Differential Equations: Fourier Series and Partial Differential Equations
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
Upcoming start dates
Inquire for more information
- Virtual Classroom
Who should attend?
- Introduction to Differential Equations (basic)
- some linear algebra preferred
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
Course delivery details
This course is offered through Massachusetts Institute of Technology, a partner institute of EdX.
5-8 hours per week
- Verified Track -$75
- Audit Track - Free
Certification / Credits
What you'll learn
- 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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