Xukai Yan

Directed reading and research culminating in the PhD or EdD thesis.Offered for variable credit, 1-9 credit hours, maximum of 24 credit hours.Prerequisite(s): Consent of advisory committee.

Directed reading and research culminating in the master's report or master's thesis.Offered for variable credit, 1-6 credit hours, maximum of 6 credit hours.Prerequisite(s): Consent of advisory committee.

Methods of solution of ordinary differential equations with applications. First order equations, linear equations of higher order, series solutions and Laplace transforms. Combined credit toward a degree for MATH 2233, MATH 3013, and MATH 3263 limited to six hours. Previously offered as MATH 2613.Prerequisite(s): MATH 2153 with grade of 'C' or better.

Directed reading and research culminating in the PhD or EdD thesis.Offered for variable credit, 1-9 credit hours, maximum of 24 credit hours.Prerequisite(s): Consent of advisory committee.

Solution of the standard partial differential equations (Laplace’s equation, transport equation, heat equation, wave equation) by separation of variables and transform methods, including eigenfunction expansions, Fourier and Laplace transform. Boundary value problems, Sturm-Liouville theory, orthogonality, Fourier, Bessel, and Legendre series, spherical harmonics. May not be used for degree credit with MATH 5263.Prerequisite(s): MATH 2163 and MATH 2233 and MATH 3013 with grades of 'C' or better.

Solution of the standard partial differential equations (Laplace’s equation, transport equation, heat equation, wave equation) by separation of variables and transform methods, including eigenfunction expansions, Fourier and Laplace transform. Boundary value problems, Sturm-Liouville theory, orthogonality, Fourier, Bessel, and Legendre series, spherical harmonics. May not be used for degree credit with MATH 4263.Prerequisite(s): MATH 2163 and MATH 2233 and MATH 3013 with grades of 'C' or better.

Methods of solution of ordinary differential equations with applications. First order equations, linear equations of higher order, series solutions and Laplace transforms. Combined credit toward a degree for MATH 2233, MATH 3013, and MATH 3263 limited to six hours. Previously offered as MATH 2613.Prerequisite(s): MATH 2153 with grade of 'C' or better.

Systems of differential equations, series solutions, special functions, elementary partial differential equations, Sturm-Liouville problems, stability and applications. Previously offered as MATH 4653. May not be used for degree credit with MATH 5203.Prerequisite(s): MATH 2233 and MATH 3013 with grades of 'C' or better.

Systems of differential equations, series solutions, special functions, elementary partial differential equations, Sturm-Liouville problems, stability and applications. Previously offered as MATH 4653. May not be used for degree credit with MATH 4233.Prerequisite(s): MATH 2233 and MATH 3013 with grades of 'C' or better.

Directed reading and research culminating in the PhD or EdD thesis.Offered for variable credit, 1-9 credit hours, maximum of 24 credit hours.Prerequisite(s): Consent of advisory committee.

Directed reading and research culminating in the master's report or master's thesis.Offered for variable credit, 1-6 credit hours, maximum of 6 credit hours.Prerequisite(s): Consent of advisory committee.

Directed reading and research culminating in preliminary doctoral research project.Offered for variable credit, 1-6 credit hours, maximum of 6 credit hours.Prerequisite(s): Consent of advisory committee.

A survey of optimization theory and methods for functions of several variables. Unconstrained optimization, gradient methods. Linear programming, simplex method, duality. Nonlinear constrained optimization. May not be used for degree credit with MATH 5503.Prerequisite(s): MATH 2163 and MATH 3013 with grades of 'C ' or better.

A survey of optimization theory and methods for functions of several variables. Unconstrained optimization, gradient methods. Linear programming, simplex method, duality. Nonlinear constrained optimization. May not be used for degree credit with MATH 4553.Prerequisite(s): MATH 2163 and MATH 3013 with grades of 'C ' or better.

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.Prerequisite(s): MATH 4013, MATH 4143 and MATH 4233 or consent of instructor.

Directed reading on advanced topics in mathematics.Offered for variable credit, 1-3 credit hours, maximum of 12 credit hours.Prerequisite(s): Consent of instructor and student's advisory committee.

Methods of solution of ordinary differential equations with applications. First order equations, linear equations of higher order, series solutions and Laplace transforms. Combined credit toward a degree for MATH 2233, MATH 3013, and MATH 3263 limited to six hours. Previously offered as MATH 2613.Prerequisite(s): MATH 2153 with grade of 'C' or better.

Systems of differential equations, series solutions, special functions, elementary partial differential equations, Sturm-Liouville problems, stability and applications. Previously offered as MATH 4653. May not be used for degree credit with MATH 5203.Prerequisite(s): MATH 2233 and MATH 3013 with grades of 'C' or better.

Systems of differential equations, series solutions, special functions, elementary partial differential equations, Sturm-Liouville problems, stability and applications. Previously offered as MATH 4653. May not be used for degree credit with MATH 4233.Prerequisite(s): MATH 2233 and MATH 3013 with grades of 'C' or better.

Schwarz class, tempered distributions, basic linear functional analysis, Holder spaces, Sobolev spaces, spaces involving time, Sobolev inequalities, existence and regularity theory of second-order elliptic, parabolic, and hyperbolic equations, semigroup theory.Prerequisite(s): MATH 5233 or consent of instructor.

A survey of optimization theory and methods for functions of several variables. Unconstrained optimization, gradient methods. Linear programming, simplex method, duality. Nonlinear constrained optimization. May not be used for degree credit with MATH 5503.Prerequisite(s): MATH 2163 and MATH 3013 with grades of 'C ' or better.

A survey of optimization theory and methods for functions of several variables. Unconstrained optimization, gradient methods. Linear programming, simplex method, duality. Nonlinear constrained optimization. May not be used for degree credit with MATH 4553.Prerequisite(s): MATH 2163 and MATH 3013 with grades of 'C ' or better.

Directed reading on advanced topics in mathematics.Offered for variable credit, 1-3 credit hours, maximum of 12 credit hours.Prerequisite(s): Consent of instructor and student's advisory committee.

Methods of solution of ordinary differential equations with applications. First order equations, linear equations of higher order, series solutions and Laplace transforms. Combined credit toward a degree for MATH 2233, MATH 3013, and MATH 3263 limited to six hours. Previously offered as MATH 2613.Prerequisite(s): MATH 2153 with grade of 'C' or better.

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.Prerequisite(s): MATH 4013, MATH 4143 and MATH 4233 or consent of instructor.