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Introduction

First-order differential equations

This unit introduces the topic of differential equations. The subject is developed without assuming that you have come across it before, but it is taken for granted that you have a basic grounding in calculus. In particular, you will need to have a good grasp of the basic rules for differentiation and integration.

Learning Outcomes

During this unit you will:

learn some basic definitions and terminology associated with differential equations and their solutions;
be able to visualize the direction field associated with a first-order differential equation and be able to use a numerical method of solution known as Euler's method;
be able to use analytical methods of solution by direct integration; separation of variables; and the integrating factor method.

First-order differential equations

The main teaching text of this unit is provided in the workbook below. The answers to the exercises that you'll find throughout the workbook are given in the answer book. You can access it by clicking on the link under the workbook.

Click 'View document' to open the workbook (PDF, 1.6 MB).

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Click 'View document' to open the answer book (PDF, 0.5 MB).

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Workbook contents

Introduction

1 Some basics

1.1 Why differential equations?

1.2 Differential equations and solutions

1.3 Approximations in calculations

2 Direction of fields and Euler's methods

2.1 Direction fields

2.2 Euler's method

3 Finding analytic solutions

3.1 Direct integration

3.2 Separation of variables

4 Solving linear differential equatios

4.1 Linear differential equations

4.2 The integrating factor method

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Acknowledgements

The content acknowledged below is Proprietary (see terms and conditions) and is used under licence.

All materials included in this unit are derived from content originated at the Open University.

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Fri, 01 Aug 2008 08:45:00 GMT

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