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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 course, 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 course 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 course are an understanding of ordinary differential equations and basic familiarity with partial differential equations.
This OpenLearn course provides a sample of level 2 study in.
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: Tuesday, 23rd February 2016
- 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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