Linear integral equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
1997
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 318 S. graph. Darst. |
| ISBN: | 0817639403 3764339403 |
Staff View
MARC
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| 100 | 1 | |a Kanwal, Ram P. |d 1924-2006 |e Verfasser |0 (DE-588)1055774505 |4 aut | |
| 245 | 1 | 0 | |a Linear integral equations |c Ram P. Kanwal |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 1997 | |
| 300 | |a VIII, 318 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Integral equations | |
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Record in the Search Index
| _version_ | 1804125728250265600 |
|---|---|
| adam_text | CONTENTS
Preface ix
Chapter 1. Introduction 1
1.1 Definition 1
1.2 Regularity Conditions 3
1.3 Special Kinds of Kernels 4
1.4 Eigenvalues and Eigenfunctions 4
1.5 Convolution Integral 4
1.6 The Inner or Scalar Product of Two Functions 5
1.7 Notation 6
Chapter 2. Integral Equations with Separable Kernels 7
2.1 Reduction to a System of Algebraic Equations 7
2.2 Examples 8
2.3 Fredholm Alternatives 12
2.4 Examples 18
2.5 An Approximate Method 20
2.6 Fredholm Integral Equation of the First Kind 22
Exercises 23
Chapter 3. Method Of Successive Approximations 25
3.1 Iterative Scheme 25
3.2 Examples 29
3.3 Volterra Integral Equation 34
3.4 Examples 34
3.5 Some Results about the Resolvent Kernel 36
Exercises 39
Chapter 4. Classical Fredholm Theory 41
4.1 The Method of Solution of Fredholm 41
4.2 Fredholm s First Theorem 43
4.3 Examples 49
4.4 Fredholm s Second Theorem 51
4.5 Fredholm s Third Theorem 57
Exercises 60
vi Contents
Chapter 5. Applications to Ordinary Differential Equations 61
5.1 Initial Value Problems 61
5.2 Boundary Value Problems 64
5.3 Examples 66
5.4 Dirac Delta Function 68
5.5 Green s Function Approach 76
5.6 Examples 85
5.7 Green s Function for Nth Order Ordinary Differential Equation 88
5.8 Modified Green s Function 90
Examples 92
Exercises 95
Chapter 6. Applications to Partial Differential Equations 97
6.1 Introduction 97
6.2 Integral Representation Formulas for the Solution
of the Laplace and Poisson Equations 98
6.3 Examples 106
6.4 Green s Function Approach 118
6.5 Examples 123
6.6 The Helmholtz Equation 128
6.7 Examples 130
Exercises 141
Chapter 7. Symmetric Kernels 146
7.1 Introduction 146
7.2 Fundamental Properties of Eigenvalues and
Eigenfunctions for Symmetric Kernels 152
7.3 Expansion in Eigenfunctions and Bilinear Form .... 155
7.4 Hilbert Schmidt Theorem and Some Immediate ....
Consequences 159
7.5 Solution of a Symmetric Integral Equation 167
7.6 Examples 169
7.7 Approximation of a General £2 Kernel (Not
Necessarily Symmetric) by a Separable Kernel 172
7.8 The Operator Method in the Theory of Integral
Equations 173
7.9 Rayleigh Ritz Method for Finding the First Eigenvalue 176
Exercises 179
Contents vii
Chapter 8. Singular Integral Equations 181
8.1 The Abel Integral Equation 181
8.2 Examples 184
8.3 Cauchy Principal Value for Integrals 188
8.4 The Cauchy Type Integrals 192
8.5 The Cauchy Type Integral Equation on the
Real Line 195
8.6 Solution of the Cauchy Type Singular Integral
Equation in a Complex Plane 201
8.7 Singular Integral Equations with Logarithmic
Kernel 204
8.8 The Hilbert Kernel 210
8.9 Solution of the Hilbert Type Singular Integral
Equation 212
8.10 Examples 216
Exercises 216
Chapter 9. Integral Transformation Methods 219
9.1 Introduction 219
9.2 Fourier Transform 220
9.3 Laplace Transform 221
9.4 Applications to Volterra Integral Equations
with Convolution Type Kernels 222
9.5 Examples 224
9.6 Hilbert Transform 229
9.7 Examples 232
Exercises 234
Chapter 10. Applications to Mixed Boundary Value Problems 237
10.1 Two Part Boundary Value Problems 237
10.2 Three Part Boundary Value Problems 240
10.3 Generalized Two Part Boundary Value Problems .... 248
10.4 Generalized Three Part Boundary Value Problems . . . 253
10.5 Further Examples 260
Exercises 270
Chapter 11. Integral Equations Perturbation Methods 272
11.1 Basic Procedure 272
11.2 Applications to Electrostatics 275
viii Contents
11.3 Low Reynolds Number Hydrodynamics 278
11.4 Elasticity 291
11.5 Theory of Scattering 299
Exercises 303
Appendix 306
Bibliography 311
Index 314
|
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| ctrlnum | (OCoLC)35450539 (DE-599)BVBBV011228694 |
| dewey-full | 515/.45 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.45 |
| dewey-search | 515/.45 |
| dewey-sort | 3515 245 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV011228694 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:06:10Z |
| institution | BVB |
| isbn | 0817639403 3764339403 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007534632 |
| oclc_num | 35450539 |
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| owner_facet | DE-91G DE-BY-TUM DE-703 DE-384 DE-29T DE-824 DE-19 DE-BY-UBM DE-634 DE-83 DE-11 DE-188 |
| physical | VIII, 318 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Birkhäuser |
| record_format | marc |
| spelling | Kanwal, Ram P. 1924-2006 Verfasser (DE-588)1055774505 aut Linear integral equations Ram P. Kanwal 2. ed. Boston [u.a.] Birkhäuser 1997 VIII, 318 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Integral equations Integralgleichung (DE-588)4027229-1 gnd rswk-swf Lineare Integralgleichung (DE-588)4114426-0 gnd rswk-swf Lineare Integralgleichung (DE-588)4114426-0 s DE-604 Integralgleichung (DE-588)4027229-1 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007534632&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 |
| spellingShingle | Kanwal, Ram P. 1924-2006 Linear integral equations Integral equations Integralgleichung (DE-588)4027229-1 gnd Lineare Integralgleichung (DE-588)4114426-0 gnd |
| subject_GND | (DE-588)4027229-1 (DE-588)4114426-0 |
| title | Linear integral equations |
| title_auth | Linear integral equations |
| title_exact_search | Linear integral equations |
| title_full | Linear integral equations Ram P. Kanwal |
| title_fullStr | Linear integral equations Ram P. Kanwal |
| title_full_unstemmed | Linear integral equations Ram P. Kanwal |
| title_short | Linear integral equations |
| title_sort | linear integral equations |
| topic | Integral equations Integralgleichung (DE-588)4027229-1 gnd Lineare Integralgleichung (DE-588)4114426-0 gnd |
| topic_facet | Integral equations Integralgleichung Lineare Integralgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007534632&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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