3214: Fundamental calculus of functions of two or more variables. Typical vector calculus topics include the implicit function theorem, Taylor expansion, line integrals, Green's theorem, surface integrals, Lagrange multipliers, and their applications. MATH 2224 is a prerequisite.
5466: The second semeseter of Numerical Analysis emphasizes elements of approximation theory such as approximation by polynomials, quadrature, as well as nonlinear equations and optimization and an overview of numerical methods for ordinary differential equations. MATH 5465 is not a prerequisite, but students should be familiar with analysis and implementation of numerical algorithms.
In the fall semester, I am scheduled to teach MATH 5545 (Calculus of Variations and Optimal Control) as well as the one semester course: Principles and Techniques of Applied Mathematics.
My research is in the development and analysis of computational tools for optimal design and control of nonlinear PDEs (usually Navier-Stokes equations). This covers a wide range of areas. A partial list is given below.
- Sensitivity Analysis:
- Adaptive Finite Element Calculations,
- Automatic Differentiation,
- Nearby Solutions,
- Uncertainty Quantification
- Optimal Design Algorithms:
- Convergence Theory Based on Asymptotic Consistency,
- Forebody Simulator Design Problem,
- Parameter Estimation
- Computational Methods for Control of PDEs:
- Approximation to PDE Riccati Equations,
- Data Assimilation,
- Optimal Actuator and Sensor Placement
- Model Reduction Methods:
- Principal Interval Decomposition,
- Proper Orthogonal Decomposition,
- Extensions to Parameter Dependent Models,
- Extensions to Complex Turbulent Flows,
- Fluid Flow Control
- Applied Mathematics / Computational Science:
- Design of Energy Efficient Buildings,
- Optimal Zonation for Groundwater Models
A more complete description of my research can be found here.