A First Course in Differential Equations with Modeling Applications (with CD-ROM and iLrn Tutorial) / Edition 8by Dennis G. Zill
Pub. Date: 10/20/2004
Publisher: Cengage Learning
Now enhanced with the innovative DE Tools CD-ROM and the iLrn teaching and learning system, this proven text explains the "how" behind the material and strikes a balance between the analytical, qualitative, and quantitative approaches to the study of differential equations. This accessible text speaks to students through a wealth of pedagogical aids, including an
Now enhanced with the innovative DE Tools CD-ROM and the iLrn teaching and learning system, this proven text explains the "how" behind the material and strikes a balance between the analytical, qualitative, and quantitative approaches to the study of differential equations. This accessible text speaks to students through a wealth of pedagogical aids, including an abundance of examples, explanations, "Remarks" boxes, definitions, and group projects. Author Dennis G. Zill wrote this book with the student's understanding kept firmly in mind. He presents the material in a straightforward, readable, and helpful manner, while keeping the level of theory consistent with the notion of a "first course."
Table of Contents
1. INTRODUCTION TO DIFFERENTIAL EQUATIONS. Definitions and Terminology. Initial-Value Problems. Differential Equations as Mathematical Models. Chapter 1 in Review. Project 1: Diving Deception Pass. 2. FIRST-ORDER DIFFERENTIAL EQUATIONS. Solution Curves Without a Solution. Separable Variables. Linear Equations. Exact Equations. Solutions by Substitutions. A Numerical Method. Chapter 2 in Review. Project 2: Harvesting Natural Resources. 3. MODELING WITH FIRST-ORDER DIFFERENTIAL EQUATIONS. Linear Models. Nonlinear Models. Modeling with Systems of Differential Equations. Chapter 3 in Review. Project 3: Swimming the Salmon River. 4. HIGHER-ORDER DIFFERENTIAL EQUATIONS. Linear Differential Equations: Basic Theory. Reduction of Order. Homogeneous Linear Equations with Constant Coefficients. Undetermined Coefficients- Superposition Approach. Undetermined Coefficients- Annihilator Approach. Variation of Parameters. Cauchy-Euler Equation. Solving Systems of Linear Equations by Elimination. Nonlinear Differential Equations. Chapter 4 in Review. Project 4: Bungee Jumping. 5. MODELING WITH HIGHER-ORDER DIFFERENTIAL EQUATIONS. Linear Models: Initial-Value Problems. Linear Models: Boundary-Value Problems. Nonlinear Models. Chapter 5 in Review. Project 5: The Collapse of Galloping Gertie. 6: SERIES SOLUTIONS OF LINEAR EQUATIONS. Solutions About Ordinary Points. Solutions About Singular Points. Special Functions. Chapter 6 in Review. Project 6: Defeating Tamarisk. 7. LAPLACE TRANSFORM. Definition of the Laplace Transform. Inverse Transform and Transforms of Derivatives. Operational Properties I. Operational Properties II. Dirac Delta Function. Systems of Linear Differential Equations. Chapter 7 in Review. Project 7: Murder at the Mayfair. 8. SYSTEMS OF LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS. Preliminary Theory. Homogeneous Linear Systems. Nonhomogeneous Linear Systems. Matrix Exponential. Chapter 8 in Review. Project 8: Designing for Earthquakes. 9. NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS. Euler Methods and Error Analysis. Runge-Kutta Methods. Multistep Methods. Higher-Order Equations and Systems. Second-Order Boundary-Value Problems. Chapter 9 in Review. Project 9: The Hammer. Appendix I: Gamma Function. Appendix II: Introduction to Matrices. Appendix III: Laplace Transforms. Selected Answers for Odd-Numbered Problems.
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