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Mathematics (MATH)
MATH 5043 Advanced Calculus I Prerequisites: MATH 2163, MATH 3013, and MATH 4023 with grades of “C” or better; grades of “B” or better recommended. Description: A rigorous treatment of calculus for functions of one and several variables. Elementary topology of Euclidean and metric spaces, continuity and uniform continuity, differentiation and integration in one variable. Meets with MATH 4143. May not be used for degree credit with MATH 4143. Credit hours: 3 Contact hours: Lecture: 3 Levels: Graduate Schedule types: Lecture Department/School: Mathematics MATH 5053 Advanced Calculus II Prerequisites: A grade of “C” or better in one of MATH 4143 or MATH 5043; grade of “B” or better recommended. Description: Continuation of MATH 5043. A rigorous treatment of sequences and series of functions, uniform convergence, and differentiation and integration of vector-valued functions. Meets with MATH 4153. May not be used for degree credit with MATH 4153. Credit hours: 3 Contact hours: Lecture: 3 Levels: Graduate Schedule types: Lecture
MATH 5193 Differentiable Manifolds Prerequisites: MATH 4153 or MATH 5053; recommended MATH 4343 or MATH 5303. Description: Differentiable manifolds and maps, tangent vectors, vector fields, integral curves, submanifolds, differential forms, and integration. Additional topics may be selected from: flows, Lie derivatives, the Frobenius theorem, structures defined by differential forms, vector bundles and de Rham theory. Credit hours: 3 Contact hours: Lecture: 3 Levels: Graduate Schedule types: Lecture Department/School: Mathematics
MATH 5213 Fourier Analysis and Wavelets Prerequisites: MATH 4013 or MATH 4023.
Description: Orthogonal series expansions, Fourier series and integrals and boundary value problems. Haar wavelets and multiresolution analysis. Applications. Credit hours: 3 Contact hours: Lecture: 3 Levels: Graduate Schedule types: Lecture Department/School: Mathematics MATH 5233 Partial Differential Equations Prerequisites: MATH 4013, MATH 4143 and MATH 4233 or consent of instructor. Description: Representation formulas for solutions of transport equation, Laplace's equation, heat equation and wave equation, mean value theorems, maximum principle, Green's functions, characteristics, eigenvalue problems, separation of variables, transform methods, variational methods, general theory of first order equations. Credit hours: 3 Contact hours: Lecture: 3 Levels: Graduate Schedule types: Lecture Department/School: Mathematics MATH 5243 Ordinary Differential Equations Prerequisites: MATH 4143 or MATH 5043; MATH 4233; MATH 5023. Description: Banach space, contraction mapping principle, existence and uniqueness theorems, linear systems, higher-order linear equations, boundary value and eigenvalue problems, stability and asymptotic behavior, attractors, Gronwall's inequality, Liapunov method. Credit hours: 3 Contact hours: Lecture: 3 Levels: Graduate Schedule types: Lecture Department/School: Mathematics MATH 5253 Advanced Ordinary Differential Equations Prerequisites: MATH 5243. Description: Selected topics in ordinary differential equations. Credit hours: 3 Contact hours: Lecture: 3 Levels: Graduate Schedule types: Lecture Department/School: Mathematics
Department/School: Mathematics MATH 5133 Stochastic Processes Prerequisites: MATH 2233, MATH 3013 and STAT 5123.
Description: Definition of stochastic processes, probability structure, mean and covariance function, the set of sample functions, stationary processes and their spectral analysis, renewal processes, counting analysis, discrete and continuous Markov chains, birth and death processes, exponential model, queuing theory. Same course as IEM 5133 & STAT 5133. Credit hours: 3 Contact hours: Lecture: 3 Levels: Graduate Schedule types: Lecture Department/School: Mathematics MATH 5143 Real Analysis I Prerequisites: MATH 4153 or MATH 5053. Description: Measure theory, measurable functions, integration and differentiation with respect to measures. Credit hours: 3 Contact hours: Lecture: 3 Levels: Graduate Schedule types: Lecture Department/School: Mathematics
MATH 5153 Real Analysis II Prerequisites: MATH 5143.
Description: Aspects of point set topology: nets, locally compact spaces, product spaces, Stone-Weierstrass theorem. Elementary functional analysis: Hahn-Banach, uniform boundedness, and open mapping theorems, Hilbert spaces. Riesz representation theorems: duals of Lebesgue spaces and spaces of continuous functions. Credit hours: 3 Contact hours: Lecture: 3 Levels: Graduate Schedule types: Lecture Department/School: Mathematics
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