Overview
Linearity plays a critical role in the study of elementary differential equations; linear differential equations, especially systems thereof, demonstrate a fundamental application of linear algebra. In Differential Equations with Linear Algebra, we explore this interplay between linear algebra and differential equations and examine introductory and important ideas in each, usually through the lens of important problems that involve differential equations. Written at a sophomore level, the text is accessible to students who have completed multivariable calculus. With a systems-first approach, the book is appropriate for courses for majors in mathematics, science, and engineering that study systems of differential equations. Because of its emphasis on linearity, the text opens with a full chapter devoted to essential ideas in linear algebra. Motivated by future problems in systems of differential equations, the chapter on linear algebra introduces such key ideas as systems of algebraic equations, linear combinations, the eigenvalue problem, and bases and dimension of vector spaces. This chapter enables students to quickly learn enough linear algebra to appreciate the structure of solutions to linear differential equations and systems thereof in subsequent study and to apply these ideas regularly. The book offers an example-driven approach, beginning each chapter with one or two motivating problems that are applied in nature. The following chapter develops the mathematics necessary to solve these problems and explores related topics further. Even in more theoretical developments, we use an example-first style to build intuition and understanding before stating or proving general results. Over 100 figures provide visual demonstration of key ideas; the use of the computer algebra system Maple and Microsoft Excel are presented in detail throughout to provide further perspective and support students' use of technology in solving problems. Each chapter closes with several substantial projects for further study, many of which are based in applications. Errata sheet available at: www.oup.com/us/companion.websites/9780195385861/pdf/errata.pdf
Full Product Details
Author: Matthew R Boelkins (Associate Professor of Mathematics, Grand Valley State University) ,
Jack L Goldberg (Professor Emeritus of Mathematics, University of Michigan) ,
Merle C Potter (Professor Emeritus of Engineering, Michigan State University)
Publisher: Oxford University Press Inc
Imprint: Oxford University Press Inc
Dimensions:
Width: 16.30cm
, Height: 3.30cm
, Length: 24.20cm
Weight: 0.922kg
ISBN: 9780195385861
ISBN 10: 0195385861
Pages: 576
Publication Date: 12 November 2009
Audience:
College/higher education
,
Professional and scholarly
,
Undergraduate
,
Postgraduate, Research & Scholarly
Format: Hardback
Publisher's Status: Out of Print
Availability: In Print
Limited stock is available. It will be ordered for you and shipped pending supplier's limited stock.
Reviews
<br>Summary in Mathematical Reviews<p><br> A very good reference for teachers or students. Recommended. --Choice<p><br>
"Summary in Mathematical Reviews ""A very good reference for teachers or students. Recommended.""--Choice"
Summary in Mathematical Reviews ""A very good reference for teachers or students. Recommended.""--Choice
<br>Summary in Mathematical Reviews<br> A very good reference for teachers or students. Recommended. --Choice<br>
Author Information
Matt Boelkins is Associate Professor of Mathematics at Grand Valley State University. Merle C. Potter is Professor Emeritus of Engineering at Michigan State University and was the first recipient of the Teacher-Scholar award. He has authored or coauthored twenty-four textbooks and exam review books. Jack Goldberg is Professor Emeritus of Mathematics at the University of Michigan. He has published several textbooks and numerous research papers.
