Wiley College: Borrelli/Coleman

DIFFERENTIAL EQUATIONS: A MODELING PERSPECTIVE

PRELIMINARY EDITION

ROBERT L. BORRELLI, Harvey Mudd College
COURTNEY COLEMAN, Harvey Mudd College
ISBN: 0-471-04181-5, 800 Pages, Paper, 1996

Description:

Differential Equations: A Modeling Perspective goes beyond the traditional development of ODEs to emphasize modeling and graphical visualization. Taking advantage of modern, easy to use computers and software, it shows students how to numerically solve complicated differential equations, and via striking graphical displays, derive insight into complex, real-world systems.
Students learn to model systems early, to create and explore graphs of solutions, and work open-ended exercises that reinforce ODE concepts. Throughout the text the authors are careful to treat basic solution techniques and theory and link both to the models. Intended for the first course called differential equations, ordinary differential equations, engineering math, engineering analysis, or modeling, found in math or engineering departments. Prerequisites are calculus through multivariable.

Features:

Takes full advantage of the graphing and numerical power of computers.
Carefully developed modeling theme coordinates with theory throughout the text to help students use ODEs to describe real phenomena. Models derive from rate processes (including population dynamics and compartment systems), electrical circuits, and mechanics.
Emphasizes graphical displays to provide compelling visual evidence of the theory, and a clear understanding of solutions. An atlas of instructive graphs appears as Appendix D, and is coordinated with the text.
Introduces numerical solutions early so students can examine the geometry of solutions and how they change when an ODE's initial conditions and rate functions change.
Discusses systems of ODEs very early on (sect 1.1 and 1.6) because systems are a natural way to think about what ODEs model. Treats systems fully in Chapters 6-9.
Uses short, constructive proofs to remind students of the importance of basic theory.
Exercise sets include computer exercises and open-ended, group projects that reinforce the main themes of the text. Both are denoted by icons. Titles on problems simplifies the selection process.
Authors are founding members of the NSF Sponsored Consortium for Ordinary Differential Equations Experiments (CODEE).

Supplements:

Instructor's Manual
0-471-13596-8
Written by the text authors, this manual contains hints for teaching, suggestions, complete solutions to all text problems including all graphs, and the author's favorite problems.
Student Solutions Manual
0-471-13599-2
Written by the text authors, contains approximately half of the text problems in worked-out solutions including all graphs.

Brief TOC:

1. First Order Equations: Solution and Modeling Techniques
2. Initial Value Problems and Their Approximate Solutions
3. Second-Order Differential Equations
4. Applications of Second-Order Differential Equations
5. The Laplace Transform
6. Introduction to Systems
7. Linear Systems of Differential Equations
8. Nonlinear Systems: Stability
9. Nonlinear Systems: Cycles, Bifurcations, and Chaos
10. Fourier Series and Separation of Variables
11. Series Solutions: Bessel Functions, Legendre Polynomials
12. Partial Differential Equations and Orthogonal Series
Appendix A: Basic Theory of Initial Value Problems
Appendix B: Numerical Methods
Appendix C: Background Information
Appendix D: Atlas
Index