| PREFACE ACKNOWLEDGMENTS 1 INTRODUCTION TO DIFFERENTIAL EQUATIONS 1.1 Definitions and Terminology 1.2 Initial-Value Problems 1.3 Differential Equations as Mathematical Models Chapter 1 in Review 2 FIRST-ORDER DIFFERENTIAL EQUATIONS 2.1 Solution Curves Without the Solution 2.2 Separable Variables 2.3 Linear Equations 2.4 Exact Equations 2.5 Solutions by Substitutions 2.6 A Numerical Solution Chapter 2 in Review 3 MODELING WITH FIRST-ORDER DIFFERENTIAL EQUATIONS 3.1 Linear Equations 3.2 Nonlinear Equations 3.3 Systems of Linear and Nonlinear Differential Equations Chapter 3 in Review Project Module: Harvesting of Renewable Natural Resources, by Gilbert N. Lewis 4 HIGHER-ORDER DIFFERENTIAL EQUATIONS 4.1 Preliminary Theory: Linear Equations 4.1.1 Initial-Value and Boundary-Value Problems 4.1.2 Homogeneous Equations 4.1.3 Nonhomogeneous Equations 4.2 Reduction of Order 4.3 Homogeneous Linear Equations with Constant Coefficients 4.4 Undetermined Coefficients--Superposition Approach 4.5 Undetermined Coefficients--Annihilator Approach 4.6 Variation of Parameters 4.7 Cauchy-Euler Equation 4.8 Solving Systems of Linear Equations by Elimination 4.9 Nonlinear Equations Chapter 4 in Review 5 MODELING WITH HIGHER-ORDER DIFFERENTIAL EQUATIONS 6 SERIES SOLUTIONS Of LINEAR EQUATIONS 7 THE LAPLACE TRANSFORM 8 SYSTEMS OF LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS 9 NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS APPENDIXES SELECTED ANSWERS FOR ODD-NUMBERED PROBLEMS INDEX |
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