MST209_2 Mathematical methods and models

Differential equations

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This free course provides a sample of level 2 study in Mathematics: www.open.ac.uk/courses/find/mathematics.

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Contents

- Introduction

- Learning outcomes

- 1 Differential equations

- Conclusion

- Keep on learning

- Acknowledgements

Introduction

This course extends the ideas introduced in the course on first-order differential equations to a particular type of second-order
differential equation which has a variety of applications. The course assumes that you have previously had a basic grounding
in calculus, know something about first-order differential equations and have some familiarity with complex numbers.

This OpenLearn course provides a sample of level 2 study in Mathematics.

Learning outcomes

After studying this course, you should be able to:

- solve homogeneous second-order equations

- identify a general method for constructing solutions to inhomogeneous linear constant-coefficient second-order equations

- show an awareness of initial and boundary conditions to obtain particular values of constants in the general solution of second-order
differential equations.

1 Differential equations

The main teaching text of this course 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 the link below to open the workbook (PDF, 1.4 MB).

Workbook

Click the link below to open the answer book (PDF, 0.3 MB).

Answer book

Workbook contents

- Introduction

- 1 Homogeneous differential equations

- 1.1 First thoughts

- 1.2 Method of solution

- 1.3 The general solution

- 2 Inhomogeneous differential equations

- 2.1 General method of solution

- 2.2 Finding a particular integral by the method of undetermined coefficients

- 2.3 Exceptional cases

- 2.4 Combining cases

- 3 Initial conditions and boundary conditions

- 3.1 Initial-value problems

- 3.2 Boundary-value problems

Conclusion

This free course provided an introduction to studying Mathematics. It took you through a series of exercises designed to develop
your approach to study and learning at a distance and helped to improve your confidence as an independent learner.

Keep on learning

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Acknowledgements

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

Course image: Nicolas Raymond in Flickr made available under Creative Commons Attribution 2.0 Licence.

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

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