Starting with the right matrices

Over the past 20 years we have developed a course that combines applied mathematics with scientific computing. Each lecture discusses a model problem and a code to solve it. The course is popular with engineering students and their departments, who want exposure to ideas and also to software (including MATLAB). The need to move beyond the old formula- based approach is widely recognized. The starting point is to understand the second difference matrices that appear everywhere in scientific computing and simulation. Four special matrices with fixed and free and periodic boundary conditions (and -1,2,-1 on all interior diagonals) have names. They become familiar. We discuss the “A'CA framework” for so many numerical methods and engineering applications. The Computational Science and Engineering course 18.085 will be videotaped for MIT's OpenCourseWare ocw.mit.edu. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)