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Mathematical techniques and physical applications
1 online resource (xiv, 715 pages) illustrations
Front Cover; Mathematical Techniques and Physical Applications; Copyright Page; Contents; Preface; Comment on Notation; Chapter 1. Vector Analysis; 1.1. Scalars, Tensors, and Vectors; 1.2. Scalar, Vector, and Tensor Fields; 1.3. Vector Components, Unit Vectors, Right-Handed Cartesian Axes; 1.4. Vector Sums and Products; 1.5. Derivatives of a Vector or Vector Field; 1.6. Integral Theorems; 1.7. Dyadic Formalism; 1.8. Orthogonal Curvilinear Coordinates; 1.9. Uses of Vector Analysis; 1.10. Further Examples Involving the Vector Product; Chapter 2. Matrices
2.1. Simultaneous Linear Equations and Matrix Algebra2.2. Some Common Types of Matrix; 2.3. Inverse of a Matrix, Determinant; 2.4. Theorems Concerning Matrix Products; 2.5. Eigenvectors and Eigenvalues of a Matrix; 2.6. Matrices as Representations of Linear Operators; 2.7. Application of Matrix Theory to Physical Problems; Chapter 3. Tensor Analysis; 3.1. Cartesian Tensors; 3.2. Tensors in Nonorthogonal Frames; 3.3. General Tensors; 3.4. The Christoffel Symbols; 3.5. Length of a Curve, Geodesics; 3.6. Covariant Derivatives; 3.7. The Determinant IgI, Tensor Densities
3.8. Tensor Form of Gradient, Divergence, and Curl3.9. Curvature Tensor; 3.10. Theory of Elasticity; 3.11. Lorentz Covariance of Maxwell's Equations; 3.12. A Summary of Tensor Theory; Chapter 4. Sequences and Series; 4.1. Sequences, Cauchy Sequences, Convergence; 4.2. Series, Absolute and Conditional Convergence; 4.3. Convergence Tests for Series; 4.4. Multiplication and Addition of Series; 4.5. Sequences and Series of Functions, Uniform Convergence; 4.6. Radius of Convergence of a Series, Term-by-Term Differentiation and Integration; 4.7. Dirichlet Conditions for Fourier Series
4.8. Exponential Function4.9. Results Involving Integrals; 4.10. Series in Physical Theory; 4.11. Convergence of Iterative Processes; 4.12. Perturbation Theory; 4.13. Partial Summation Procedures; Chapter 5. Complex Variables and Analytic Functions; 5.1. Complex Numbers and Polynomial Equations; 5.2. Argand Diagram; 5.3. de Moivre's Theorem; 5.4. Complex Numbers in Physical Problems; 5.5. Differentiation, Analytic Functions; 5.6. Taylor Series for the Complex Variable; 5.7. Analytic Continuation; 5.8. Singularities, Poles, and Residues; 5.9. Quaternions
5.10. Principal Part of an Integral, Kramers-Kronig Relations5.11. Fourier Transforms; 5.12. Truncated Fourier Series for Real Variables; 5.13. Laplace Transform; 5.14. Laplace's Equation; 5.15. Use of Closed Contour Integrals in Physics; Chapter 6. Variational Calculus; 6.1. Stationary and Extreme Values of Ordinary Functions; 6.2. Functionals and Functional Derivatives; 6.3. Variation with Auxiliary Conditions, Lagrange Multipliers; 6.4. Variational Principles in Mechanics; 6.5. Schrödinger Equation and Related Variational Principles; 6.6. Continuous Fields, Wave Equation
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