微分方程基本教程
2004-11
世界图书出版公司北京
D.G.Zill
489
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 EQUATIONS6 SERIES SOLUTIONS Of LINEAR EQUATIONS7 THE LAPLACE TRANSFORM8 SYSTEMS OF LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS 9 NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONSAPPENDIXES SELECTED ANSWERS FOR ODD-NUMBERED PROBLEMS INDEX
