Teaching mechanics with maple

Abstract

Classical mechanics is a disciple of theoretical physics and is one of the main constituent parts of physics. The instruction of theoretical physics courses plays an important role in the research of basic science and training physics skill sets. Most students consider that the knowledge of theoretical physics to be very abstract thus causing many difficulties in its study and understanding. Teachers can implement some teaching reform strategies to improve the quality of theoretical physics instruction in the context of classical mechanics. Such strategies may include: stimulate students' interest in learning, perfect students' cognitive structure and knowledge structure of theoretical physics; optimize the system of theoretical physics curriculum, enrich the instruction contents; apply heuristic instruction in theoretical physics teaching; establish virtual theoretical physics experiments and improve assessment and appraisal methods, promote students' all-round development. Physics is guided by simple principles, but for many topics, physics tends to be obscured in the profusion of mathematics. This paper describes some of the merits of using computer algebra in teaching mechanics. We report on our experience in teaching, during the course of several years, dynamical systems and mechanics courses to second-year engineering students by using symbolic computation. When they enter this course they have already taken one to two semesters of calculus, and during their high-school studies they must have already studied particle kinematics and dynamics. Simulation software and computer algebra systems allow students to experiment with phenomena which are too complex to calculate or too expensive to be reproduced in a laboratory, or are simply not accessible to the senses. A computer algebra system is essentially the ability to manipulate concepts, using computer expressions, which are symbolic, algebraic and not limited to numerical evaluation. A computer algebra systems can perform many of the mathematical techniques which are part and parcel of a traditional physics course. The successful use of computer algebra systems does not imply that the mathematical skills are no longer at a premium: such skills are important as ever. However, computer algebra systems may remove the need for those poorly understood mathematical techniques, which are practiced and taught simply because they serve as useful tools. The conceptual and reasoning difficulties that students have in introductory and advanced physics courses, including calculus-based honors courses, are well-documented by the physics education community. The appropriate use of computer algebra systems can therefore be an important aid in the training of better physicists and engineers. In this paper we will discuss ways in which computer algebra systems like Maple can be used by instructors and students in order to help students make these connections and to use them once they are made. Benefits that accrue to upper-class students able to make effective use of a computer algebra system provide a further rationale for introducing student to use of these systems in our courses, especially for those who plan to major in physics or other technical fields. © 2011 American Society for Engineering Education.