This corrected third printing retains the authors'main emphasis on ordinary differential equations. It is most appropriate for upper level undergraduate and graduate students in the fields of mathematics, engineering, and applied mathematics, as well as the life sciences, physics and economics. The authors have taken the view that a differential equations theory defines functions; the object of the theory is to understand the behaviour of these functions. The tools the authors use include qualitative and numerical methods besides the traditional analytic methods, and the companion software, MacMath, is designed to bring these notions to life.
An updated collection of twelve interactive graphics programs for the Macintosh computer, addressing differential equations and iteration. These versatile programs greatly enhance the understanding of the mathematics in these topics. Qualitative analysis of the pictures leads to quantitative results and even to new mathematics. The MacMath programs encourage experimentation and vastly increase the number of examples to which a student may be quickly exposed. The are also ideal for exploring applications of differential equations and iteration, which roughly speaking form the interface between mathematics and the realworld. This is how mathematics models a changing situation, whether it be physical forces or predator-prey populations. MacMath permits easy investigation of various models, particularly in showing the effects of a change in parameters on ultimate behavior of the system.
MacMath is a scientific toolkit for the Macintosh computer 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 textbooks Differential Equations: A Dynamical Systems Approach Part I & II. The text and software was developed for a junior-senior level course in applicable mathematics at Cornell University, in order to take advantage of excellent and easily accessible graphics. MacMath addresses differential equations and iteration such as: analyzer, diffeq, phase plane, diffeq 3D views, numerical methods, periodic differential equations, cascade, 2D iteration, eigenfinder, jacobidraw, fourier, planets. These versatile programs greatly enhance the understanding of the mathematics in these topics. Qualitative analysis of the picture leads to quantitative results and even to new mathematics. This new edition includes the latest version of the Mac Math diskette, 9.2.
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