Current and Upcoming Courses
MATH 228-2: Multiple Integration and Vector Calculus – Winter 2023
Cylindrical and spherical coordinates, double and triple integrals, line and surface integrals. Change of variables in multiple integrals; gradient, divergence, and curl.
ES_APPM 411-2 : Differential Equations of Mathematical Physics – Winter 2023
Methods for solving linear, ordinary, and partial differential equations of mathematical physics. Green’s functions, distribution theory, integral equations, transforms, potential theory, diffusion equation, wave equation, maximum principles, and variational methods.
ES_APPM 420-2: Asymptotic and Perturbation Methods in Applied Mathematics – Winter 2023
Asymptotic expansions of integrals. Regular and singular perturbation methods for ordinary and partial differential equations. Boundary layer theory. Matched asymptotic expansions. Homogenization. Two-time and uniform expansions. Wave propagation and WKBJ method. Turning point theory. Nonlinear oscillations. Bifurcation and stability theory.
Past Courses
ES_APPM 426: Theory of Flows with Small Inertia – Winter 2022
Asymptotic methods for flows with small inertia: flows past bodies, matching procedures. Slowly varying flows: lubrication theory, Hele-Shaw flow; swimming of microorganisms, suspension of particles.
ES_APPM 411-1: Differential Equations of Mathematical Physics – Fall 2021
Methods for solving linear, ordinary, and partial differential equations of mathematical physics. Green’s functions, distribution theory, integral equations, transforms, potential theory, diffusion equation, wave equation, maximum principles, and variational methods.
ES_APPM 449: Numerical Methods for Moving Interfaces – Fall 2021
Methods for simulating sharp interfaces. Marker particle, level set, fast marching, volume of fluid, and phase field methods.
ES_APPM 447: Boundary Integral Method – Spring 2021
Numerical solution of Fredholm and Volterra integral equations. Boundary integral equations. Greens functions. Boundary element and singularity methods. Vortex methods. Free boundary problems. Applications to problems in science and engineering.
ES_APPM 445: Iterative Methods for Elliptic Equations– Winter 2021/Spring 2019
Analysis and application of numerical methods for solving elliptic equations. Stationary iterative, multigrid, conjugate gradient, GMRES methods, and preconditioners.
ES_APPM 411-2: Differential Equations of Mathematical Physics – Winter 2021/Winter 2020
Methods for solving linear, ordinary, and partial differential equations of mathematical physics. Green’s functions, distribution theory, integral equations, transforms, potential theory, diffusion equation, wave equation, maximum principles, and variational methods.
ES_APPM 421-1: Models in Applied Mathematics – Fall 2019/Fall 2017
Applications to illustrate typical problems and methods of applied mathematics. Mathematical formulation of models for phenomena in science and engineering, problem solution, and interpretation of results. Examples from solid and fluid mechanics, combustion, diffusion phenomena, chemical, and nuclear reactors, and biological processes.
Es_APPM 426: Theory of Flows with Small Inertia – Fall 2019
Asymptotic methods for flows with small inertia: flows past bodies, matching procedures. Slowly varying flows: lubrication theory, Hele-Shaw flow; swimming of microorganisms, suspension of particles.
ES_APPM 420-1: Asymptotic and Perturbation Methods in Applied Mathematics – Fall 2018
Asymptotic expansions of integrals. Regular and singular perturbation methods for ordinary and partial differential equations. Boundary layer theory. Matched asymptotic expansions. Homogenization. Two-time and uniform expansions. Wave propagation and WKBJ method. Turning point theory. Nonlinear oscillations. Bifurcation and stability theory.
ES_APPM 206-4: Honors Engineering Analysis IV
Solution methods for ordinary differential equations, including exact, numerical, and qualitative methods. Applications and modeling principles; solution techniques. Covers topics at a deeper level.
ES_APPM 411-3: Differential Equations in Mathematical Physics – Spring 2017
Methods for solving linear, ordinary, and partial differential equations of mathematical physics. Green’s functions, distribution theory, integral equations, transforms, potential theory, diffusion equation, wave equation, maximum principles, and variational methods.
GEN_ENG 205-4: Engineering Analysis IV – Fall 2015
Solution methods for ordinary differential equations, including exact, numerical, and qualitative methods. Applications and modeling principles; solution techniques.
ES_APPM 311-1: Methods of Applied Mathematics – Fall 2014/Fall 2013
Ordinary differential equations; Sturm-Liouville theory, properties of special functions, solution methods including Laplace transforms. Fourier series: eigenvalue problems and expansions in orthogonal functions. Partial differential equations: classification, separation of variables, solution by series and transform methods.