## EXPLORING DIFFERENTIAL EQUATIONS VIA GRAPHICS AND DATA

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

### Description:

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.

### Features:

• Investigates ODEs with the Rule of 4: graphical, algebraic, numerical, and descriptive models are used to fully understand behavior of solutions.

• Informal, intuitive approach gets students to understand what an ODE is and what information it contains.

• Emphasizes visual solutions via slope fields, directions fields, and phase plane solutions.

• Problem- or data-driven, students use and collect real data to develop ODEs and check the applicability of their solution.

• Includes modeling, so the origin of the differential equation and the interpretation of the solution are thoroughly covered.

• Exercises vary from those that help hone skills with analytical techniques to those that emphasize graphical or numerical techniques. Some exercises utilize technology and there are many exploratory problems.

• Laplace transforms are presented as an alternative method of solution in appropriate chapters.

### Reviewer Quotes

• "Imagine my surprise when I discovered that students had read further ahead than I had because they were interested in the examples."

• "The applications are very realistic, the best I've seen."

• "The outstanding features are the applications, the graphical approach, the interesting real world (some not physical science) examples and the interesting exercises."

• "The future of differential equations courses is not to explore mathematics for its own sake, but rather to show the power of differential equations as a modeling tool, and to teach students to USE differential equations in a variety of disciplinary and interdisciplinary applications. This book does the best job in that area of any on the market."

### Student Quotes:

• "The real-world models make the material much more interesting, by showing that there is much, much more involved with differential equations than simple number crunching."

• "I think that mixing the numerical, graphical, and analytical methods to analyze any differential equation gives you a better understanding of what you are doing."

### Supplements:

• Instructor's Manual
0-471-13580-1
Contains solutions to all text exercises and teaching suggestions.

• Student Solutions Manual
0-471-15645-0
Contains solutions to a sampling of problems.

• Multimedia ODE Software
Coming in 1998

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