Using Mathematica In A Graduate Numerical Methods Course
Shirley B. Pomeranz · 2024
IntroductionThis paper is a continuation of observations on the use of the Computer Algebra System (CAS), Mathematica (Wolfram Research, Inc.), as the software of choice for a graduate numerical methods course 1 .Currently, there are many software tools that can be used for numerical methods.In the "old days" FORTRAN was the primary tool.Today there are procedural, functional, and/or rule based programming languages.There are computer mathematics systems: Axiom, Derive, Macsyma, Magma, Maple, Mathcad, Mathematica, Mathview, Matlab, Milo, Reduce, etc. Spreadsheets, especially Microsoft Excel, are very popular with engineering students.This bewildering array of tools makes the choice of software very difficult.The course, Numerical Methods for Engineers and Scientists (MA7273), taught at The University of Tulsa, and offered through the Department of Mathematical and Computer Sciences, deals with numerical methods for solving partial differential equations.The students are beginning graduate students from diverse engineering and math/computer science disciplines.The students enrolled in the course in the 1998 fall semester represented the Departments of Mathematical and Computer Sciences (five students), Mechanical Engineering (four students), Petroleum Engineering (two students), and Chemical Engineering (one student).My experiences and observations, as well as student comments, are presented in the following sections of this paper. Mathematica version of the courseThe new features of the course this 1998 fall semester, included the use of a text that specifically chooses Mathematica as its associated software package.The text is Numerical Solutions for Partial Differential Equations, Victor Ganzha and Evgenii Vorozhtsov, CRC Press, 1996.The authors provide a disk with Mathematica notebooks that is integrated with the text.The text's use of Mathematica is not restricted to numerically solving and graphically representing the finite difference and finite element solutions of problems.The symbolic capabilities of Mathematica Page 4.580.1