Reflections on Teaching Computational Physics and Applied Mathematics

Abstract

In most applied mathematics and computational physics courses, simulation and modelling are taught by stressing numerical techniques, while visualisation often requires a range of specialised software tools. One approach is to use a procedural programming language such as Fortran or C. Although learning procedural programming is very useful it can detract from the desired goal of teaching computation. A second approach is to develop “black-box” applications for illustrating physical concepts. When well done this approach requires little instruction, and the focus is entirely on the situation under investigation. A disadvantage is that the student may not learn any computational techniques. A third way is to use an integrated computational environment, for example Mathematica, which couples an excellent graphical user interface to a high-level programming language. In this talk I will demonstrate my approach, developed over the last 20 years, by working through the solutions to selected problems from assignments and exams.