Analysis for applied mathematics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2001
|
| Series: | Graduate texts in mathematics
208 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 429 - 436 |
| Physical Description: | VIII, 444 S. graph. Darst. |
| ISBN: | 0387952799 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Preface v
Chapter 1. Normed Linear Spaces 1
1.1 Definitions and Examples 1
1.2 Convexity, Convergence, Compactness, Completeness 6
1.3 Continuity, Open Sets, Closed Sets 15
1.4 More About Compactness 19
1.5 Linear Transformations 24
1.6 Zorn s Lemma, Hamel Bases, and the Hahn Banach Theorem 30
1.7 The Baire Theorem and Uniform Boundedness 40
1.8 The Interior Mapping and Closed Mapping Theorems 47
1.9 Weak Convergence 53
1.10 Reflexive Spaces 58
Chapter 2. Hilbert Spaces 61
2.1 Geometry 61
2.2 Orthogonality and Bases 70
2.3 Linear Functional and Operators 81
2.4 Spectral Theory 91
2.5 Sturm Liouville Theory 105
Chapter 3. Calculus in Banach Spaces 115
3.1 The Frechet Derivative 115
3.2 The Chain Rule and Mean Value Theorems 121
3.3 Newton s Method 125
3.4 Implicit Function Theorems 135
3.5 Extremum Problems and Lagrange Multipliers 145
3.6 The Calculus of Variations 152
Chapter 4. Basic Approximate Methods of Analysis 170
4.1 Discretization 170
4.2 The Method of Iteration 176
4.3 Methods Based on the Neumann Series 186
4.4 Projections and Projection Methods 191
4.5 The Galerkin Method 198
4.6 The Rayleigh Ritz Method 205
4.7 Collocation Methods 213
4.8 Descent Methods 226
4.9 Conjugate Direction Methods 232
4.10 Methods Based on Homotopy and Continuation 237
vii
vjjj Contents
Chapter 5. Distributions 246
5.1 Definitions and Examples 246
5.2 Derivatives of Distributions 253
5.3 Convergence of Distributions 257
5.4 Multiplication of Distributions by Functions 260
5.5 Convolutions 268
5.6 Differential Operators 273
5.7 Distributions with Compact Support 280
Chapter 6. The Fourier Transform 287
6.1 Definitions and Basic Properties 287
6.2 The Schwartz Space 294
6.3 The Inversion Theorems 301
6.4 The Plancherel Theorem 305
6.5 Applications of the Fourier Transform 310
6.6 Applications to Partial Differential Equations 318
6.7 Tempered Distributions 321
6.8 Sobolev Spaces 325
Chapter 7. Additional Topics 333
7.1 Fixed Point Theorems 333
7.2 Selection Theorems 339
7.3 Separation Theorems 342
7.4 The Arzela Ascoli Theorems 347
7.5 Compact Operators and the Fredholm Theory 351
7.6 Topological Spaces 361
7.7 Linear Topological Spaces 367
7.8 Analytic Pitfalls 373
Chapter 8. Measure and Integration 381
8.1 Extended Reals, Outer Measures, Measurable Spaces 381
8.2 Measures and Measure Spaces 386
8.3 Lebesgue Measure 391
8.4 Measurable Functions 394
8.5 The Integral for Nonnegative Functions 399
8.6 The Integral, Continued 404
8.7 The // Spaces 409
8.8 The Radon Nikodym Theorem 413
8.9 Signed Measures 417
8.10 Product Measures and Fubini s Theorem 420
References 429
Index 437
Symbols 443
|
| any_adam_object | 1 |
| author | Cheney, Elliott W. 1929- |
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| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:54:21Z |
| institution | BVB |
| isbn | 0387952799 |
| language | English |
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| physical | VIII, 444 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Cheney, Elliott W. 1929- Verfasser (DE-588)122199545 aut Analysis for applied mathematics Ward Cheney New York [u.a.] Springer 2001 VIII, 444 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 208 Literaturverz. S. 429 - 436 ANÁLISE MATEMÁTICA (FUNÇÕES ESPECIAIS) larpcal Analyse (wiskunde) gtt Analyse mathématique Toepassingen gtt Mathematical analysis Analysis (DE-588)4001865-9 gnd rswk-swf Analysis (DE-588)4001865-9 s DE-604 Graduate texts in mathematics 208 (DE-604)BV000000067 208 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009521759&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cheney, Elliott W. 1929- Analysis for applied mathematics Graduate texts in mathematics ANÁLISE MATEMÁTICA (FUNÇÕES ESPECIAIS) larpcal Analyse (wiskunde) gtt Analyse mathématique Toepassingen gtt Mathematical analysis Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4001865-9 |
| title | Analysis for applied mathematics |
| title_auth | Analysis for applied mathematics |
| title_exact_search | Analysis for applied mathematics |
| title_full | Analysis for applied mathematics Ward Cheney |
| title_fullStr | Analysis for applied mathematics Ward Cheney |
| title_full_unstemmed | Analysis for applied mathematics Ward Cheney |
| title_short | Analysis for applied mathematics |
| title_sort | analysis for applied mathematics |
| topic | ANÁLISE MATEMÁTICA (FUNÇÕES ESPECIAIS) larpcal Analyse (wiskunde) gtt Analyse mathématique Toepassingen gtt Mathematical analysis Analysis (DE-588)4001865-9 gnd |
| topic_facet | ANÁLISE MATEMÁTICA (FUNÇÕES ESPECIAIS) Analyse (wiskunde) Analyse mathématique Toepassingen Mathematical analysis Analysis |
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