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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.
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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
Prerequisite
- Introduction to Differential Equations (basic)
- some linear algebra preferred
Syllabus
Unit 1: Fourier Series
- Introduction to Fourier series
- Fourier series with arbitrary periods
- Using Fourier series to solve differential equations
Unit 2: Partial Differential Equations
- Boundary conditions and boundary value problems
- The heat equation
- The wave equation
Instructors
David Jerison
Professor of Mathematics
Massachusetts Institute of Technology
Arthur Mattuck
Emeritus Professor of Mathematics
Massachusetts Institute of Technology
Jennifer French
Digital Learning Scientist and Lecturer
Massachusetts Institute of Technology
Duncan Levear
Postdoctoral Associate/DLL
Massachusetts Institute of Technology
Content Designer
MIT is a world-class educational institution where teaching and research — with relevance to the practical world as a guiding principle — continue to be its primary purpose.
MIT is independent, coeducational, and privately endowed. Its five schools and one college encompass numerous academic departments, divisions and degree-granting programs, as well as interdisciplinary centers, laboratories and programs whose work cuts across traditional departmental boundaries.
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