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# Differential Equations: Fourier Series and Partial Differential Equations

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### Overview

Differential equations are the mathematical language we use to describe the world around us. Many phenomena are not modeled by differential equations, but by partial differential equations depending on more than one independent variable. In this course, we will use Fourier series methods to solve ODEs and separable partial differential equations (PDEs). You will learn how to describe any periodic function using Fourier series, and will be able to use resonance and to determine the behavior of systems with periodic input signals that can be described in terms of Fourier series. This course will use MATLAB to assist computations.

In this course we will explore:

• How to process noisy sound files
• The way a beam bends in response to external forces
• How to design of ovens to create strong but lightweight composites
• The motion of a violin string

The five modules in this seriesare being offered as an XSeries on edX. Please visit theDifferential EquationsXSeries Program Pageto learn more and to enroll in the modules.

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### Syllabus

Unit 1: Fourier Series

1. Introduction to Fourier series
2. Fourier series with arbitrary periods
3. Using Fourier series to solve differential equations

Unit 2: Partial Differential Equations

1. Boundary conditions and boundary value problems
2. The heat equation
3. The wave equation

### Taught by

David Jerison, Arthur Mattuck and Jennifer French

## Reviews

5.0 rating, based on 3 Class Central reviews

Start your review of Differential Equations: Fourier Series and Partial Differential Equations

• Michael Levin
I think an in-depth understanding of Fourier analysis is very important for doing well in signal processing later on. Often not enough time is spent on this topic. Great class. Very important. You may consider getting C. Langton's book, "Intuitive Guide to Fourier analysis." It will fill in all the missing details.
• Dna47a
Another excellent course from MIT. The content (great videos) explaining the heat equation and the wave equation was too good. The MATLAB programs, together with problem sets and an active discussion forum where fellow students and staff were always present to help makes this a truly enjoyable course for me.
• nice and well teached course with both theory and practice problems on Fourier Series and related applications on solving Differential Equations.

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