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Linear algebra in R^n, standard Euclidean inner product in R^n, general linear spaces, general inner product spaces, least squares, determinants, eigenvalues and eigenvectors, symmetric matrices.
This course includes topics on professional development and responsible conduct of research. The course satisfies the GT RCR Academic Policy for Doctoral Students to complete in-person RCR training.
Scientific computational algorithms on vector and parallel computers. Speedup, algorithm complexity, interprocesses communication, synchronization, modern algorithms for linear systems, programming techniques, code optimization.
Fourier series, Fourier integrals, boundary value problems for partial differential equations, eigenvalue problems
A broad introduction to the local and global behavior of nonlinear dynamical systems arising from maps and ordinary differential equations.
The theory of curves, surfaces, and more generally, manifolds. Curvature, parallel transport, covariant differentiation, Gauss-Bonet theorem
Point set topology, topological spaces and metric spaces, continuity and compactness, homotopy and covering spaces
Method of characteristics for first and second order partial differential equations, conservation laws and shocks, classification of second order systems and applications.
Topics from complex function theory, including contour integration and conformal mapping
Differentiation of functions of one real variable, Riemann-Stieltjes integral, the derivative in R^n and integration in R^n
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