
AST 392D · Mathematical Techniques in Astronomy 
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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)
 Vector Analysis
 A Brief review of Vector Analysis: Gradient, Divergence Curl, and Integrations
 Some Useful Theorems: Gauss', Stokes', and Helmholtz's
 Vector Spaces and Matrices
 Linear Vector Spaces
 Linear Operators
 Introduction to Matrices
 Coordinate Transformations
 Eigenvalue Problems
 Diagonalization of Matrices
 Spaces of Infinite Dimensionality, Hilbert Spaces
 An Introduction to Tensor Analysis and Differential Geometry
 Cartesian Tensors in ThreeSpace
 Coordinate Transformations and General Tensor Analysis
 The Metric Tensor
 Geodesics
 Christoffel Symbols
 Covariant Derivatives
 Parallel Transport
 Geodesics Through Parallel Transport
 The RiemannChristoffel Curvature Tensor
 Parallel Transport around a Closed Loop and Curvature
 The Absolute Derivative, Geodesic Deviation and Curvature

