date_range Starts on March 22, 2023
event_note Ends on May 17, 2023
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assignment Level : Intermediate
chat_bubble_outline Language : English
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Key Information

credit_card Free access
verified_user Fee-based Certificate
timer 55 hours in total

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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• 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

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Prerequisite

• Introduction to Differential Equations (basic)
• some linear algebra preferred

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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
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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

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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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Platform

Harvard University, the Massachusetts Institute of Technology, and the University of California, Berkeley, are just some of the schools that you have at your fingertips with EdX. Through massive open online courses (MOOCs) from the world's best universities, you can develop your knowledge in literature, math, history, food and nutrition, and more. These online classes are taught by highly-regarded experts in the field. If you take a class on computer science through Harvard, you may be taught by David J. Malan, a senior lecturer on computer science at Harvard University for the School of Engineering and Applied Sciences. But there's not just one professor - you have access to the entire teaching staff, allowing you to receive feedback on assignments straight from the experts. Pursue a Verified Certificate to document your achievements and use your coursework for job and school applications, promotions, and more. EdX also works with top universities to conduct research, allowing them to learn more about learning. Using their findings, edX is able to provide students with the best and most effective courses, constantly enhancing the student experience.

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