This course introduces students to the concepts, techniques, and central theorems of vector calculus. It includes a study of line integrals, conservative vector fields, the flux of vector fields across curves and surfaces, Green’s Theorem, the Divergence Theorem, and Stokes’ Theorem. Credit may not be earned for this class if it is earned in COS-MATH-221.

Dissertation research by the candidate for an appropriate topic as arranged between the candidate and the research advisor.

Masters-level research by the candidate on an appropriate topic as arranged between the candidate and the research advisor.

This course is an introduction to the basic concepts of linear algebra, and techniques of matrix manipulation. Topics include linear transformations, Gaussian elimination, matrix arithmetic, determinants, vector spaces, linear independence, basis, null space, row space, and column space of a matrix, eigenvalues, eigenvectors, change of basis, similarity and diagonalization. Various applications are studied throughout the course.

Continuation of Thesis

The study of the dynamics of fluids is a central theme of modern applied mathematics. It is used to model a vast range of physical phenomena and plays a vital role in science and engineering. This course provides an introduction to the basic ideas of fluid dynamics, with an emphasis on rigorous treatment of fundamentals and the mathematical developments and issues. The course focuses on the background and motivation for recent mathematical and numerical work on the Euler and Navier-Stokes equations, and presents a mathematically intensive investigation of various models equations of fluid dynamics.

This course is a faculty-directed tutorial of appropriate topics that are not part of the formal curriculum. The level of study is appropriate for student in their final two years of study.