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Course Criteria
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3.00 Credits
Prerequisite: MATH 4224 or consent of department. Topics in modern linear and nonlinear partial differential equations, distributions and weak solutions, method of characteristics, shock waves, Green functions, fixed point theorems, reaction diffusion equations.
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3.00 Credits
Prerequisites: MATH 4224 or consent of department; Mathematics 4230 is recommended; some knowledge of computer programming is required. Galerkin method, linear triangular elements, bilinear rectangular elements, axisymmetric elements, isoparametric elements, heat transfer by conduction and convection, torsion of noncircular sections, ground water with sources and sinks, biharmonic equation, vibration of membrane, iterative methods, software maintenance and development.
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3.00 Credits
Prerequisite: MATH 4102 or consent of department. Topics will be selected from the following: metric spaces, normed spaces, Banach spaces, functionals, dual spaces and weak topology, inner product spaces, Hilbert spaces, compact operators, spectral analysis, fixed point theorems, implicit function theorem, Fredholm theory.
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3.00 Credits
Prerequisite: MATH 4252 or consent of department. Existence and approximation theorems for ordinary differential equations and systems of ordinary differential equations. Convergence, stability, and error analysis.
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3.00 Credits
Prerequisites: MATH 2115, 2221 and 2511 or consent of department; Mathematics 4101 is recommended; some knowledge of computer programming is required. Introduction to finite difference methods for solving partial differential equations. Convergence, consistency, stability, description and analysis of various explicit and implicit schemes for paraboilc and hyperbolic equations.
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3.00 Credits
Prerequisites: MATH 2221 and 4102 or consent of department. The calculus of variations and the Pontryagin maximum principle. Optimal control of linear and nonlinear systems. Algorithms for computing optimal controls.
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3.00 Credits
Prerequisite: MATH 4101 or consent of department; Mathematics 4270 is recommended. Theory and application of advanced computational methods for extremizing linear and nonlinear functions of many variables including constrained and unconstrained problems. Particular topics include a review of the simplex method an introduction to interior point methods for linear programming problems, descent methods, Newton-like methods, conjugate direction methods, and quadratic and nonlinear programming.
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3.00 Credits
Prerequisite: consent of department.
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3.00 Credits
Prerequisites: Previous experience using the SAS statistical package or consent of department. Proc IML, SAS macros and applications, Monte Carlo methods, resampling methods including bootstrap and jackknife, selected SAS procedures, statistical report writing with SAS.
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3.00 Credits
Prerequisite: MATH 4301 or consent of department. Only one of MATH 4301 or 6301 may be counted toward a master's degree in mathematics. Data analysis, analysis of variance, regression analysis, nonparametric methods, use of computer packages.
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