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AST 392D · Mathematical Methods in Astrophysics    1   2   3  

Current Detailed Contents (Subject to Revision)
  1. Vector Analysis
    1. A Brief review of Vector Analysis: Gradient, Divergence Curl, and Integrations
    2. Some Useful Theorems: Gauss', Stokes', and Helmholtz's

  2. Vector Spaces and Matrices
    1. Linear Vector Spaces
    2. Linear Operators
    3. Introduction to Matrices
    4. Coordinate Transformations
    5. Eigenvalue Problems
    6. Diagonalization of Matrices
    7. Spaces of Infinite Dimensionality, Hilbert Spaces

  3. An Introduction to Tensor Analysis and Differential Geometry
    1. Cartesian Tensors in Three-Space
    2. Coordinate Transformations and General Tensor Analysis
    3. The Metric Tensor
    4. Geodesics
    5. Christoffel Symbols
    6. Covariant Derivatives
    7. Parallel Transport
    8. Geodesics Through Parallel Transport
    9. The Riemann-Christoffel Curvature Tensor
    10. Parallel Transport around a Closed Loop and Curvature
    11. The Absolute Derivative, Geodesic Deviation and Curvature
  4. Calculus of Variations
    1. Euler-Lagrange Equation
    2. Generalizations of the Basic Problem

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

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

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