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Hi guys, I am trying to decide between these two courses. Which one is more useful for a physics major?
MATH 481 Intro to Differential Geometry (Vector and Tensor Analysis)
The basic tools of differential geometry will be introduced at the undergraduate level, by focusing on examples. This is a good first course for those interested in, or curious about, modern differential geometry, and in applying differential geometric methods to other areas.
Manifolds: configuration spaces, differentiable manifolds, tangent spaces, tangent bundles, orientability.
Calculus on manifolds: Vector fields, flows, tensor fields.
Differential forms and exterior calculus.
Integration theory: Generalized Stokes theorem, de Rham cohomology.
Riemannian geometry: Riemannian metrics, geodesics.
Text: The Geometry of Physics, An Introduction, T. Frankel, Cambridge U.P. 1997
Or
CS 457 Numerical Methods II
Orthogonalization methods for linear least squares problems. QR factorization and singular value decomposition
Iterative methods for systems of linear algebraic equations. Stationary iterative methods. Krylov subspace methods
Eigenvalue problems. Power, inverse power, and QR iterations. Krylov subspace methods
Nonlinear equations and optimization in n dimensions. Newton and Quasi-Newton methods. Nonlinear least squares
Initial and boundary value problems for ordinary differential equations. Accuracy and stability. Multistep methods for initial value problems. Shooting, finite difference, collocation, and Galerkin methods for boundary value problems
Partial differential equations. Finite difference methods for heat, wave, and Poisson equations. Consistency, stability, and convergence
Fast Fourier transform. Trigonometric interpolation. Discrete Fourier transform. FFT algorithm
MATH 481 Intro to Differential Geometry (Vector and Tensor Analysis)
The basic tools of differential geometry will be introduced at the undergraduate level, by focusing on examples. This is a good first course for those interested in, or curious about, modern differential geometry, and in applying differential geometric methods to other areas.
Manifolds: configuration spaces, differentiable manifolds, tangent spaces, tangent bundles, orientability.
Calculus on manifolds: Vector fields, flows, tensor fields.
Differential forms and exterior calculus.
Integration theory: Generalized Stokes theorem, de Rham cohomology.
Riemannian geometry: Riemannian metrics, geodesics.
Text: The Geometry of Physics, An Introduction, T. Frankel, Cambridge U.P. 1997
Or
CS 457 Numerical Methods II
Orthogonalization methods for linear least squares problems. QR factorization and singular value decomposition
Iterative methods for systems of linear algebraic equations. Stationary iterative methods. Krylov subspace methods
Eigenvalue problems. Power, inverse power, and QR iterations. Krylov subspace methods
Nonlinear equations and optimization in n dimensions. Newton and Quasi-Newton methods. Nonlinear least squares
Initial and boundary value problems for ordinary differential equations. Accuracy and stability. Multistep methods for initial value problems. Shooting, finite difference, collocation, and Galerkin methods for boundary value problems
Partial differential equations. Finite difference methods for heat, wave, and Poisson equations. Consistency, stability, and convergence
Fast Fourier transform. Trigonometric interpolation. Discrete Fourier transform. FFT algorithm