Differential Equations - Hardcover

Blanchard, Paul; Devaney, Robert L.; Hall, Glen R.

Hardcover

ISBN 10: 0534345506 ISBN 13: 9780534345501

Publisher: Brooks Cole, 1998

Synopsis

This is one of those rare texts that pioneers a new way of teaching a subject. It balances analytic, numeric, and graphical techniques. It emphasizes modeling, stresses qualitative theory throughout the course, uses technology significantly and consistently, presents linear and nonlinear systems in parallel, and includes an introduction to discrete models of dynamical systems. Throughout this text, technology is used as a tool for illustration, experimentation, and discovery. Using computer graphics as a tool, students investigate systems such as the Lorenz attractor, the double pendulum, and chaotic behavior in logistic models. Students will gain a greater conceptual understanding with this text's emphasis on interpretation, qualitative description, lab reports, and written explanations. This text grew out of the Boston University Differential Equations Project endowed in part by the National Science Foundation.

About this title

About the Author:

Paul Blanchard is Associate Professor of Mathematics at Boston University. Paul grew up in Sutton, Massachusetts, spent his undergraduate years at Brown University, and received his Ph.D. from Yale University. He has taught college mathematics for twenty-five years, mostly at Boston University. In 2001, he won the Northeast Section of the Mathematical Association of America's Award for Distinguished Teaching in Mathematics. He has coauthored or contributed chapters to four different textbooks. His main area of mathematical research is complex analytic dynamical systems and the related point sets, Julia sets and the Mandelbrot set. Most recently his efforts have focused on reforming the traditional differential equations course, and he is currently heading the Boston University Differential Equations Project and leading workshops in this innovative approach to teaching differential equations. When he becomes exhausted fixing the errors made by his two coauthors, he usually closes up his CD store and heads to the golf course with his caddy, Glen Hall.

Review:

"I liked the emphasis on qualitative and numerical solution methods in addition to the more traditional analytic techniques. Students come away from a course using this text with a better understanding of what an ordinary differential equation (ODE) is and what it means to "solve" such an equation."

"It is clearly the best undergraduate ODE text that I have ever looked at, and I am pushing to have the text adopted for all our undergraduate differential courses. . . The authors have jettisoned the classic "cookbook" approach in favor of one which fosters critical thinking. The students need to formulate, solve and interpret the solutions to the problems. In order to do this effectively, the students are taught some fundamentals of modeling and are presented with an arsenal of tools, including qualitative, numeric, and analytic approaches for solving differential equations."

"I really liked the way that systems are introduced at the beginning of the text and stressed throughout the remainder of the text. I thoroughly enjoyed the systems approach to solving DE's and my students did, too. In fact, when we hit the "lucky guess" methods in later sections, my students found these traditional methods of solving DE's to be a snap compared to the algebra they used when solving systems. . . I liked the continuous emphasis on qualitative analysis. It was made evident in the first section of the text that graphical analysis would be used as a significant problem solving tool and the value of qualitative analysis was repeatedly stressed throughout the remainder of the text. . . I liked the balance between graphical analysis and the traditional symbolic analysis required in your typical DE course. I do not feel in the least that my students were shortchanged on symbolic manipulations required to be successful in later courses. On the other hand, the authors were careful not to go overboard and introduce one symbolic technique after another. I really feel they struck a fair balance."

"There are many texts that claim to be written in the spirit of the so-called calculus reform movement. In my opinion, the text under review achieves this goal better than any book that I have seen. This book presents at a very elementary level the kinds of material that opens the door for the understanding of many of the great achievements in dynamical systems that have been accomplished over the last 30 years."

About this edition

• Publisher: Brooks Cole
• Publication date: 1998
• ISBN 10: 0534345506
• ISBN 13: 9780534345501
• Binding: Hardcover
• Edition number: 1
• Number of pages: 736