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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.

Differential Equations: Fourier Series and Partial Differential Equations
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11 semanas estimadas
5–8 horas por semana
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Sobre este curso

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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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Lo que aprenderás

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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

Plan de estudios

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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

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Preguntas frecuentes

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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!

¿Quién puede hacer este curso?

Lamentablemente, las personas residentes en uno o más de los siguientes países o regiones no podrán registrarse para este curso: Irán, Cuba y la región de Crimea en Ucrania. Si bien edX consiguió licencias de la Oficina de Control de Activos Extranjeros de los EE. UU. (U.S. Office of Foreign Assets Control, OFAC) para ofrecer nuestros cursos a personas en estos países y regiones, las licencias que hemos recibido no son lo suficientemente amplias como para permitirnos dictar este curso en todas las ubicaciones. edX lamenta profundamente que las sanciones estadounidenses impidan que ofrezcamos todos nuestros cursos a cualquier persona, sin importar dónde viva.

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