Course Materials

Materials for current courses will be posted here at the appropriate time, and past courses will be archived for posterity. If you would like to use these assignments in your own courses please contact me.

GraduatE Courses

Computational PDEs, NYU, Spring 2021

This course can be thought of as the third part of the Numerical Methods series meant to introduce Ph.D. students in mathematics to the computational methods for solving classical PDEs.Test This class largely supersedes the Computational Fluid Dynamics (CFD) class I taught in the past; the new lecture notes are cleaned up and improved.

Numerical Methods II, NYU, Spring 2019

This course is the second part of a two-course series meant to introduce Ph.D. students in mathematics to the fundamentals of numerical mathematics. It covers numerical methods for ordinary and partial differential equations.

Written and Oral Presentation, NYU, Spring 2018

This seminar will help Ph.D. students in mathematical fields with their technical writing and teaching/presentation skills. It is co-taught with Prof. Mutiara Sondjaja.

Numerical Methods I, NYU, Fall 2014 and Fall 2010

This course is the first part of a two-course series meant to introduce Ph.D. students in mathematics to the fundamentals of numerical mathematics. It covers most subjects except for differential equations.

Coarse-Grained Models of Materials, NYU, Fall 2013 and 2011

In this special-topic course we will discuss the fundamental ideas behind coarse-grained models of materials, as well as computational algorithms for mesoscopic modeling of gases, liquids, solids, and granular materials. Students will study a review or seminal paper and present what they have learned in class.

Computational Fluid Dynamics, NYU, Fall 2018/2016/2014 and Spring 2013

This course is a graduate-level course advanced numerical techniques for solving PDEs, with a particular focus on fluid dynamics. This includes advection-diffusion-reaction equations, compressible and incompressible Navier-Stokes equations, and fluid-structure coupling.

Scientific Computing, NYU, Fall 2020, 2019, 2015, Spring 2012 and 2011

This course is a graduate-level practical introduction to computational problem solving, including numerical linear algebra, optimization, interpolation, numerical integration, Fourier transforms, and Monte Carlo methods. Since Fall 2020 the course webpage is on github.

Undergraduate Courses

Numerical Analysis, NYU, Spring 2021

This course covers classical topics in Numerical Analysis: The solution of linear and nonlinear equations, conditioning, least squares, numerical computation of eigenvalues, interpolation, quadrature, and numerical methods for ODEs..

Ordinary Differential Equations, NYU, Fall 2012

This course is an introduction to differential equations for both majors and non-majors. Topics covered include first and second order equations, series solutions, numerical methods, dynamical systems, and integral transforms.

Partial Differential Equations, NYU, Spring 2020, 2018 and 2016

This course will be primarily focused on the theory of linear partial differential equations such as the heat equation, the wave equation and the Laplace equation, including separation of variables, Fourier series and transforms, Laplace transforms, and Green's functions, and some basic numerical methods.

Physics Computations, MSU, Fall 2000

Some of the materials that I designed under the supervision of Dr. Phil Duxbury for the Physics Computation course series at Michigan State University can be found here (this is a local copy of the old site). Here is the Fortran manual that I wrote for that course.