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DAVID LOMEN, University of Arizona
DAVID LOVELOCK, University of Arizona
ISBN: 0-471-07649-X, 500 Pages, Paper, 1996


Written by two members of the Calculus Consortium based at Harvard University, Exploring Differential Equations via Graphics and Data provides an intuitive approach that gets students actively involved in their own learning. It transforms the traditional ODE course from its reliance on formal methods of solution to one where students think, experiment, explore and understand.
Students learn how to determine properties of a solution directly from the differential equation. Wherever possible, concepts are explored graphically, algebraically, numerically, and descriptively. The authors assume the user has access to mathematical software that draws slope fields, generates numerical solutions, and allows data and graphs of functions to be displayed simultaneously.
This book is intended for a standard ordinary differential equation course usually taught in mathematics departments (occasionally found in the engineering colleges) with a prerequisite of single variable calculus.


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Brief Table of Contents:

  1. Basic Concepts
  2. Autonomous Differential Equations
  3. General First Order Differential Equations
  4. Separable Differential Equations and Applications
  5. Applications Leading to New Techniques
  6. First Order Linear Differential Equations and Applications
  7. Second Order Differential Equations with Constant Coefficients
  8. Applications
  9. Second Order Linear Differential Equations
  10. Generalized Power Series Solutions
  11. Nonhomogenous Second Order Linear Differential Equations
  12. Autonomous Systems
  13. Systems of Ordinary Differential Equations