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Introduction to Differential Equations

Scientists and engineers understand the world through differential equations. You can too.

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Introduction to Differential Equations
Este curso está archivado

Introduction to Differential Equations

Scientists and engineers understand the world through differential equations. You can too.

Introduction to Differential Equations
14 semanas
3–6 horas por semana
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Avanza a tu ritmo
Este curso está archivado

Sobre este curso

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How do you design:

  • A boat that doesn’t tip over as it bobs in the water?
  • The suspension system of a car for a smooth ride?
  • Circuits that tune to the correct frequencies in a cell phone?

How do you model:

  • The growth of antibiotic resistant bacteria?
  • Gene expression?
  • Online purchasing trends?

The answer: Differential Equations.

Differential equations are the language of the models we use to describe the world around us. In this mathematics course, we will explore temperature, spring systems, circuits, population growth, and biological cell motion to illustrate how differential equations can be used to model nearly everything in the world around us.

We will develop the mathematical tools needed to solve linear differential equations. In the case of nonlinear differential equations, we will employ graphical methods and approximation to understand solutions.

The five modules in this seriesare being offered as an XSeries on edX. Please visit the Differential EquationsXSeries Program Pageto learn more and to enroll in the modules.

Photo by user: bizoo_n. Copyright © 2016 Adobe Systems Incorporated. Used with permission.

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De un vistazo

  • Institución: MITx
  • Tema: Matemáticas
  • Nivel: Introductory
  • Prerrequisitos:

    Single variable calculus

  • Idioma: English
  • Transcripción de video: English
  • Programas asociados:
  • Associated skills:Sales, Antibiotic Resistance, Differential Equations

Lo que aprenderás

Omitir Lo que aprenderás
  • Use linear differential equations to model physical systems using the input / system response paradigm.
  • Solve linear differential equations with constant coefficients.
  • Gain intuition for the behavior of a damped harmonic oscillator.
  • Understand solutions to nonlinear differential equations using qualitative methods.

Plan de estudios

Omitir Plan de estudios

Unit 1

  1. Introduction to differential equations and modeling
  2. Complex numbers
  3. Solving first order linear differential equations

Unit 2

  1. The complex exponential
  2. Sinusoids
  3. Higher order linear differential equations
  4. Characteristic polynomial

Unit 3

  1. Harmonic oscillators
  2. Operators
  3. Complex replacement
  4. Resonance

Unit 4

  1. Graphical methods and nonlinear differential equations
  2. Autonomous equations
  3. Numerical methods

Acerca de los instructores

¿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.

This course is part of18.03x Differential Equations XSeries Program

Más información 
Instrucción por expertos
5 cursos de alta calidad
1 año 2 meses
4 - 7 horas semanales

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