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MacMath is a scientific toolkit for the Macintosh ™ computer developed by John H. Hubbard and Beverly H. West, consisting of twelve graphics programs. It supports mathematical computation and experimentation in dynamical systems, both for differential equations and for iteration. The MacMath package was designed to accompany the textbook Differential Equations: A Dynamical Sys tems Approach, also by J. H. Hubbard and B. H. West (Part I, One Dimensional Equations, 1990; Part II, Higher Dimensional Systems, 1991; Springer-Verlag). We have developed this text and software for a junior-senior level course in Applicable Mathematics at Cornell University, in order to take advantage of the new qualitative and geometric insights made possible by the advent of excellent and easily accessible graphics. Our primary reasons are two: 1. A picture is worth a thousand words. Graphics are far more than just a luxury - the human brain is made to process visual information; more information can be assimilated in a few seconds of looking at a graphics output than in months of analyzing a tabulated computer printout, perhaps a centimeter thick, carrying the same numerical information. 2. From qualitative analysis we can obtain excellent quantitative information. |
