Appendix A - Courses
Mathematics
|
MATH*6011 Dynamical Systems I U [0.50]
|
| Basic theorems on existence, uniqueness and differentiability; phase space, flows, dynamical systems; review of linear systems, Floquet theory; Hopf bifurcation; perturbation theory and structural stability; differential equations on manifolds. Applications drawn from the biological, physical, and social sciences. |
|
MATH*6012 Dynamical Systems II U [0.50]
|
| The quantitative theory of dynamical systems defined by differential equations and discrete maps, including: generic properties; bifurcation theory; the center manifold theorem; nonlinear oscillations, phase locking and period doubling; the Birkhoff-Smale homoclinic theorem; strange attractors and deterministic chaos. |
|
MATH*6021 Optimization I U [0.50]
|
| A study of the basic concepts in: linear programming, convex programming, non-convex programming, geometric programming and related numerical methods. |
|
MATH*6031 Functional Analysis U [0.50]
|
| Review of metric, normed, and inner product spaces; Banach contraction principle; brief introduction to measure and integration; elementary Fourier analysis; adjoint and compact operators; nonlnear operators and the Frechet derivative; Baire category theorem; principle of uniform boundedness; open mapping theorem; principle ot uniform boundedness; closed graph theorem. |
|
MATH*6041 Partial Differential Equations I U [0.50]
|
| Classification of partial differential equations. The Hyperbolic type, the Cauchy problem, range of influence, well- and ill-posed problems, successive approximation, the Riemann function. The elliptic type: fundamental solutions, Dirichlet and Neumann problems. The parabolic type: boundary conditions, Green's functions and separation of variables. Introduction to certain non-linear equations and transformations methods. |
|
MATH*6071 Biomathematics U [0.50]
|
| The application of mathematics to model and analyze biological systems. Specific models to illustrate the different mathematical approaches employed when considering different levels of biological function. |
|
MATH*6181 Topics in Applied Mathematics I U [0.50]
|
| This course provides graduate students, either individually or in groups, with the opportunity to pursue topics in applied mathematics under the guidance of graduate faculty. Course topics will normally be advertised by faculty in the semester prior to their offering. Courses may be offered in any of lecture, reading/seminar, or individual project formats. |
|
MATH*6182 Topics in Applied Mathematics II U [0.50]
|
| This course provides graduate students, either individually or in groups, with the opportunity to pursue topics in applied mathematics under the guidance of graduate faculty. Course topics will normally be advertised by faculty in the semester prior to their offering. Courses may be offered in any of lecture, reading/seminar, or individual project formats. |
|
MATH*6400 Numerical Analysis I U [0.50]
|
| Topics selected from numerical problems in: matrix operations, interpolation, approximation theory, quadrature, ordinary differential equations, partial differential equations, integral equations, nonlinear algebraic and transcendental equations. |
|
