圣智学习

In recent years, partially due to evolving technology and its expanding importance in pedagogy and to the reform movement in calculus, changes have occurred in the course called "Differential Equations." Instructors are questioning aspects of both the traditional teaching methods used and the traditional content of the course. This healthy introspection is important in making the subject matter not only more interesting for students but also more relevant to the world in which they live.

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