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This free course, Modelling with Fourier series, shows how partial differential equations can be used to model phenomena such as waves and heat transfer. The prerequisite requirements to gain full advantage from this free course are an understanding of ordinary differential equations and basic familiarity with partial differential equations.
After studying this unit you should be able to:
- understand how the wave and diffusion partial differential equations can be used to model certain systems;
- determine appropriate simple boundary and initial conditions for such models;
- find families of solutions for the wave equation, damped wave equation, diffusion equation and similar homogeneous linear second-order partial differential equations, subject to simple boundary conditions, using the method of separating the variables;
- combine solutions of partial differential equations to satisfy given initial conditions by finding the coefficients of a Fourier series.
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Modelling with Fourier series
This unit shows how partial differential equations can be used to model phenomena such as waves and heat transfer. The prerequisite requirements to gain full advantage from this unit are an understanding of ordinary differential equations and basic familiarity with partial differential equations.
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: Thursday, 31st March 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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