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Course Criteria
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3.00 Credits
Exposure to UMD mathematics-related colloquia. Sixteen points required: one for attending a colloquium; one for writing an acceptable report on a colloquium (at least four must be earned through writing); up to eight for giving a colloquium.
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3.00 Credits
Topics not available in standard curriculum.
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3.00 Credits
(3 cr; QP-3350, 3699; SP-3280; A-F only) Complex numbers and analytic functions; complex integration; complex power series, Taylor series, and Laurent series; theory of residues; conformal mapping.
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3.00 Credits
(3 cr; QP-3380; SP-3280; A-F only) Laplace transform; Fourier series, integrals, and transforms; Sturm-Liouville operator- and boundaryvalue problems; orthogonal functions; operator solutions of partial differential equations.
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6.00 Credits
Systems of linear equations, matrix algebra, determinants, vector spaces, subspaces, linear independence, span, basis, coordinates, linear transformations, matrix representations of linear transformations, eigenvalues and eigenvectors, diagonalization, Gram-Schmidt orthogonalization, orthogonal projection and least squares.
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3.00 Credits
(3 cr; QP-1297, 3320, proficiency in FORTRAN or Pascal; SP-3280 or 4326, proficiency in FORTRAN or C or C++) Computer representation of numbers; sources of error; introduction to interpolation, approximation, numerical integration, solution of linear and nonlinear systems, initial-value problem approximation; use of computer software.
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3.00 Credits
Limits, sequence and series of real numbers, tests for convergence, rearrangements, summability, and the class [l][2]. Metric spaces; continuous functions, connectedness, completeness, compactness. Banach fixed-point theorem and Piccard existence theorem for differential equations.
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3.00 Credits
Introduction to control theory of linear systems. Controllability, stabilizability, linear quadratic regulator problem. (offered alt yrs)
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3.00 Credits
Fundamentals of differential equations (existence, uniqueness, continuation of solutions); linear systems, autonomous systems, and Poincare-Bendixson theory; periodic systems; discrete dynamical systems; bifurcation theory; chaos. (offered alt yrs)
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3.00 Credits
Application and analysis of continuous and discrete dynamical systems. Model construction, simulation, and interpretation. (offered alt yrs)
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