In order to make this work totally self-contained, we have developed the fundamentals of differential equations from the very beginning. This includes the solution methods for the traditional classes of solvable equations (first-order linear, second-order constant-coefficients, linear systems, Laplace transforms, power series solutions and so forth) as well as a presentation of the basic theory of existence/uniqueness and the traditional numerical methods for first-order equations. In the process some new mathematical points have been developed, to be noted below. It is our firm belief that a solid mastery of the subject of differential equations can only be achieved through a strong traditional course. This is enhanced by the graphical capabilities of Mathematica, which have allowed the incorporation of many more graphs than are normally available in books at this level.
When we move beyond the traditional course and envisage the integration of computers, many potential problems arise in redesigning the syllabus. A well-known first attempt was the development of BASIC and similar programs in the 1970s. The ease with which numerical routines such as the Euler method could be implemented made the new software a very useful pedagogical device. However, computer technology distracted students from learning about differential equations.
The scene changed dramatically with the advent of symbolic manipulation programs---first Macsyma, then Derive, Maple, Mathematica and others---which made symbolic as well as numerical solutions of differential equations possible via computers. In principle symbolic manipulation programs can perform routine calculations, permitting students to cover more theory and applications. In practice, it may be necessary for students to learn a fair amount about a symbolic manipulation program for a course in differential equations. Certainly, using Mathematica is far simpler than writing programs in C or BASIC. Nevertheless, students and professors frequently become frustrated when Mathematica does not behave exactly as mathematics does, and valuable time is wasted. It is for this reason that our text provides a parallel development of classical solution methods as well as a special Mathematica package, ODE.m. No prior knowledge of Mathematica is required either to use this book or the programs contained in ODE.m.
To access the electronic media that enhances this book, simply click on
Mathematica Notebooks and Related Files. After choosing the version of Mathematica you wish to use (2.x or 3.x) and the type of computer you are using (PC, Mac or other), you will arrive at the front page of the electronic component corresponding to these two choices. From here,
you may take a tour of the complete resource by following the button. This button will take you through the following sections: the authors' pages including pictures and bios, Mathematica solutions to the examples in the book, Mathematica solutions to most of the exercises in the book, some sample Mathematica lab exercises, a collection of miscellaneous Mathematica notebooks, movies of linear and nonlinear dynamical systems, ODE.m and other packages, and finally to the reference manual for ODE.m.
Introduction to Ordinary Differential Equations with Mathematica - An Integrated Multimedia Approach
Gray, Mezzino, and Pinsky
CD-ROM and Web site designed by Michael J. Mezzino, Jr.
Department of Mathematics
University of Houston - Clear Lake, all rights reserved.
Graphics/partial HTML by Patrick Reich using Mathematica®,
Corel Photo Paint®, and Paint Shop Pro®.