Learning Differential Equations through DERIVE

Contents

Preface

Series Preface

Chapter 1: A Modelling Approach to Differential Equations
1.1 Mathematical Modelling
1.2 Some Mathematical Models
1.3 Classification of Differential Equations

Chapter 2: Analytical Solution of First Order Differential Equations
2.1 Direction Fields
2.2 Analytical Solutions
2.3 Equations Solved by Direct Integration
2.4 Separation of Variables
2.5 First Order Linear Equations
2.6 Bernoulli Equations
2.7 Homogeneous Equations
2.8 Exact Equations
2.9 Miscellaneous Substitutions

Chapter 3: Numerical Solution of First Order Differential Equations
3.1 Introduction
3.2 Numerical Methods for Solving First Order Differential Equations
3.3 The Analysis of Numerical Methods
3.4 Stability
3.5 Systems of Linear First Order Equations

Chapter 4: Applications of First Order Differential Equations
4.1 Emptying the Bath
4.2 Heating and Cooling
4.3 Population Models
4.4 Mechanics

Chapter 5: Analytical Solution of Second Order Differential Equations
5.1 Classification of Second Order Differential Equations
5.2 Homogeneous Linear Equations with Constant Coefficients
5.3 Non-Homogenous Linear Equations with Constant Coefficients
5.4 Other Linear Differential Equations With Constant Coefficients
5.5 Linear Second Order Equations in General
5.6 Systems of Linear Differential Equations
5.7 Numerical Solution of Second Order Differential Equations

Chapter 6: Applications of Second Order and Simultaneous First Order Differential Equations
6.1 Oscillations and Vibrations
6.2 Mixing Problems
6.3 Projectile Motion in Two Dimensions

Appendix 1 Glossary of DERIVE FOR WINDOWS Commands

Appendix 2 Functions and Utility Commands

Answers to Exercises

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