department of astronomy - courses  
home dept of astronomy mcdonald observatory research hobby-eberly telescope directory university of texas  
home
department of astronomy
mcdonald observatory
research
hobby-eberly telescope
directory
university of texas
  
 
AST 392D · Mathematical Techniques in Astronomy    1   2   3  


  1. Calculus of Variations
    1. Euler-Lagrange Equation
    2. Generalizations of the Basic Problem

  2. Infinite Series
    1. Fundamental Concepts
    2. Convergence Tests
    3. Familiar Series
    4. Taylor's Expansion
    5. Transformation of Series

  3. Complex Analysis Part I: Analytic Functions
    1. Complex Algebra
    2. Cauchy-Riemann Conditions
    3. Cauchy's Integral Theorem and Formula
    4. Laurent Expansions

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

  5. Probability and Statistics
    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

  6. 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

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

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

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

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


   1   2   3  
 



13 June 2003
Astronomy Program · The University of Texas at Austin · Austin, Texas 78712
prospective student inquiries: studentinfo@astro.as.utexas.edu
site comments: www@www.as.utexas.edu