
10.5 Infinite Products 318
Problems 320
CHAPTER 11 APPLICATIONS OF IMPROPER INTEGRALS 327
11.1 Improper Integrals 328
11.2 Some Further Convergence Theorems 331
11.3 Some Special Functions 335
11.4 Dirac Sequences and Convolutions 339
11.5 The Fourier Transform 344
11.6 The Laplace Transform 353
11.7 Generalized Functions 358
Problems 359
CHAPTER 12 THE GENERALIZED STOKES THEOREM 368
12.1 Manifolds and Partitions of Unity 368
12.2 The Stokes Theorem 370
Problems 375
Bibliography 381
Index 383
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T16:00:04Z |
| institution | BVB |
| isbn | 0444006389 |
| language | Undetermined |
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| spelling | Borden, Robert S. Verfasser aut A course in advanced calculus Robert S. Borden New York [u.a.] North Holland 1983 XII, 388 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Infinitesimalrechnung (DE-588)4072798-1 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Infinitesimalrechnung (DE-588)4072798-1 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002182042&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Borden, Robert S. A course in advanced calculus Infinitesimalrechnung (DE-588)4072798-1 gnd |
| subject_GND | (DE-588)4072798-1 (DE-588)4123623-3 |
| title | A course in advanced calculus |
| title_auth | A course in advanced calculus |
| title_exact_search | A course in advanced calculus |
| title_full | A course in advanced calculus Robert S. Borden |
| title_fullStr | A course in advanced calculus Robert S. Borden |
| title_full_unstemmed | A course in advanced calculus Robert S. Borden |
| title_short | A course in advanced calculus |
| title_sort | a course in advanced calculus |
| topic | Infinitesimalrechnung (DE-588)4072798-1 gnd |
| topic_facet | Infinitesimalrechnung Lehrbuch |
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