- Current section: Introduction
- Learning outcomes
- 1 Modelling with Fourier series
- Acknowledgements
from The Open University
Alternatively you can skip the navigation by pressing 'Enter'.
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)]
Other pages You might like

Try: English: Personal Experiences
How has the English language influenced your life? How would you define your relationship...

Try: Maths for science and technology
You're about to start a course in science and technology and you're wondering whether...

Study: Graduate Diploma in Mathematics...
If you’re teaching maths, but without a specialist background, this diploma will help...

Try: Starting with maths: Patterns and...
Patterns occur everywhere in art, nature, science and especially mathematics. Being able...

Try: Encouraging book talk in the school...
As adults we sometimes struggle to justify our feelings about particular books, but...

Try: Numbers: An introduction to subtraction
Do you want to improve your ability to subtract one number from another, especially if...

Try: Why teach art?
What value does art have in the school curriculum? This unit, primarily aimed at...

Try: Essay and report writing skills
Writing reports and assignments can be a daunting prospect. This unit is designed to help...

Try: Key skill assessment unit: Problem...
Problem solving runs through many activities. Often problems are contexts for focusing...

Try: Learning how to learn
Learning how to learn: a process we all engage in throughout our lives, but no single...

Try: Open education
There are many different 'flavours' or interpretations of what openness means in...

Try: Working with charts, graphs and tables
Your course might not include any maths or technical content but, at some point during...
Comments
Be the first to post a comment
Copyright & revisions
Copyright information
- 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.
Feeds
If you enjoyed this, why not follow a feed to find out when we have new things like it? Choose an RSS feed from the list below. (Don't know what to do with RSS feeds?)
Remember, you can also make your own, personal feed by combining tags from around OpenLearn.
Alternative Formats
Tags, Ratings and Social Bookmarking
Page Tags
Sign in or create a free account to add tags to your personal tag cloud using:
Have you tried our free courses?
Back on the streets
More Or Less returns
OU TV & Radio
-
Keeping Britain Alive - Ep 8BBC Two (Northern Ireland only)
Saturday 0:10 -
Life In The UndergrowthEden
Saturday 9:00 -
History Of ScotlandBBC Two
Saturday 10:00 -
More Or LessBBC Radio 4
Sunday 20:00 -
Thinking Allowed: Plenty & stammeringBBC Radio 4
Monday 0:15
Views
Votes
Comments
Tags
- climate change (373)
- business (277)
- diaries (194)
- bottom line (169)
- food (168)
- Rough Science (162)
- internet (147)
- BBC Two (145)
- BBC Radio 4 (140)
- BBC (133)
- Scotland (121)
- listings (120)
- points for debate (120)
- Bang goes the Theory (116)
- Creative Climate (116)
- children (116)
- English Civil War (115)
- astronomy (108)
- Thinking Allowed (104)
- religion (98)
- marketing (94)
- 20th century (94)
- Charles I (93)
- communication (92)
- evolution (92)
- research (89)
- sustainability (89)
- architecture (86)
- energy (83)
- National Health Service (NHS) (78)
OpenLearn Links
Copyrighted imageCredit: Background image Lucian Milasan | Dreamstime.com 

