Southern Methodist University
Spring 2014 -- Math 2339 -- Calculus 3
A continuation of MATH 1339 (Calculus 2) including parametric equations, polar coordinates, partial differentiation, multiple integrals, and vector analysis.
Fall 2013 -- Math 1338 -- Calculus 1
Differential and integral calculus for algebraic, trigonometric and transcendental functions, with applications to curve sketching, velocity, maximum-minimum problems, areas and volumes.
Northwestern University
Spring 2013 -- Math 234 -- Multiple Integration and Vector Calculus
Cylindrical and spherical coordinates, double and triple integrals, line and surface integrals. Change of variables in multiple integrals; gradient, divergence, and curl.
New Jersey Institute of Technology
Spring 2011 -- Math 337-- Linear Algebra
Matrices, determinants, systems of linear equations, vector spaces, linear transformations, eigenvalues, eigenvectors, and related topics.
Fall 2010 -- Math 211 -- Calculus III A
Topics include vectors, curvature, partial derivatives, multiple integrals, line integrals, and Green's theorem. Students who are considering a major in Mathematical Sciences or who are undecided about their major should take Math 213. This course is concerned with the development of calculus for functions of several variables. This includes the application of concepts from calculus to the study of curves and surfaces in space, and the study of 'vector fields' (an example of a vector field is the map of wind patterns often shown on the nightly news). The topics covered in this course are interesting as well as important, with numerous technological and scientific applications. Mastery of the material in this course will be critical if you go on to study classical dynamics (required for mechanical engineering or physics majors), electrodynamics (EE majors), fluid dynamics (chemical engineering majors), or a host of other topics in engineering and science.
Spring 2010 -- Math 450 (Honors) -- Methods of Applied Mathematics II (Capstone)
The project combined analysis and computation with modeling and simple experiments to see how an electrostatic field can alter the shape of a soap film or fluid membrane.
Fall 2009 -- Math 450 (Honors) -- Methods of Applied Mathematics I (Capstone)
Combines mathematical modeling with physical and computational experiments conducted in the Undergraduate Mathematics Computing Laboratory. Students will learn fundamental tools of applied mathematics used to solve problems from linear and nonlinear physics, including analytical, numerical, and asymptotic methods. Perform physics experiments, make predictions, and understand the results using the above techniques. Specifically, a successful student should be able to:
- analyze and understand the dynamics of the mass-spring system, the pendulum, and other simple mechanical systems using perturbation methods, phase-plane analysis, and numerical simulation.
- derive ODE's for simple mechanical models using Newton's laws or variational methods.
- conduct simple experiments, analyze them, and present the results in a lab report.
- understand and apply the basic theory of chaotic dynamics.
- understand Laplace's equation as the governing PDE of electrostatics and be able to apply different tools to its study
Spring 2009 -- Math 450 (Honors) -- Methods of Applied Mathematics II (Capstone)
Theoretical, computational, and experimental research in the percolation and topological properties of granular media
Theoretical component:
- Learning the basics about physics of granular systems, including the issues related to the formation of force networks in granular media
- applying novel topological measures to the structures that form when granular systems are exposed to external forcing.
- analyze percolation properties of these systems.
- discuss connections between topological measures and percolation properties.
Computational component:
- Image processing: further develop matlab-based codes used to analyze experimental images.
- applying novel topological measures to the structures that form when granular systems are exposed to external forcing.
- applying computational homology approach to analyze the results.
Experimental component:
- Performing experiments involving two dimensional particulate systems Visualization of photoelastic granular systems using CCD camera and appropriate software; Data analysis.