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AST 392D · Mathematical Methods in Astrophysics    1   2   3  

  1. Complex Analysis Part II: Calculus of Residues
    1. Singularities
    2. Calculus of Residues
    3. The Evaluation of Real Integrals

  2. Probability and Statistics
    tethys and dione
    1. Introduction
    2. Fundamental Probability Laws
    3. Combinations and Permutations
    4. The Binomial, Poisson, and Gaussian Distributions
    5. General Properties of Distributions
    6. Fitting of Exprimental Data

  3. Eigenfunctions, Eigenvalues, and Green's Functions
    1. Simple Examples of Eigenvalue Problems
    2. General Discussion
    3. Solutions of Boundary-Value Problems as Eigenfunction Expansions
    4. Inhomogeneous Problems, Green's Functions
    5. Green's Functions in Electrodynamics

  4. Evaluations of Integrals
    1. Elementary Methods
    2. Use of Symmetry Arguments
    3. Contour Integration
    4. Tabulated Integrals
    5. Approximate Expansions
    6. Saddle-Point Methods

  5. Integral Transforms
    1. Fourier Series
    2. Fourier Transforms
    3. Laplace Transforms
    4. Other Transform Pairs
    5. Applications of Integral Transforms

  6. Perturbation Theory
    1. Conventional Nondegenerate Theory
    2. A Rearranged Series
    3. Degenerate Perturbation Theory

  7. Special Functions
    1. Legendre Functions
    2. Bessel Functions
    3. Hypergeometric Functions
    4. Confluent Hypergeometric Functions
    5. Mathieu Functions
    6. Elliptic Functions

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31 August 2005
Astronomy Program · The University of Texas at Austin · Austin, Texas 78712
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