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Course Criteria
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3.00 Credits
(3:3:0) Prerequisite: MATH 3360 or consent of instructor. Groups, rings, fields, linear algebra, Galois theory.
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3.00 Credits
(3:3:0) Prerequisite: MATH 4351, 4354, or consent of instructor. Existence and uniqueness results, continuation of solutions, continuous dependence on data, linear equations, oscillation and comparison theorems, boundary value problems, and stability analysis.
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3.00 Credits
(3:3:0) Prerequisite: MATH 5330 or consent of instructor. Advanced existence, uniqueness, continuation, and continuity results; symmetry and variance; center manifold theorem.
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3.00 Credits
(3:3:0) Prerequisite: MATH 4351, 4354, or consent of instructor. Topics include first order equations, method of characteristics, parabolic, hyperbolic and elliptic equations, variational and Hilbert space methods.
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3.00 Credits
(3:3:0). Prerequisite: MATH 4351, 4354, or consent of instructor. Topics include first order equations, method of characteristics, parabolic, hyperbolic and elliptic equations, variational and Hilbert space methods.
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3.00 Credits
(3:3:0) Prerequisite: MATH 5316 or equivalent. Stability and error analysis, numerical solution of ordinary and partial differential equations, integral equations.
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3.00 Credits
(3:3:0) Prerequisite: MATH 5316 or equivalent. Stability and error analysis, numerical solution of ordinary and partial differential equations, integral equations.
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3.00 Credits
(3:3:0) Prerequisite: MATH 5322. Hilbert and Banach space theory, linear operator theory, the closed graph theorem, the open mapping theorem, the principle of uniform boundedness, linear functionals, dual spaces and weak topologies, distribution theory, topological vector spaces, spectral theory of compact and unbounded self-adjoint and unitary operators, and semigroup theory.
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3.00 Credits
(3:3:0) Prerequisite: MATH 5322. Hilbert and Banach space theory, linear operator theory, the closed graph theorem, the open mapping theorem, the principle of uniform boundedness, linear functionals, dual spaces and weak topologies, distribution theory, topological vector spaces, spectral theory of compact and unbounded self-adjoint and unitary operators, and semigroup theory.
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3.00 Credits
(3:3:0) Prerequisite: Consent of instructor. Current topics in analysis. May be repeated for credit.
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