Differential Equations, Preliminary Edition - Softcover

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

3.5

58 ratings by Goodreads

9780534950040: Differential Equations, Preliminary Edition

Softcover

ISBN 10: 0534950043 ISBN 13: 9780534950040

Publisher: Brooks Cole, 1995

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More than 30 schools adopted prepublication versions of this innovative new text before its release. The excitement is spreading - and your students should be a part of it! We are in the midst of a technological revolution, for which no other course on the mathematics curriculum is more significant than differential equations. Computers and graphing calculators can now rapidly graph approximate solutions that students must be prepared to interpret and evaluate for validity. Now more than ever, students must learn to think graphically as well as analytically, since graphical illustration of quantitative information shapes how we communicate today. There is also a "nonlinear revolution" occurring in the sciences, engineering, and mathematics. Approaches that embrace a multitude of perspectives are growing in popularity, finding a place alongside conventional linear thinking. In differential equations, this means students should emerge from a course of study able to distinguish the difference between linear and nonlinear phenomena. They must also be able to evaluate the validity of techniques applied to nonlinear systems as well as linear ones. If you've recognized the signals of this revolution in your department, you should take a look at the fresh new approach taken in this text.

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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."

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