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This free course, First-order differential equations, 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.
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.
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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.
This free course is an adapted extract from the Open University course MST209 Mathematical methods and models, which is no longer taught by the University. If you want to study formally with us, you may wish to explore other courses we offer in this.
This free course includes adapted extracts from an Open University course which is no longer available to new students. If you found this interesting you could explore more free Mathematics Education courses or view the range of currently available OU Mathematics Education courses.
Copyright & revisions
Originally published: Friday, 22nd July 2011
Last updated on: Thursday, 6th March 2014
- Creative-Commons: The Open University is proud to release this free course under a Creative Commons licence. However, any third-party materials featured within it are used with permission and are not ours to give away. These materials are not subject to the Creative Commons licence. See terms and conditions. Full details can be found in the Acknowledgements and our FAQs section.
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