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Course Criteria
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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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3.00 Credits
Introduction, emphasizing use of Fourier series, Green's functions, and other classical techniques.
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3.00 Credits
Vector spaces over fields, subspaces, linear transformations, matrix representations, change of basis, inner-product spaces, singular value decomposition, eigenspaces, diagonalizability, annihilating polynomials, Jordan form.
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3.00 Credits
Properties of integers, primes, divisibility, congruences, and quadratic reciprocity. Computational aspects include factoring algorithms and RSA cryptosystem. (offered alt yrs)
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3.00 Credits
Finite graphs, including trees, connectivity, traversability, planarity, colorability, labeling, and matchings.
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3.00 Credits
Permutations, combinations, binomial coefficients, inclusion-exclusion, recurrence relations, ordinary and exponential generating functions, Catalan numbers, selected topics from designs, finite geometries, Polya's enumeration formula.
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