Scientific Computing

What follows are my lecture notes for Math 164: Scientific Computing, taught at Harvey Mudd College during Spring 2013 while I was on a one semester sabbatical leave from the Hong Kong University of Science & Technology. These lecture notes are based on two courses previously taught by me at HKUST: Introduction to Scientific Computation and Introduction to Numerical Methods.

Math 164 at Harvey-Mudd is primarily for Math majors and supposes no previous knowledge of numerical analysis or methods. This course consists of both numerical methods and computational physics. The numerical methods content includes standard topics such as IEEE arithmetic, root finding, linear algebra, interpolation and least-squares, integration, differentiation, and differential equations. The physics content includes nonlinear dynamical systems with the pendulum as a model and computational fluid dynamics with a focus on the steady two-dimensional flow past either a rectangle or a circle.

Course work is divided into three parts. In the first part, numerical methods are learned and MATLAB is used to solve various computational math problems. The second and third parts requires students to work on project assignments in dynamical systems and in computational fluid dynamics. In the first project, students are given the freedom to choose a dynamical system to study numerically and to write a paper detailing their work. In the second project, students compute the steady flow past either a rectangle or a circle. Here, students are given the option to focus on either the efficiency of the numerical methods employed or on the physics of the flow field solutions. Written papers should be less than eight pages in length and composed using the LATEX typesetting software.