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Modelling with Fourier series

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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.

By: The Open University

  • Duration 16 hours
  • Updated Tuesday 23rd February 2016
  • Intermediate level
  • Posted under Mathematics Education
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Modelling with Fourier series

Introduction

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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 Mathematics [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] .

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