Linear methods of applied analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Reading, Mass. u.a.
Addison-Wesley
1973
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 706 S. |
| ISBN: | 0201039028 0201039036 |
Staff View
MARC
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| 100 | 1 | |a Krall, Allan M. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Linear methods of applied analysis |
| 264 | 1 | |a Reading, Mass. u.a. |b Addison-Wesley |c 1973 | |
| 300 | |a XIV, 706 S. | ||
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| 650 | 4 | |a Analyse mathématique | |
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| 650 | 4 | |a Differential equations | |
| 650 | 4 | |a Mathematical analysis | |
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Record in the Search Index
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| adam_text | Table of Contents
Introduction xi
I. Some Inequalities 1
1. Young s Inequality 1
2. Holder s Inequality 4
3. Minkowski s Inequality 6
4. A Relation between Different Norms 8
5. An Abstract Integral 11
II. Linear Spaces and Linear Operators 17
1. Linear Spaces 17
2. Linear Operators 24
3. Norms and Banach Spaces 32
4. Operator Convergence 38
III. Existence and Uniqueness Theorems 48
1. The Contraction Mapping Theorem 48
2. Existence and Uniqueness of Solutions for
Ordinary Differential Equations 60
3. First Order Linear Systems 70
4. n th Order Differential Equations 76
5. Some Extensions 82
IV. Linear Ordinary Differential Equations 88
1. First Order Linear Systems 88
2. Fundamental Matrices 90
3. Nonhomogeneous Systems 96
4. n th Order Equations 98
5. Nonhomogeneous n th Order Equations 102
6. Reduction of Order 106
7. Constant Coefficients 110
V. Second Order Ordinary Differential Equations 126
1. A Brief Review ^26
2. The Adjoint Operator 128
3. An Oscillation Theorem 133
4. The Regular Sturm Liouville Problem 136
5. The Inverse Problem, Green s Functions 138
VI. The Stone Weierstrass Theorem 151
1. Preliminary Remarks 151
2. Algebras and Subalgebras 154
3. The Stone Weierstrass Theorem 156
4. Extensions and Special Cases 160
viii
VII. Hilbert Spaces 165
1. Hermitian Forms 165
2. Inner Product Spaces 170
3. Hilbert Spaces 174
4. Orthogonal Subspaces 181
5. Continuous Linear Functionals 189
6. Fourier Expansions 191
7. Isometric Hilbert Spaces 198
VIII. Linear Operators on a Hilbert Space 204
1. Regular Operators on a Hilbert Space 204
2. Bilinear Forms, the Adjoint Operator 208
3. Self Adjoint Operators 215
4. Projections 223
5. Some Spectral Theorems 228
6. Operator Convergence 238
7. The Spectral Resolution of a Self Adjoint Operator 250
8. The Spectral Resolution of a Normal Operator 260
9. The Spectral Resolution of a Unitary Operator 264
IX. Compact Operators on a Hilbert Space 276
1. Compact Operators 276
2. Some Special Examples 280
3. The Spectrum of a Compact Self Adjoint Operator 286
4. The Spectral Resolution of a Compact, Self Adjoint Operator 290
5. The Regular Sturm Liouville Problem 295
X. Special Functions 307
1. Orthogonal Polynomials 307
2. The Legendre Polynomials 313
3. The Laguerre Polynomials 318
4. The Hermite Polynomials 322
5. Bessel Functions 327
XI. The Fourier Integral 338
1. The Lebesgue Integral 338
2. The Fourier Integral in L.( »,») 351
3. The Fourier Integral in _(—,») 367
XII. The Singular Sturm Liouville Problem 385
1. Circles under Bilinear Transformations 387
2. Helly s Convergence Theorems 393
3. Limit Points and Limit Circles 398
4. The Limit Point Case 407
5. The Limit Circle Case 432
6. Examples 439
ix
XIII. An Introduction to Partial Differential Equations 453
1. The Cauchy Kowaleski Theorem 453
2. First Order Equations 457
3. Second Order Equations 464
4. Green s Formula 473
XIV. Distributions 482
1. Test Functions and Distributions 482
2. Limits of Distributions 491
3. Fourier Transforms of Distributions 501
4. Applications of Distributions to Ordinary
Differential Equations 507
5. Applications of Distributions to Partial
Differential Equations 519
XV. Laplace s Equation 536
1. Introduction, Well Posed Problems 536
2. Dirichlet, Neumann, and Mixed Boundary Value Problems 542
3. The Dirichlet Problem 546
4. The Dirichlet Problem on the Unit Circle 561
5. Other Examples 570
XVI. The Heat Equation 588
1. Introduction, the Cauchy Problem 588
2. The Cauchy Problem with Dirichlet Boundary Data 592
3. The Solution to the Nonhomogeneous Cauchy Problem 595
4. Examples 599
5. Homogeneous Problems 607
XVII. The Wave Equation 614
1. Introduction, the Cauchy Problem 614
2. Solutions in 1, 2 and 3 Dimensions 625
3. The Solution to the Nonhomogeneous Cauchy Problem 642
4. Examples 648
Appendix I The Spectral Resolution of an Unbounded Self
Adjoint Operator 668
1. Unbounded Linear Operators 669
2. The Graph of an Operator 670
3. Symmetric and Self Adjoint Operators 674
4. The Spectral Resolution of an Unbounded Self
Adjoint Operator 678
X
Appendix II The Derivation of the Heat, Wave, and Laplace Equations 687
1. The Heat Equation 687
2. Boundary Conditions 690
3. The Wave Equation 693
4. Boundary Conditions 696
5. Laplace s Equation 697
Index 699
|
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| ctrlnum | (OCoLC)698794 (DE-599)BVBBV002503019 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.3/5 |
| dewey-search | 515.3/5 |
| dewey-sort | 3515.3 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002503019 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:46:00Z |
| institution | BVB |
| isbn | 0201039028 0201039036 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001612322 |
| oclc_num | 698794 |
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| owner | DE-91G DE-BY-TUM DE-706 |
| owner_facet | DE-91G DE-BY-TUM DE-706 |
| physical | XIV, 706 S. |
| publishDate | 1973 |
| publishDateSearch | 1973 |
| publishDateSort | 1973 |
| publisher | Addison-Wesley |
| record_format | marc |
| spelling | Krall, Allan M. Verfasser aut Linear methods of applied analysis Reading, Mass. u.a. Addison-Wesley 1973 XIV, 706 S. txt rdacontent n rdamedia nc rdacarrier Analyse mathématique Analyse mathématique ram Équations différentielles Differential equations Mathematical analysis HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001612322&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Krall, Allan M. Linear methods of applied analysis Analyse mathématique Analyse mathématique ram Équations différentielles Differential equations Mathematical analysis |
| title | Linear methods of applied analysis |
| title_auth | Linear methods of applied analysis |
| title_exact_search | Linear methods of applied analysis |
| title_full | Linear methods of applied analysis |
| title_fullStr | Linear methods of applied analysis |
| title_full_unstemmed | Linear methods of applied analysis |
| title_short | Linear methods of applied analysis |
| title_sort | linear methods of applied analysis |
| topic | Analyse mathématique Analyse mathématique ram Équations différentielles Differential equations Mathematical analysis |
| topic_facet | Analyse mathématique Équations différentielles Differential equations Mathematical analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001612322&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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