FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS. COURSE BOOK. Anita Ciekot, Izabela Zamorska

CONTENTS

FOREWORD

CHAPTER 1. INTRODUCTION
1.1. Overview of differential equations
1.2. General definitions
1.3. Do it yourself tasks

CHAPTER 2. FIRST ORDER DIFFERENTIAL EQUATIONS
2.1. Basic definitions and theorems
2.2. Equation with separable variables
2.3. First order non-separable equations – solutions by substitutions
2.4. Do it yourself tasks

CHAPTER 3. LINEAR FIRST ORDER DIFFERENTIAL EQUATIONS
3.1. Basic terminology
3.2. Euler-Lagrange method for solving the linear first order differential equation
3.3. Integrating factor for linear first order equations
3.4. Bernoulli differential equation
3.5. Do it yourself tasks

CHAPTER 4. EXACT DIFFERENTIAL EQUATION
4.1. Basic concepts and definitions
4.2. Method of solution to the exact differential equation
4.3. Integrating factor for nonexact equation
4.4. Do it yourself tasks

CHAPTER 5. MODELING USING FIRST ORDER DIFFERENTIAL EQUATIONS
5.1. Population problems
5.2. Cooling problems
5.3. Mixing problems
5.4. Elementary mechanics problems

6. APPENDIX. REVIEW OF INTEGRATION
6.1. Basic definitions and integral rules
6.2. Table of common integrals
6.3. Examples

ANSWERS FOR SELECTED TASKS

BIBLIOGRAPHY