Partial differential equations: an introduction
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Random House
1988
|
| Ausgabe: | 1. ed. |
| Schriftenreihe: | The Random House/Birkhäuser mathematics series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 308 S. graph. Darst. |
| ISBN: | 0394358279 |
Internformat
MARC
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| 245 | 1 | 0 | |a Partial differential equations |b an introduction |c David Colton |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a New York |b Random House |c 1988 | |
| 300 | |a IX, 308 S. |b graph. Darst. | ||
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| 650 | 4 | |a Differential equations, Partial | |
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Datensatz im Suchindex
| _version_ | 1804122884312924160 |
|---|---|
| adam_text | Contents
Chapter 1 INTRODUCTION 1
1.1 Physical Examples 3
1.2 First Order Linear Equations 6
1.3 Classification of Second Order Equations and Canonical
Forms 11
Types of Second Order Equations 11
Reduction of Second Order Equations with Constant Coefficients
to Canonical Form 12
Reduction of Second Order Equations in Two Independent
Variables to Canonical Form 13
1.4 Fourier Series and Integrals 18
*1.5 Analytic Functions 29
Power Series and Analytic Functions 29
Integration of Analytic Functions 33
Singularities of Analytic Functions and the Residue Theorem 39
A Linear Partial Differential Equation with No Solution 46
1.6 A Brief History of the Theory of Partial Differential
Equations 49
Chapter 2 THE WAVE EQUATION 61
2.1 The Wave Equation in Two Independent Variables 62
2.2 The Cauchy Problem for Hyperbolic Equations in Two
Independent Variables 65
2.3 The Cauchy Problem for the Wave Equation in More Than
Two Independent Variables 70
2.4 The Initial Boundary Value Problem for the Wave Equation
in Two Independent Variables 78
2.5 Fourier s Method for the Wave Equation in Three
Independent Variables 83
2.6 The Equations of Gas Dynamics 90
vii
viii / Contents
Chapter 3 THE HEAT EQUATION 106
3.1 The Weak Maximum Principle for Parabolic Equations 106
3.2 The Initial Boundary Value Problem for the Heat Equation
in a Rectangle 112
3.3 Cauchy s Problem for the Heat Equation 115
3.4 Regularity of Solutions to the Heat Equation 123
*3.5 The Strong Maximum Principle for the Heat Equation 126
*3.6 The Stefan Problem and Analytic Continuation 130
3.7 Hermite Polynomials and the Numerical Solution of the Heat
Equation in a Rectangle 134
3.8 Nonlinear Problems in Heat Conduction 136
Chapter 4 LAPLACE S EQUATION 151
4.1 Green s Formulas 152
4.2 Basic Properties of Harmonic Functions 154
4.3 Boundary Value Problems for Laplace s Equation 157
4.4 Separation of Variables in Polar and Spherical Coordinates 159
4.5 Green s Function and Poisson s Formula 166
4.6 Finite Difference Methods for Laplace s Equation 173
4.7 Poisson s Equation 175
4.8 Time Harmonic Wave Propagation in a Nonhomogeneous
Medium 181
Chapter 5 POTENTIAL THEORY AND FREDHOLM INTEGRAL
EQUATIONS 195
5.1 Potential Theory 196
5.2 The Fredholm Alternative 206
5.3 Applications to the Dirichlet and Neumann Problems 215
The Interior Dirichlet Problem 216
The Interior Neumann Problem 217
The Exterior Neumann Problem 218
The Exterior Dirichlet Problem 220
5.4 Hilbert Schmidt Theory and Eigenvalue Problems 222
5.5 The Numerical Solution of Fredholm Integral Equations of
the Second Kind 235
?Chapter 6 SCATTERING THEORY 243
6.1 The Gamma Function 244
6.2 Bessel Functions 248
Definitions 248
Contents / ix
Wronskians 249
A Generating Function for Jn(z) 250
Integral Representations 251
Asymptotic Expansions for Positive z 253
Addition Formulas 258
6.3 The Scattering of Acoustic Waves 260
6.4 Maxwell s Equations 264
6.5 Scattering by a Cylinder of Arbitrary Cross Section 267
6.6 The Inverse Scattering Problem 277
Preliminaries 277
Herglotz Wave Functions 280
Optimal Solutions to the Inverse Scattering Problem 285
REFERENCES 300
INDEX 305
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T17:20:58Z |
| institution | BVB |
| isbn | 0394358279 |
| language | English |
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| owner_facet | DE-824 |
| physical | IX, 308 S. graph. Darst. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
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| publisher | Random House |
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| series2 | The Random House/Birkhäuser mathematics series |
| spelling | Colton, David 1943- Verfasser (DE-588)115774173 aut Partial differential equations an introduction David Colton 1. ed. New York Random House 1988 IX, 308 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier The Random House/Birkhäuser mathematics series Mathematische Physik swd Partielle Differentialgleichung swd Differential equations, Partial Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Mathematische Physik (DE-588)4037952-8 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=005619052&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 | Colton, David 1943- Partial differential equations an introduction Mathematische Physik swd Partielle Differentialgleichung swd Differential equations, Partial Mathematische Physik (DE-588)4037952-8 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4037952-8 (DE-588)4044779-0 |
| title | Partial differential equations an introduction |
| title_auth | Partial differential equations an introduction |
| title_exact_search | Partial differential equations an introduction |
| title_full | Partial differential equations an introduction David Colton |
| title_fullStr | Partial differential equations an introduction David Colton |
| title_full_unstemmed | Partial differential equations an introduction David Colton |
| title_short | Partial differential equations |
| title_sort | partial differential equations an introduction |
| title_sub | an introduction |
| topic | Mathematische Physik swd Partielle Differentialgleichung swd Differential equations, Partial Mathematische Physik (DE-588)4037952-8 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Mathematische Physik Partielle Differentialgleichung Differential equations, Partial |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005619052&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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