[share_ebook] A Modern Introduction to Differential Equations,Second Edition.Henry Richardo.Academic Press.2009

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A Modern Introduction to Differential Equations,Second Edition Authors Henry Richardo Publisher: Academic Press Pub Date: 2009 Pages: 533 ISBN 978-0-12-374746-4 (hardcover : alk. paper) Preface PHILOSOPHY The evolution of differential equations courses I described in the Preface to the first edition of this book has progressed nicely. In particular, the quantitative, graphical, and qualitative aspects of the subject have been receiving increased attention, due in large part to the availability of technology in the classroom and at home. As before, this text presents a solid yet highly accessible introduction to differential equations, developing the concepts from a dynamical systems perspective and employing technology to treat topics graphically, numerically, and analytically. In particular, the book acknowledges that most differential equations cannot be solved in closed form and makes extensive use of qualitative and numerical methods to analyze solutions. The text includes discussions of several significant mathematical models, although there is no systematic attempt to teach the art of modeling. Similarly, the text introduces only the minimal amount of linear algebra necessary for an analysis of systems. This book is intended to be the text for the one-semester ordinary differential equations course that is typically offered at the sophomore–junior level, but with some differences. The prerequisite for the course is two semesters of calculus.No prior knowledge of multivariable calculus and linear algebra is needed, because essential concepts from these subjects are developed within the text itself. This book is aimed primarily at students majoring in mathematics, the natural sciences, and engineering. However, students in economics, business, and the social sciences who have the necessary background should also benefit. USE OF TECHNOLOGY This text assumes that the student has access to a computer algebra system (CAS) or perhaps some specialized software that will enable him or her to construct the required graphs (solution curves, phase planes, etc.) and numerical approximations. For example, a spreadsheet program can be used effectively to implement Euler’s method of approximating solutions. Although I use Maple? inmy own course, no specific software or hardware platform is assumed for this book. To a large extent, even a graphing calculator will suffice.

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