Partial differential equations of mathematical physics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
North Holland
1980
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 380 S. |
| ISBN: | 0444003525 |
Staff View
MARC
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| 245 | 1 | 0 | |a Partial differential equations of mathematical physics |c Tyn Myint-U |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface xi
chapter one Introduction 1
1.1 Basic Concepts and Definitions 1
1.2 Mathematical Problems 4
1.3 Linear Operators 5
1.4 Superposition 7
Exercises 9
chapter two Mathematical Models 11
2.1 The Classical Equations 11
2.2 The Vibrating String 11
2.3 The Vibrating Membrane 13
2.4 Waves in Elastic Medium 15
2.5 Conduction of Heat in Solids 20
2.6 The Gravitational Potential 21
Exercises 23
chapter three Classification of Second-order Equations 26
3.1 Second-order Equations in Two
Independent Variables 26
3.2 Canonical Forms 28
3.3 Equations with Constant Coefficients 34
3.4 General Solution 38
3.5 Summary and Further Simplification 40
Exercises 41
chapter four The Cauchy Problem 43
4.1 The Cauchy Problem 43
4.2 Cauchy-Kowalewsky Theorem 46
vii
viii Contents
4.3 Homogeneous Wave Equation 47
4.4 Initial-boundary Value Problems 55
4.5 Nonhomogeneous Boundary Conditions 58
4.6 Finite String with Fixed Ends 60
4.7 Nonhomogeneous Wave Equation 63
4.8 Riemann Method 66
4.9 Goursat Problem 73
Exercises 77
chapter five Fourier Series 82
5.1 Piecewise Continuous Functions 82
5.2 Even and Odd Functions 85
5.3 Periodic Functions 88
5.4 Orthogonality 89
5.5 Fourier Series 90
5.6 Convergence in the Mean 92
5.7 Examples of Fourier Series 93
5.8 Cosine and Sine Series 98
5.9 Complex Fourier Series 102
5.10 Change of Interval 104
5.11 Pointwise Convergence 107
5.12 Uniform Convergence 112
5.13 Differentiation and Integration 115
5.14 Double Fourier Series 120
Exercises 122
chapter six Method of Separation of Variables 128
6.1 Separation of Variables 128
6.2 The Vibrating String Problem 131
6.3 Existence and Uniqueness of Solution of the
Vibrating String Problem 136
6.4 The Heat Conduction Problem 142
6.5 Existence and Uniqueness of Solution of the
Heat Conduction Problem 145
6.6 The Laplace and Beam Equations 148
6.7 Nonhomogeneous Problems 151
6.8 Finite Fourier Transforms 158
Exercises 162
chapter seven Eigenvalue Problems 171
7.1 Sturm- Liouville Systems 171
7.2 Eigenvalues and Eigenfunctions 174
7.3 Eigenf unction Expansions 179
7.4 Convergence in the Mean 181
7.5 Completeness and Parseval s Equality 182
7.6 Bessel s Equation 186
7.7 Adjoint Forms: Lagrange Identity 191
7.8 Singular Sturm-Liouville Systems 193
Contents ix
7.9 Legendre s Equation 198
7.10 Boundary Value Problems Involving Ordinary
Differential Equations 204
7.11 Green s Function 206
7.12 Construction of Green s Function 211
7.13 Nonhomogeneous Boundary Conditions 214
7.14 Eigenvalue Problems and Green s Function 216
Exercises 218
chapter eight Boundary Value Problems 223
8.1 Boundary Value Problems 223
8.2 Maximum and Minimum Principles 225
8.3 Uniqueness and Continuity Theorems 227
8.4 Dirichlet Problem for a Circle 228
8.5 Dirichlet Problem for a Circular Annulus 232
8.6 Neumann Problem for a Circle 234
8.7 Dirichlet Problem for a Rectangle 235
8.8 Dirichlet Problem Involving Poisson Equation 238
8.9 Neumann Problem for a Rectangle 240
Exercises 243
chapter nine Higher Dimensional Problems 251
9.1 Dirichlet Problem for a Cube 251
9.2 Dirichlet Problem for a Cylinder 253
9.3 Dirichlet Problem for a Sphere 256
9.4 Wave and Heat Equations 260
9.5 Vibrating Membrane 261
9.6 Heat Flow in a Rectangular Plate 263
9.7 Waves in Three Dimensions 265
9.8 Heat Conduction in a Rectangular Volume 266
9.9 The Hydrogen Atom 267
9.10 Method of Eigenfunctions 270
9.11 Forced Vibration of Membrane 271
9.12 Time-dependent Boundary Conditions 273
Exercises 276
chapter ten Green s Function 282
10.1 The Delta Function 282
10.2 Green s Function 283
10.3 Method of Green s Function 285
10.4 Dirichlet Problem for the Laplace Operator 287
10.5 Dirichlet Problem for the Helmholtz Operator 290
10.6 Method of Images 291
10.7 Method of Eigenf unctions 294
10.8 Higher Dimensional Problems 297
10.9 Neumann Problem 300
Exercises 302
X
chapter eleven Integral Transforms 306
11.1 Fourier Transforms 306
11.2 Properties of Fourier Transform 312
11.3 Convolution (Fourier Transform) 316
11.4 Step Function and Impulse Function (Fourier Transform) 319
11.5 Semiinfinite Region 322
11.6 Hankel and Mellon Transforms 324
11.7 Laplace Transforms 325
11.8 Properties of Laplace Transforms 327
11.9 Convolution (Laplace Transform) 331
11.10 Step Function and Impulse Function (Laplace Transform) 334
11.11 Application of Green s Function 341
Exercises 343
Appendix 351
I Gamma Function 351
II Table of Fourier Transforms 352
III Table of Laplace Transforms 353
Bibliography 355
Answers to Exercises 359
Index 377
i
|
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| dewey-ones | 515 - Analysis |
| dewey-raw | 515.3/53 |
| dewey-search | 515.3/53 |
| dewey-sort | 3515.3 253 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| indexdate | 2024-07-09T15:43:17Z |
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| language | English |
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| spelling | Tyn Myint-U Verfasser (DE-588)132477033 aut Partial differential equations of mathematical physics Tyn Myint-U 2. ed. New York u.a. North Holland 1980 XIII, 380 S. txt rdacontent n rdamedia nc rdacarrier Mathematische fysica gtt Partiële differentiaalvergelijkingen gtt Équations aux dérivées partielles Differential equations, Partial Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Physik (DE-588)4045956-1 gnd rswk-swf Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Mathematische Physik (DE-588)4037952-8 s DE-604 Physik (DE-588)4045956-1 s 1\p DE-604 Mathematische Methode (DE-588)4155620-3 s 2\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001498499&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Tyn Myint-U Partial differential equations of mathematical physics Mathematische fysica gtt Partiële differentiaalvergelijkingen gtt Équations aux dérivées partielles Differential equations, Partial Partielle Differentialgleichung (DE-588)4044779-0 gnd Physik (DE-588)4045956-1 gnd Mathematische Methode (DE-588)4155620-3 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4045956-1 (DE-588)4155620-3 (DE-588)4037952-8 |
| title | Partial differential equations of mathematical physics |
| title_auth | Partial differential equations of mathematical physics |
| title_exact_search | Partial differential equations of mathematical physics |
| title_full | Partial differential equations of mathematical physics Tyn Myint-U |
| title_fullStr | Partial differential equations of mathematical physics Tyn Myint-U |
| title_full_unstemmed | Partial differential equations of mathematical physics Tyn Myint-U |
| title_short | Partial differential equations of mathematical physics |
| title_sort | partial differential equations of mathematical physics |
| topic | Mathematische fysica gtt Partiële differentiaalvergelijkingen gtt Équations aux dérivées partielles Differential equations, Partial Partielle Differentialgleichung (DE-588)4044779-0 gnd Physik (DE-588)4045956-1 gnd Mathematische Methode (DE-588)4155620-3 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| topic_facet | Mathematische fysica Partiële differentiaalvergelijkingen Équations aux dérivées partielles Differential equations, Partial Partielle Differentialgleichung Physik Mathematische Methode Mathematische Physik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001498499&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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