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AST 392D · Mathematical Techniques in Astronomy    1   2   3  

The weekly assignments will count for 50 percent of your grade, exams will count 30 percent and class participation will count for 20 percent. There will be no exams, and there will be no late problem sets! Because of the nature of your interests in astronomy may make your interest in a particular subject or subjects nearly zero, and because of the realities of observing runs and conferences which are part of the life of every active professional astrophysicist, you will have two "passes" or as Yancy Shirley put it, two "get out of jail free" cards. You can use these to excuse yourself from any two weekly (or sections) assignments and class participation.

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

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13 June 2003
Astronomy Program · The University of Texas at Austin · Austin, Texas 78712
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