Boundary value problems in physics and engineering:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Nichtbestimmte Sprache |
| Veröffentlicht: |
London
Reinhold
1969
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004744429&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | 250 S. graph. Darst. |
Internformat
MARC
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| 245 | 1 | 0 | |a Boundary value problems in physics and engineering |
| 264 | 1 | |a London |b Reinhold |c 1969 | |
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Datensatz im Suchindex
| _version_ | 1819295173356552192 |
|---|---|
| adam_text | CONTENTS
Preface 5
Sources of Examination Questions 10
Key to Abbreviations 10
1 PARTIAL DIFFERENTIATION TECHNIQUES AND THE
FORMATION OF PARTIAL DIFFERENTIAL EQUATIONS
1.1 Functions ofSeveral Variables, Continuity and Partial Derivatives 11
1.2 Change of Variable in Partial Differentiation 15
1.3 Taylor s Theorem for a Function of Two Variables 22
1.4 Exact and Non Exact Differentials 23
1.4.1 Some Thermodynamic Aspects 27
1.5 Formation of Partial Differential Equations 29
1.6 The Partial Differential Equations and Boundary Value Problems
of Mathematical Physics 30
1.7 Uniqueness Theorems of Boundary Value Problems 33
1.8 Use of Dimensional Analysis 38
Exercise 1 39
2 SPECIAL TECHNIQUES FOR SOLVING THE SIMPLER
TYPES OF PARTIAL DIFFERENTIAL EQUATIONS
2.1 Some Simple First and Second Order Equations 41
2.2 The One Dimensional Wave Equation 42
2.3 Method of Separation of Variables 45
2.4 Lagrange s Equation 48
2.4.1 Case of n Independent Variables 52
7
8 CONTENTS
2.5 Linear Partial Differential Equations with Constant Coefficients 52
Exercise 2 59
3 THE THEORY AND APPLICATIONS OF ORTHOGONAL
FUNCTIONS
3.1 Some Properties of Vectors 68
3.2 The Sturm Liouville Differential Equation and Orthogonal
Functions 71
3.3 General Fourier Series or Eigenfunction Expansions 73
3.4 Trigonometric Fourier Series 76
3.4.1 Half Range Trigonometric Fourier Series 80
3.5 Formal Solution of Boundary Value Problems using Trigono¬
metric Fourier Series 81
3.6 Some Properties of Bessel Functions 87
3.6.1 Fourier Bessel Expansions 90
Exercise 3 93
4 SOLUTIONS OF LAPLACE S EQUATION
4.1 Nature of the Problems to be Discussed 102
4.2 Use of Polar Coordinates for Solution of the Two Dimensional
Laplace Equation 103
4.3 Use of Cylindrical Polar Coordinates for the Solution of La¬
place s Equation 106
4.4 Use of Spherical Polar Coordinates for the Solution of Laplace s
Equation 111
4.5 Methods due to Green: Three Dimensional Results 122
4.5.1 Methods due to Green: Two Dimensional Results 128
4.6 Equipotential Surfaces 130
Exercise 4 132
5 COMPLEX VARIABLE APPLICATIONS
5.1 Resume of Elementary Properties of a Function of a Complex
Variable 139
5.2 Infinite Series Expansions, Singularities, Residues and Contour
Integrals 142
5.3 Conformal Transformation 143
5.4 Potential Problems in Two Dimensional Electrostatics 144
5.5 Solution of Laplace s Equation by Conjugate Functions 149
5.6 Dirichlet Problem for the Unit Circle 151
5.7 Neumann Problem for the Unit Circle 153
5.8 Some Elastostatic Applications 154
Exercise 5 160
CONTENTS 9
6 SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS
6.1 Characterization of Second Order Partial Differential Equations 163
6.2 Reduction of Second Order Partial Differential Equations to
Canonical Form 167
6.3 Riemann s Method for the Solution of a Second Order Linear
Hyperbolic Equation 172
6.3.1 Numerical Integration of Second Order Hyperbolic Equa¬
tions 178
6.4 Some Further Aspects of the Adjoint Equation 182
Exercise 6 183
7 INTEGRAL TRANSFORMS
7.1 Notion of an Integral Transform 187
7.2 Some Particular Integral Transforms and Their Inverses 188
7.3 The Fourier Integral Formula and Its Applications for Finding
Inverse Transforms 189
7.3.1 Fourier s Integral Formula—Formal Establishment 189
7.3.2 Inversion Formulae for Fourier Sine and Cosine Trans¬
formations 190
7.3.3 Inversion Formula for Complex Fourier Transform 193
7.3.4 Inversion Formula for Laplace Transform 193
7.4 Some Properties and Applications of the Laplace Transform and
Its Inverse 194
7.4.1 Resume of Elementary Properties 194
7.4.2 Evaluation of Inverse Laplace Transforms 198
7.4.3 The Error and Complementary Error Functions 201
7.4.4 Some Applications of the Laplace Transform to the Solu¬
tion of Boundary and Initial Value Problems 204
7.5 Some Applications of the Complex Fourier Transform 208
7.6 Some Applications of the Fourier Sine and Cosine Transforms 210
7.7 Inversion Formula for the Hankel Transform 212
7.7.1 Some Applications of the Hankel Transform 213
7.8 Inversion Formula for the Mellin Transform 217
7.9 Finite Transforms 220
7.10 Generalized Integral Transforms 228
Exercise 7 230
References 243
Solutions 245
Index 249
|
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| indexdate | 2024-12-20T09:02:47Z |
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| spellingShingle | Chorlton, Frank Boundary value problems in physics and engineering Randwertproblem (DE-588)4048395-2 gnd |
| subject_GND | (DE-588)4048395-2 |
| title | Boundary value problems in physics and engineering |
| title_auth | Boundary value problems in physics and engineering |
| title_exact_search | Boundary value problems in physics and engineering |
| title_full | Boundary value problems in physics and engineering |
| title_fullStr | Boundary value problems in physics and engineering |
| title_full_unstemmed | Boundary value problems in physics and engineering |
| title_short | Boundary value problems in physics and engineering |
| title_sort | boundary value problems in physics and engineering |
| topic | Randwertproblem (DE-588)4048395-2 gnd |
| topic_facet | Randwertproblem |
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