A first course in integral equations:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey [u.a.]
World Scientific
2015
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XIV, 312 S. 24 cm |
| ISBN: | 9789814675116 9814675113 9789814675123 9814675121 |
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MARC
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| 245 | 1 | 0 | |a A first course in integral equations |c Abdul-Majid Wazwaz |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New Jersey [u.a.] |b World Scientific |c 2015 | |
| 300 | |a XIV, 312 S. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
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Record in the Search Index
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| adam_text | Titel: A first course in integral equations
Autor: Wazwaz, Abdul-Majid
Jahr: 2015
Contents
Preface to the Second Edition xi
Preface to the First Edition xiii
1 Introductory Concepts 1
1.1 Definitions........................................................1
1.2 Classification of Linear Integral Equations....................2
1.2.1 Fredholm Linear Integral Equations..................3
1.2.2 Volterra Linear Integral Equations....................4
1.2.3 Integro-Differential Equations..........................6
1.2.4 Singular Integral Equations............................7
1.2.5 Volterra-Fredholm Integral Equations................8
1.2.6 Volterra-Fredholm Integro-Differential Equations . . 8
1.3 Solution of an Integral Equation ..............................12
1.4 Converting Volterra Equation to an ODE....................16
1.4.1 Differentiating Any Integral: Leibniz Rule............17
1.5 Converting IVP to Volterra Equation..........................20
1.6 Converting EVP to Fredholm Equation ......................25
1.7 Taylor Series....................................................28
1.8 Infinite Geometric Series........................................32
2 Fredholm Integral Equations 35
2.1 Introduction......................................................35
2.2 The Adomian Decomposition Method ........................37
2.2.1 The Modified Decomposition Method................41
2.2.2 The Noise Terms Phenomenon........................45
2.3 The Variational Iteration Method..............................49
2.4 The Direct Computation Method..............................54
2.5 The Successive Approximations Method......................60
2.6 The Method of Successive Substitutions......................64
2.7 Comparison between Alternative Methods....................67
2.8 Homogeneous Fredholm Integral Equations..................71
2.9 Fredholm Integral Equations of the First Kind ..............76
2.9.1 The Method of Regularization ........................76
3 Volterra Integral Equations 81
3.1 Introduction......................................................81
3.2 The Adomian Decomposition Method ........................82
3.2.1 The Modified Decomposition Method ................87
3.2.2 The Noise Terms Phenomenon........................89
3.3 The Variational Iteration Method..............................92
3.4 The Series Solution Method....................................96
3.5 Converting Volterra Equation to IVP..........................190
3.6 Successive Approximations Method............................104
3.7 The Method of Successive Substitutions......................109
3.8 Comparison between Alternative Methods....................112
3.9 Volterra Integral Equations of the First Kind................117
3.9.1 The Series Solution Method............................117
3.9.2 Conversion of First Kind to Second Kind ............119
4 Fredholm Integro-Differential Equations 123
4.1 Introduction......................................................123
4.2 Fredholm Integro-Differential Equations......................124
4.3 The Direct Computation Method..............................125
4.4 The Adomian Decomposition Method ........................129
4.4.1 The Modified Decomposition Method ................132
4.4.2 The Noise Terms Phenomenon........................132
4.5 The Variational Iteration Method..............................138
4.6 Converting to Fredholm Integral Equations..................142
5 Volterra Integro-Differential Equations 145
5.1 Introduction......................................................145
5.2 Volterra Integro-Differential Equations........................146
5.3 The Series Solution Method....................................147
5.4 The Adomian Decomposition Method ........................151
5.5 The Variational Iteration Method..............................156
5.6 Converting to Volterra Integral Equation......................159
5.7 Converting to Initial Value Problems..........................162
5.8 Volterra Integro-Differential Equations of the First Kind . . 165
6 Singular Integral Equations 171
6.1 Introduction......................................................171
6.2 Abel s Problem..................................................173
6.3 The Generalized Abel s Integral Equation....................178
6.4 The Weakly-Singular Volterra Integral Equations............181
6.4.1 The Adomian Decomposition Method................182
6.5 The Weakly-Singular Fredholm Integral Equations..........187
6.5.1 The Modified Decomposition Method ................188
7 Nonlinear Fredholm Integral Equations 191
7.1 Introduction......................................................191
7.2 Nonlinear Fredholm Integral Equations of the Second Kind 192
7.2.1 The Direct Computation Method......................192
7.2.2 The Adomian Decomposition Method................197
7.2.3 The Variational Iteration Method......................207
7.3 Nonlinear Fredholm Integral Equations of the First Kind . . 211
7.3.1 The Method of Regularization ........................212
7.4 Nonlinear Weakly-Singular Fredholm Integral Equations . . 216
7.4.1 The Modified Decomposition Method ................217
8 Nonlinear Volterra Integral Equations 223
8.1 Introduction......................................................223
8.2 Nonlinear Volterra Integral Equations of the Second Kind . 224
8.2.1 The Series Solution Method............................225
8.2.2 The Adomian Decomposition Method................228
8.2.3 The Variational Iteration Method......................233
8.3 Nonlinear Volterra Integral Equations of the First Kind . . 236
8.3.1 The Series Solution Method............................236
8.3.2 Conversion to a Volterra Equation of the Second Kind 239
8.4 Nonlinear Weakly-Singular Volterra Integral Equations . . . 242
8.4.1 The Modified Decomposition Method ................243
9 Applications of Integral Equations 249
9.1 Introduction......................................................249
9.2 Volterra Integral Form of the Lane-Emden Equation .... 250
9.2.1 Lane-Emden Equation of the First Kind..............251
9.2.2 Lane-Emden Equation of the Second Kind............254
9.3 The Schlomilch s Integral Equation............................257
9.3.1 The Linear Schlomilch s Integral Equation............257
9.3.2 The Method of Regularization ........................258
9.3.3 The Nonlinear Schlomilch s Integral Equation .... 260
9.4 Bratu-Type Problems ..........................................263
9.4.1 First Bratu-Type Problem..............................264
9.4.2 Second Bratu-Type Problem..........................266
9.4.3 Third Bratu-Type Problem............................268
9.5 Systems of Integral Equations..................................269
9.5.1 Systems of Fredholm Integral Equations..............270
9.5.2 Systems of Volterra Integral Equations................272
9.6 Numerical Treatment of Fredholm Integral Equations .... 274
9.7 Numerical Treatment of Volterra Integral Equations .... 279
A Table of Indefinite Integrals 283
B Integrals Involving Irrational Algebraic Functions 287
C Series 289
D The Error and the Gamma Functions 291
Answers to Exercises 293
Bibliography 305
Index 311
|
| any_adam_object | 1 |
| author | Wazwaz, Abdul-Majid |
| author_GND | (DE-588)1076753868 |
| author_facet | Wazwaz, Abdul-Majid |
| author_role | aut |
| author_sort | Wazwaz, Abdul-Majid |
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| building | Verbundindex |
| bvnumber | BV042781786 |
| classification_rvk | SK 640 |
| ctrlnum | (OCoLC)927153915 (DE-599)GBV819879061 |
| 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 | 3515.45 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| genre_facet | Lehrbuch |
| id | DE-604.BV042781786 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:09:30Z |
| institution | BVB |
| isbn | 9789814675116 9814675113 9789814675123 9814675121 |
| language | English |
| lccn | 2015008111 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028211809 |
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| owner | DE-20 DE-19 DE-BY-UBM DE-1050 DE-188 |
| owner_facet | DE-20 DE-19 DE-BY-UBM DE-1050 DE-188 |
| physical | XIV, 312 S. 24 cm |
| publishDate | 2015 |
| publishDateSearch | 2015 |
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| publisher | World Scientific |
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| spelling | Wazwaz, Abdul-Majid Verfasser (DE-588)1076753868 aut A first course in integral equations Abdul-Majid Wazwaz 2. ed. New Jersey [u.a.] World Scientific 2015 XIV, 312 S. 24 cm txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Integralgleichung (DE-588)4027229-1 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Integralgleichung (DE-588)4027229-1 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028211809&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wazwaz, Abdul-Majid A first course in integral equations Integralgleichung (DE-588)4027229-1 gnd |
| subject_GND | (DE-588)4027229-1 (DE-588)4123623-3 |
| title | A first course in integral equations |
| title_auth | A first course in integral equations |
| title_exact_search | A first course in integral equations |
| title_full | A first course in integral equations Abdul-Majid Wazwaz |
| title_fullStr | A first course in integral equations Abdul-Majid Wazwaz |
| title_full_unstemmed | A first course in integral equations Abdul-Majid Wazwaz |
| title_short | A first course in integral equations |
| title_sort | a first course in integral equations |
| topic | Integralgleichung (DE-588)4027229-1 gnd |
| topic_facet | Integralgleichung Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028211809&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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