Applied Mathematics
This volume is a textbook for a year-long graduate level course in All research universities have applied mathematics for scientists and engineers. such a course, which could be taught in different departments, such as mathematics, physics, or engineering. I volunteered to teach this course when I r...
Main Author: | |
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Format: | eBook |
Language: | English |
Published: |
New York, NY
Springer US
2002, 2002
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Edition: | 1st ed. 2002 |
Subjects: | |
Online Access: | |
Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1. Determinants
- 1.1. Cramer’s Rule
- 1.2. Gaussian Elimination
- 1.3. Special Determinants
- 2. Matrices
- 2.1. Several Theorems
- 2.2. Linear Equations
- 2.3. Inverse of a Matrix
- 2.4. Eigenvalues and Eigenvectors
- 2.5. Unitary Transformations
- 2.6. Hon-Hermitian Matrices
- 2.7. A Special Matrix
- 2.8. Gram-Schmidt
- 2.9. Chains
- 3. Group Theory
- 3.1. Basic Properties of Groups
- 3.2. Group Representations
- 3.3. Characters
- 3.4. Direct Product Groups
- 3.5. Basis Functions
- 3.6. Angular Momentum
- 3.7. Products of Representations
- 3.8. Quantum Mechanics
- 3.9. Double Groups
- 4. Complex Variables
- 4.1. Introduction
- 4.2. Analytic Functions
- 4.3. Multivalued Functions
- 4.4. Contour Integrals
- 4.5. Meromorphic Functions
- 4.6. Higher Poles
- 4.7. Integrals Involving Branch Cuts
- 4.8. Approximate Evaluation of Integrals
- 5. Series
- 5.1. Taylor Series
- 5.2. Convergence
- 5.3. Laurent Series
- 5.4. Meromorphic Functions
- 5.5. Asymptotic Series
- 5.6. Summing Series
- 5.7. Padé Approximants
- 6. Conformal Mapping
- 6.1. Laplace’s Equation
- 6.2. Mapping
- 6.3. Examples
- 6.4. Schwartz-Christoffel Transformations
- 6.5. van der Pauw
- 7. Markov Averaging
- 7.1. Random Walk
- 7.2. Speckle
- 7.3. Inhomogeneous Broadening
- 8. Fourier Transforms
- 8.1. Fourier Transforms
- 8.2. Laplace Transforms
- 8.3. Wavelets
- 9. Equations of Physics
- 9.1. Boundary and Initial Conditions
- 9.2. Boltzmann Equation
- 9.3. Solving Differential Equations
- 9.4. Elliptic Integrals
- 10. One Dimension
- 10.1. Introduction
- 10.2. Diffusion Equation
- 10.3. Wave Equation
- 11. Two Dimensions
- 11.1. Rectangular Coordinates
- 11.2. Polar Coordinates
- 12. Three Dimensions
- 12.1. Cartesian Coordinates
- 12.2. Cylindrical Coordinates
- 12.3. Spherical Coordinates
- 12.4. Problems Inside a Sphere
- 12.5. Vector Wave Equation
- 13. Odds and Ends
- 13.1. Hypergeometric Functions
- 13.2. Orthogonal Polynomials
- 13.3. Sturm-Liouville
- 13.4. Green’s Functions
- 13.5. Singular Integral Equations