Linear integral equations: theory and technique
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2013
|
| Ausgabe: | 2. ed., [Nachdr.] |
| Schriftenreihe: | Modern Birkhäuser classics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Nachdruck der 1997 bei Birkhäuser erschienenen Ausgabe |
| Beschreibung: | XII, 318 S. graph. Darst. |
| ISBN: | 9781461460114 9781461460121 |
Internformat
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 |b theory and technique |c Ram P. Kanwal |
| 250 | |a 2. ed., [Nachdr.] | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 2013 | |
| 300 | |a XII, 318 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Modern Birkhäuser classics | |
| 500 | |a Nachdruck der 1997 bei Birkhäuser erschienenen Ausgabe | ||
| 650 | 7 | |a Integraalvergelijkingen |2 gtt | |
| 650 | 7 | |a Lineaire vergelijkingen |2 gtt | |
| 650 | 4 | |a Équations intégrales | |
| 650 | 4 | |a Integral equations | |
| 650 | 0 | 7 | |a Integralgleichung |0 (DE-588)4027229-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Lineare Integralgleichung |0 (DE-588)4114426-0 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-026163162 | ||
Datensatz im Suchindex
| _version_ | 1804150607734374400 |
|---|---|
| adam_text | CONTENTS
Preface
.......................... xiii
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
Vblterra
Integral
Equation
............. 34
3.4
Examples
.................... 34
3.5
Some Results about
lhe
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
FredhoJm s Third Theorem
............. 57
Exercises
.................... 60
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 xi
Chapters.
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 Hubert 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 Convolulion-Type Kernels
........... 222
9.5
Examples
.................... 224
9.6
Hubert 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
xii Contents
11.3
Low-Reynolds-Number Hydrodynamics
....... 278
1 1.4
Elasticity
................... 291
11.5
Theory of Scattenng
............... 299
Exercises
................... 303
Appendix
......................... 306
Bibliography
........................ 311
Index
....................... 314
|
| any_adam_object | 1 |
| author | Kanwal, Ram P. 1924-2006 |
| author_GND | (DE-588)1055774505 |
| author_facet | Kanwal, Ram P. 1924-2006 |
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| bvnumber | BV041188023 |
| classification_rvk | SK 640 |
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| discipline | Mathematik |
| edition | 2. ed., [Nachdr.] |
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| id | DE-604.BV041188023 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:41:37Z |
| institution | BVB |
| isbn | 9781461460114 9781461460121 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026163162 |
| oclc_num | 856863594 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-29T DE-20 DE-188 |
| owner_facet | DE-355 DE-BY-UBR DE-29T DE-20 DE-188 |
| physical | XII, 318 S. graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
| record_format | marc |
| series2 | Modern Birkhäuser classics |
| spelling | Kanwal, Ram P. 1924-2006 Verfasser (DE-588)1055774505 aut Linear integral equations theory and technique Ram P. Kanwal 2. ed., [Nachdr.] New York [u.a.] Springer 2013 XII, 318 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Modern Birkhäuser classics Nachdruck der 1997 bei Birkhäuser erschienenen Ausgabe Integraalvergelijkingen gtt Lineaire vergelijkingen gtt Équations intégrales 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 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026163162&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kanwal, Ram P. 1924-2006 Linear integral equations theory and technique Integraalvergelijkingen gtt Lineaire vergelijkingen gtt Équations intégrales 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 theory and technique |
| title_auth | Linear integral equations theory and technique |
| title_exact_search | Linear integral equations theory and technique |
| title_full | Linear integral equations theory and technique Ram P. Kanwal |
| title_fullStr | Linear integral equations theory and technique Ram P. Kanwal |
| title_full_unstemmed | Linear integral equations theory and technique Ram P. Kanwal |
| title_short | Linear integral equations |
| title_sort | linear integral equations theory and technique |
| title_sub | theory and technique |
| topic | Integraalvergelijkingen gtt Lineaire vergelijkingen gtt Équations intégrales Integral equations Integralgleichung (DE-588)4027229-1 gnd Lineare Integralgleichung (DE-588)4114426-0 gnd |
| topic_facet | Integraalvergelijkingen Lineaire vergelijkingen Équations intégrales Integral equations Integralgleichung Lineare Integralgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026163162&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kanwalramp linearintegralequationstheoryandtechnique |