Table of contents for Mathematical physics : applied mathematics for scientists and engineers / Bruce R. Kusse and Erik A. Westwig.


Bibliographic record and links to related information available from the Library of Congress catalog
Note: Electronic data is machine generated. May be incomplete or contain other coding.


Counter
1 A Review of Vector and Matrix Algebra Using
Subscript/Summation Conventions                                 1
1.1 Notation, 1
1.2 Vector Operations, 5
2  Differential and Integral Operations on Vector and Scalar Fields  18
2.1 Plotting Scalar and Vector Fields, 18
2.2 Integral Operators, 20
2.3 Differential Operations, 23
2.4 Integral Definitions of the Differential Operators, 34
2.5 The Theorems, 35
3  Curvilinear Coordinate Systems                                 44
3.1 The Position Vector, 44
3.2 The Cylindrical System, 45
3.3 The Spherical System, 48
3.4 General Curvilinear Systems, 49
3.5 The Gradient, Divergence, and Curl in Cylindrical and Spherical
Systems, 58
4  Introduction to Tensors                                        67
4.1 The Conductivity Tensor and Ohm's Law, 67
4.2 General Tensor Notation and Terminology, 71
4.3 Transformations Between Coordinate Systems, 71
4.4 Tensor Diagonalization, 78
4.5 Tensor Transformations in Curvilinear Coordinate Systems, 84
4.6 Pseudo-Objects, 86
5  The Dirac S-Function                                          100
5.1 Examples of Singular Functions in Physics, 100
5.2 Two Definitions of 8(t), 103
5.3 8-Functions with Complicated Arguments, 108
5.4 Integrals and Derivatives of 8(t), 111
5.5 Singular Density Functions, 114
5.6 The Infinitesimal Electric Dipole, 121
5.7 Riemann Integration and the Dirac 8-Function, 125
6  Introduction to Complex Variables                             135
6.1 A Complex Number Refresher, 135
6.2 Functions of a Complex Variable, 138
6.3 Derivatives of Complex Functions, 140
6.4 The Cauchy Integral Theorem, 144
6.5 Contour Deformation, 146
6.6 The Cauchy Integral Formula, 147
6.7 Taylor and Laurent Series, 150
6.8 The Complex Taylor Series, 153
6.9 The Complex Laurent Series, 159
6.10 The Residue Theorem, 171
6.11 Definite Integrals and Closure, 175
6.12 Conformal Mapping, 189
7  Fourier Series                                                 219
7.1 The Sine-Cosine Series, 219
7.2 The Exponential Form of Fourier Series, 227
7.3 Convergence of Fourier Series, 231
7.4 The Discrete Fourier Series, 234
8  Fourier Transforms                                             250
8.1 Fourier Series as To -- co, 250
8.2 Orthogonality, 253
8.3 Existence of the Fourier Transform, 254
8.4 The Fourier Transform Circuit, 256
8.5 Properties of the Fourier Transform, 258
8.6 Fourier Transforms-Examples, 267
8.7 The Sampling Theorem, 290
9  Laplace Transforms                                             303
9.1 Limits of the Fourier Transform, 303
9.2 The Modified Fourier Transform, 306
9.3 The Laplace Transform, 313
9.4 Laplace Transform Examples, 314
9.5 Properties of the Laplace Transform, 318
9.6 The Laplace Transform Circuit, 327
9.7 Double-Sided or Bilateral Laplace Transforms, 331
10  Differential Equations                                         339
10.1 Terminology, 339
10.2 Solutions for First-Order Equations, 342
10.3 Techniques for Second-Order Equations, 347
10.4 The Method of Frobenius, 354
10.5 The Method of Quadrature, 358
10.6 Fourier and Laplace Transform Solutions, 366
10.7 Green's Function Solutions, 376
11 Solutions to Laplace's Equation                               424
11.1 Cartesian Solutions, 424
11.2 Expansions With Eigenfunctions, 433
11.3 Cylindrical Solutions, 441
11.4 Spherical Solutions, 458
12  Integral Equations                                           491
12.1 Classification of Linear Integral Equations, 492
12.2 The Connection Between Differential and
Integral Equations, 493
12.3 Methods of Solution, 498
13 Advanced Topics in Complex Analysis                           509
13.1 Multivalued Functions, 509
13.2 The Method of Steepest Descent, 542
14  Tensors in Non-Orthogonal Coordinate Systems                 562
14.1 A Brief Review of Tensor Transformations, 562
14.2 Non-Orthonormal Coordinate Systems, 564
15  Introduction to Group Theory                                 597
15.1 The Definition of a Group, 597
15.2 Finite Groups and Their Representations, 598
15.3 Subgroups, Cosets, Class, and Character, 607
15.4 Irreducible Matrix Representations, 612
15.5 Continuous Groups, 630



Library of Congress subject headings for this publication: Mathematical physics