# Differential Equations: Fourier Series and Partial Differential Equations

Learn to use Fourier series to solve differential equations with periodic input signals and to solve boundary value problems involving the heat equation and wave equation.

## There is one session available:

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Estimated 11 weeks
5–8 hours per week
Instructor-paced
Instructor-led on a course schedule

# About this course

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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.

Violinist photo by user: DeshaCAM. Copyright © 2018 Adobe Systems Incorporated. Used with permission.

### At a glance

• Institution: MITx
• Subject: Math
• Level: Intermediate
• Prerequisites:
• Introduction to Differential Equations (basic)
• some linear algebra preferred

# What you'll learn

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• How to describe periodic functions using Fourier series
• How to solve ODEs with Fourier series input
• How to solve separable PDEs using Fourier series inputs and boundary conditions

# Syllabus

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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

# Frequently Asked Questions

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Q: What are the pre-requisites for this course?

A: We assume familiarity with 18.031x Introduction to Differential Equations and 18.032x Differential Equations: 2x2 Systems, and 18.033x Differential Equations: Linear Algebra and NxN Systems. Knowledge from 18.03Lx is not required to succeed in this course.

Q: Do I need to purchase a MATLAB license?

A: No, registering for this course gives you access to a MATLAB license for the duration of this course!

# Who can take this course?

Unfortunately, learners from one or more of the following countries or regions will not be able to register for this course: Iran, Cuba and the Crimea region of Ukraine. While edX has sought licenses from the U.S. Office of Foreign Assets Control (OFAC) to offer our courses to learners in these countries and regions, the licenses we have received are not broad enough to allow us to offer this course in all locations. edX truly regrets that U.S. sanctions prevent us from offering all of our courses to everyone, no matter where they live.