Elementary Differential Equations

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A clear, concise book that emphasizes finding solutions to differential equations where applications play an important role. Each chapter includes many illustrative examples to assist the reader. The book emphasizes methods for finding solutions to differential equations. It provides many abundant exercises, applications, and solved examples with careful attention given to readability. Elementary Differential Equations includes a thorough treatment of power series techniques. In addition, the book presents a classical treatment of several physical problems to show how Fourier series become involved in the solution of those problems. The eighth edition of Elementary Differential Equations has been revised to include a new supplement in many chapters that provides suggestions and exercises for using a computer to assist in the understanding of the material in the chapter. It also now provides an introduction to the phase plane and to different types of phase portraits. A valuable reference book for readers interested in exploring the technological and other applications of differential equations.

Title Page Dedication Table of Contents Preface 1 Definitions; Families of Curves 2 Equations of Order One 3 Numerical Methods 4 Elementary Applications 5 Additional Topics on Equations of Order One 6 Linear Differential Equations 7 Linear Equations with Constant Coefficients 8 Nonhomogeneous Equations: Undetermined Coefficients 9 Variation of Parameters 10 Applications 11 Linear Systems of Equations 12 Nonhomogeneous Systems of Equations 13 The Existence and Uniqueness of Solutions 14 The Laplace Transform 15 Inverse Transforms 16 Nonlinear Equations 17 Power Series Solutions 18 Solutions Near Regular Singular Points 19 Equations of Hypergeometric Type 20 Partial Differential Equations 21 Orthogonal Sets of Functions 22 Fourier Series 23 Boundary Value Problems 24 Additional Properties of the Laplace Transform 25 Partial Differentia1 Equations Transform Methods Answers to Odd-numbered Exercises Index In publishing a new edition of Elementary Differential Equations, we have two main goals. First, we hope to maintain the direct style that users of earlier editions have come to expect. Secondly, in response to changes in the nature of many differential equations courses, we have added some new geometric material, reorganized some sections, and added a computer component to the text.