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...

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Main Author: Mahan, Gerald D.
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY Springer US 2002, 2002
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