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In the upeer-division theoretical physics courses, the student is taught the formalisms of the theories, the analytical techniques of problem-solving, and the physical interpretation of the mathematical solutions. Whenever possible, important problems in physics are chosen as examples. Since very few physical problems can be solved exactly, the analytical methods consist mainly of working with models, making approximations, and considering special or limiting cases. It is essential that the student master the analytical techniques, because they can be used to solve many problems in physics, and, even in cases where solutions cannot be found, can be used to extract a great deal of information about the problems. These techniques are indispensable, even in the age of computers, for overcoming hardware and software limitations, and for correct and efficient programming. Computers cannot do everything. They do not replace thinking; they only enhance and extend our problem-solving skills. However, without computers, many important, real or "fun" problems in physics must be excluded from our curriculum.
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The new microcomputers and software packages usher in a new era, and the impact of computers in the classroom will most likely be substantial. Mathematica, a system for doing mathematics by computer, promises to provide a solution for the integration of computing into the undergraduate physics major. In addition to numerical calculations, Mathematica performs symbolic and graphical calculations and provides a high-level programming language. It can also animate two- and three- dimensional graphics and simulate the physical situation. ... In what follows, I shall describe my attempts at, and the results of, using Mathematica in my courses.
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