# Courses

## Required Core Courses (M.S. and Ph.D.)

#### MATH 221: Advanced Ordinary Differential Equations

Introduces advanced topics in the theory of ordinary differential equations (ODEs). This course emphasizes conceptual understanding and critical thinking. It will include simplified problems from physics and other disciplines to motivate certain topics.

#### MATH 222: Partial Differential Equations

Elements of the theory of PDEs. Topics include solving first order PDEs using the method of characteristics, determining the existence, uniqueness, and well-posedness of solution of PDEs, and solving linear second order PDEs using the methods of separation of variables and Fourier series for boundary value problems and Sturm-Liouville theory.

Prerequisite: MATH 221

#### MATH 231: Numerical Solution of Differential Equations I

Focuses on construction and analysis of numerical methods that solve common problems in science and engineering.

#### MATH 232: Numerical Solution of Differential Equations II

Fundamental methods are used as a base for discussing modern methods for solving partial-differential equations. Numerical methods include variational, finite element, collocation, spectral, and FFT. Error estimates and implementation issues are discussed.

Prerequisite: MATH 231

#### MATH 223: Asymptotics and Perturbation Methods

Asymptotic evaluation of integrals, matched asymptotic expansions, multiple scales, WKB, and homogenization. Applications are made to ODEs, PDEs, difference equations, and integral equations to study boundary and shock layers, nonlinear wave propagation, bifurcation and stability, and resonance.

Prerequisite: MATH 221

#### MATH 201: Teaching and Learning in the Sciences

Students will be introduced to ‘scientific teaching’ - an approach to teaching science that uses many of the same skills applied in research. Topics will include how people learn, active learning, designing, organizing and facilitating teachable units, classroom management, diversity in the classroom and assessment design.

#### MATH 291: Applied Mathematics Seminar

Seminar series covering various topics in applied mathematics presented by faculty, graduate students, and visiting speakers.

## Required Courses (Ph.D.)

#### MATH 224: Advanced Methods of Applied Mathematics

Basic real analysis (metric spaces, continuity, contraction mapping theorem), Banach spaces, Hilbert spaces, linear operators, bounded operators, compact operators, spectral theory, distributions, Fourier transforms, a priori estimates, energy estimates, existence/uniqueness theory, variational calculus, and applications of the above material to concrete problems in applied mathematics.

Prerequisite: MATH 221 and MATH 222

#### MATH 233: Scientific Computing

Theoretical and practical introduction to parallel scientific computing. Survey of hardware and software environments, and selected algorithms and applications. Topics will include linear systems, N-body problems, FFTs, and methods for solving PDEs. Practical implementation and performance analysis are emphasized in the context of demonstrative applications in science and engineering.

Prerequisite: MATH 232

## Other Courses

#### MATH 292: Special Topics in Applied Mathematics

Treatment of a special topic or theme in applied mathematics at the graduate level. May be repeated for credit in a different subject area.

Supervised research.

#### MATH 298: Directed Group Study

Group project under faculty supervision.

#### MATH 243: Interdisciplinary Computational Graduate Education

Focuses on teaching first-year graduate students from a variety of graduate programs skills in computational methods, programming languages, team science, project development, problem solving, social networking, and career preparation.