Fundamentals of mathematical physics /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Kraut, Edgar A.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Mineola, N.Y. : Dover Publications, 2007.
Edición:Dover ed.
Temas:
Mathematical physics.
Physique mathématique.
Mathematical physics
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Machine derived contents note: chapter one vector algebra 1
  • Introduction I
  • I-1 Definitions 3
  • 1-2 Equality of Vectors and Null Vectors 4
  • 1-3 Vector Operations 5
  • 1-4 Expansion of Vectors 9
  • 1-5 Vector Identities 14
  • 86 Problems and Applications 15
  • chapter two matrix and tensor algebra 17
  • 2-1 Definitions 17
  • 2-2 Equality of Matrices and Null Matrices 18
  • 2-3 Matrix Operations 19
  • 2-4 Determinants 23
  • 2-5 Special Matrices 25
  • 2-6 Systems of Linear Equations 30
  • 2-7 Linear Operators 33
  • 2-8 Eigenvalue Problems 37
  • 2-9 Diagonalization of Matrices 40
  • 2-10 Special Properties of Hermitian Matrices 46
  • 2-11 Tensor Algebra 47
  • 2-12 Tensor Operations 48
  • 2-13 Transformation Properties of Tensors 50
  • 2-14 Special Tensors 53
  • 2-15 Problems and Applications 55
  • chapter three vector calculus 59
  • 3-1 Ordinary Vector Differentiation 59
  • 3-2 Partial Vector Differentiation 64
  • 3-3 Vector Operations in Cylindrical and Spherical Coordinate Systems 68
  • 3-4 Differential Vector Identities 74
  • 3-5 Vector Integration over a Closed Surface 76
  • 3-6 The Divergence Theorem 80
  • 3-7 The Gradient Theorem 82
  • 3-8 The Curl Theorem 82
  • 3-9 Vector Integration over a Closed Curve 83
  • 3-0 The Two-dimensional Divergence Theorem 87
  • 3-11 The Two-dimensional Gradient Theorem 87
  • 3-12 The Two-dimensional Curl Theorem 88
  • 3-13 Mnemonic Operators 92
  • 3-14 Kinematics of Infinitesimal Volume, Surface, and Line Elements 93
  • 3-15 Kinematics of a Volume Integral 96
  • 3-1.6 Kinematics of a Surface Integral 97
  • 3-17 Kinematics of a Line Integral 99
  • 3-18 Solid Angle 100
  • 3-19 Decomposition of a Vector Field into Solenoidal and
  • Irrotational Parts 102
  • 3-20 Integral Theorems for Discontinuous and Unbounded Functions 103
  • 3-21 Problems and Applications 115
  • chapter four functions of a complex variable 127
  • 4-1 Introduction 127
  • 4-2 Definitions 127
  • 4-3 Complex Algebra 129
  • 4-4 Domain of Convergence 130
  • 4-5 IAnalytic Functions 131
  • 4-6 Cauchy's Approach 133
  • 4-7 Cauchy's Integral Theorem 134
  • 4-8 Cauchy's integral Representation of an Analytic Function 136
  • 4-9 Taylor's Series 139
  • 4-10 Cauchy's Inequalities 140
  • 4-11 Entire Functions 140
  • 4-12 Riemann's Theory of Functions of a Complex Variable 141
  • 4-13 Physical Interpretation 142
  • 4-14 Functions Defined on Curved Surfaces 145
  • 4-15 Laurent's Series 152
  • 4-16 Singularities of an Analytic Function 154
  • 4-17 Multivalued Functions 155
  • 4-18 Residues 158
  • 4-19 Residue at Infinity 161
  • 4-20 Generalized Residue Theorem of Cauchy 162
  • 4-21 Problems and Applications 167
  • chapter five integral transforms 173
  • 5-1 Introduction 173
  • 5-2 Orthogonal Functions 174
  • 5-3 Dirac's Notation 175
  • 5-4 Analogy between Expansion in Orthogonal Functions
  • and Expansion in Orthogonal Vectors 177
  • 5-5 Linear Independence of Functions 179
  • 5-6 Mean-square Convergence of an Expansion
  • in Orthogonal Functions 180
  • 5-7 In tgration and Differentiation of Orthogonal Expansions 185
  • 5-8 Pointwise Convergence of an Orthogonal Expansion 185
  • 5-9 Gibbs's bhenorenon 186
  • 5-10 The inite Sine Transform 187
  • 5411 The Finite Cosine Transform 190
  • 5-12 Properties of Finite Fourier Transforms 191
  • 5-13 Connection with Classical Theory of Fourier Series 192
  • 5-14 Applications of Finite Fourier Transforms 194
  • 5i-5 Infinite-range Fourier Transforms 206
  • 5-16 Condiions for the Applicability of the Fourier Transformation 210
  • 5-17 Fourier Sin and Cosine Transforms 211
  • 5-18 Fourier Transforms in n Dimensions 213
  • 5-19 Properties of Fourier Transforms 214
  • 5-20 Physical Interpretation of the Fourier Transform 216
  • 5-21 Applications of the Infinite-range Fourier Transform 218
  • 5-22 The L, avlace Transform 223
  • 5-23 Properties of Laplace Transforms 226
  • 5-24 Application of the Laplace Transform 228
  • 5-25 Problems and Applications 232
  • chapter six linear differential equations 239
  • 6-1 Introduction 239
  • 6-2 Linear Differential Equations with Constant Coefficients 240
  • 6-3 The Theory of the Seismograph 246
  • 6-4 Linear Differential Equations with Variable Coeffcients 252
  • 6-5 The Special Functions of Mathematical Physics 255
  • 6-6 The Gamma Function 256
  • 6-7 The Beta Function 259
  • 6-8 The Bessel Functions 261
  • 6-9 The Neumann Functions 264
  • 6 -0 Bessel Funetions of Arbitrary Order 267
  • 6-11 The Hankel Functions 269
  • "6-12 The Hyperbolic Bessel Functions 270
  • 6-13 The Associated Legendre Functions 272
  • 6-14 Representation of Associated Legendre Functions
  • in Terms of Legendre Polynomials 275
  • 6-15 Spherical Harmonies 276
  • 6-16 Spherical Bessel Functions 279
  • 6-17 Hermite Polynomials 281
  • 6-18 General Properties of Linear Second-order Differential Equations
  • with Variable Coefficients 287
  • 6-19 Evaluation of the Wronskian 291
  • 6-20 General Solution of a Homogeneous Equation
  • Using Abels Formula 292
  • 6-21 Solution of an Inhomogeneous Equation
  • Using Abel's Formula 293
  • 6-22 Green's Function 295
  • 6-23 Use of the Green's Function g(xjx') 296
  • 6-24 The Sturm-Liouville Problem 299
  • 6-25 Solution of Ordinary Differential Equations with Variable
  • Coefficients by Transform Methods 303
  • 6-26 Problems and Applications 306
  • chapter seven partial differential equations 317
  • 7-1 Introduction 317
  • 7-2 The Role of the Laplacian 317
  • 7-3 Laplace's Equation 318
  • 7-4 Poisson's Equation 318
  • 7-5 The Diffusion Equation 319
  • 7-6 The Wave Equation 321
  • 7-7 A Few General Remarks 322
  • 7-8 Solution of Potential Problems in Two Dimensions 323
  • 7-9 Separation of Variables 333
  • 7-10 The Solution of Laplace's Equation in a Half Space 338
  • 7-11 Laplace's Equation in Polar Coordinates 343
  • 7-12 Construction of a Green's Function in Polar Coordinates 344
  • 7-13 The Exterior Dirichlet Problem for a Circle 352
  • 7-14 Laplace's Equation in Cylindrical Coordinates 354
  • 7-15 Construction of the Green's Function 356
  • 7-16 An Alternative Method of Solving Boundary-value Problems 360
  • 17 Laplace's Equation in Spherical Coordinates 363
  • 7-18 Construction of the Green's Function 365
  • 7-19 Solution of the Interior and Exterior Dirichlet Problems
  • for a Grounded Conducting Sphere 368
  • "7-20 The One-dimensional Wave Equation 371
  • 7-21 The Two-dimensional Wave Equation 377
  • 7-22 The Helmholtz Equation in Cylindrical Coordinates 382
  • 7-23 The Helmholtz Equation in Rectangular Cartesian Coordinates 392.
  • 7-24 The Helmholtz Equation in Spherical Coordinates 400
  • 7-25 Interpretation of the Integral Solution of Helmholtz's Equation 403
  • 7-26 The Sommerfeld Radiation Condition 405
  • 7-27 Time-dependent Problems 409
  • 7-28 Poisson's Solution of the Wave Equation 413
  • 7-29 The Diffusion Equation 420
  • 7-30 General Solution of the Diffusion Equation 422
  • 7-31 Construction of the Infinite-medium Green's Function
  • for the Diffusion Equation 423
  • 7-32 Problems and Applications 427.

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