Elementary Differential Equations [Loose-leaf]

Elementary Differential Equations 12th Edition is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between. In this revision, new author Douglas Meade focuses on developing students conceptual understanding with new concept check questions and worksheets for each chapter. Meade builds upon Boyce and DiPrima's work to combine a sound and accurate (but not abstract) exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications. The main prerequisite for engaging with the program is a working knowledge of calculus, gained from a normal two or three semester course sequence or its equivalent. Some familiarity with matrices will also be helpful in the chapters on systems of differential equations.

Preface vii

1 Introduction 1

1.1 Some Basic Mathematical Models; Direction Fields 1

1.2 Solutions of Some Differential Equations 9

1.3 Classification of Differential Equations 17

2 First-Order Differential Equations 26

2.1 Linear Differential Equations; Method of Integrating Factors 26

2.2 Separable Differential Equations 34

2.3 Modeling with First-Order Differential Equations 41

2.4 Differences Between Linear and Nonlinear Differential Equations 53

2.5 Autonomous Differential Equations and Population Dynamics 61

2.6 Exact Differential Equations and Integrating Factors 72

2.7 Numerical Approximations: Eulers Method 78

2.8 The Existence and UniqlsÄ