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The example of the labored computations of electrical engineers is a familiar one. The mathematics are mathematical calculus and linear algebra, but with a limited number of significant terms, such as voltage, current, resistance, and capacitance. A typical analysis of an electrical circuit, performed by, say, a consultant or an engineer who solved the problem as an Act domain, involves the manipulation of large numbers of quantities. The use of a symbolic manipulation program can result in the automated computation of an analysis or design. The advantages of such automated computation are at least threefold: the SM program can check the correctness of the analysis or design, it may assist in the discovery of algebraic, geometric, or combinatorial simplification or the elimination of constraints, it can help the student discover a new design problem, or it may assist in simplifying the mathematics and thus repair the quality of the analysis or design.
Algebraic calculations are quite versatile and the range of programs is quite large. Programs that solve equations and inequalities exist for almost every specific variety of algebra. More complex problems are often handled by numerical algebraic equations; we illustrate specific programs for this type of problem. We also present three programs that use implicit differentiation: Derive, Maple, and Mathematica. We then give an overview of the use of numerical methods such as Newton's method in solving systems of algebraic equations. Finally, we give an introduction to special functions, emphasizing the discontinuities and the behavior of the square root function. The selected software packages are easily available, FREE of charge, and ideally suited for use on personal computers. We hope these programs will be useful in all schools, colleges, and universities.
This story is woven around the subject of probability. Consider a game of cards. If the probability of drawing one particular card in the sequence to be drawn is given by (2/52), we may also say that probability of drawing a particular card for the duration of the game is 2/52. James Greenwood II 20:48, 9 January 2008 (EST) d2c66b5586
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