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This text by best-selling author Dennis G. Zill provides an alternative to more traditional differential equations texts by addressing the growing influence of technology in teaching differential equations. This book will appeal to instructors who wish to integrate the computer into teaching theory and applications of differential equations. Qualitative and numerical aspects of differential equations are introduced early in the text. In this edition, computer lab experiments, projects, and writing assignments now appear in a section at the end of each chapter.
1. GETTING STARTED Definitions and Terminology / Initial-Value Problems 2. FIRST-ORDER EQUATIONS What a First-Order Equation Can Tell Us / Separable Variables / Linear Equations / Mathematical Models / Numerical Solutions 3. HIGHER-ORDER EQUATIONS Linear Equations / Homogeneous Linear Equations with Constant Coefficients / Phase Portraits and Stability / Nonhomogeneous Linear Equations / Cauchy-Euler Equation / Mathematical Models: Initial-Value Problems / Mathematical Models: Boundary-Value Problems / Systems of Differential Equations-Elimination Method / Numerical Solutions / Nonlinear Equations / 4. SYSTEMS OF FIRST-ORDER EQUATIONS Linear Systems / Homogeneous Linear Systems with Constant Coefficients / Nonhomogeneous Linear Systems / Mathematical Models / Phase Portraits and Stability 5. THE LAPLACE TRANSFORM The Laplace Transform / Translations Theorems / Derivative of a Transform, Transform of an Integral / Periodic Functions / Dirac Delta Function / Systems of Differential Equations 6. SERIES SOLUTIONS Solutions About Ordinary Points / Solutions About Singular Points / Bessel's Equation / APPENDIX I: INTRODUCTION TO MATRICES / APPENDIX II: LAPLACE TRANSFORMS / APPENDIX III: REVIEW OF POWER SERIES / ANSWERS TO SELECTED ODD-NUMBERED PROBLEMS