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- 1 Modelling with Fourier series
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Modelling with Fourier series
This unit shows how partial differential equations can be used to model...
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.
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.
- Duration: 16 hours
- Published on: Thursday 31st March 2011
- Level: Intermediate
- Posted under: Mathematics Education
Contents
Modelling with Fourier series
Introduction

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 unit is an adapted extract from the course Mathematical methods and models (MST209) [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)]
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- 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 section.
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