Differential Equations with Linear Algebra

Hardcover | November 19, 2009

byMatthew R. Boelkins, Jack L. Goldberg, Merle C. Potter

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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 algebraand 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-firstapproach, 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 anexample-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 andsupport students' use of technology in solving problems. Each chapter closes with several substantial projects for further study, many of which are based in applications.

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From the Publisher

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 algebraand differential equations and examine intr...

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 Emeritu...

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Format:HardcoverDimensions:576 pages, 6.18 × 9.29 × 1.42 inPublished:November 19, 2009Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0195385861

ISBN - 13:9780195385861

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Table of Contents

Preface1. Essentials of Linear Algebra2. First-Order Differential Equations3. Linear Systems of Differential Equations4. Higher-Order Differential Equations5. Laplace Tranforms6. Nonlinear Systems of Differential Equations7. Numerical Methods for Differential Equations8. Series Solutions for Differential EquationsA. Review of Integration TechniquesB. Complex NumbersC. Roots of PolynomialsD. Linear TransformationsE. Solutions to Selected Exercises