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Transfer Functions and the Laplace Transform

An intro to the mysteries of the frequency domain and Laplace transform and how they're used to understand mechanical and electrical systems.

Transfer Functions and the Laplace Transform

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Comienza el 16 feb 2022
10 semanas estimadas
3–6 horas por semana
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Sobre este curso

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This course is about the Laplace Transform, a single very powerful tool for understanding the behavior of a wide range of mechanical and electrical systems: from helicopters to skyscrapers, from light bulbs to cell phones. This tool captures the behavior of the system and displays it in highly graphical form that is used every day by engineers to design complex systems.

This course is centered on the concept of the transfer function of a system. Also called the system function, the transfer function completely describes the response of a system to any input signal in a highly conceptual manner. This visualization occurs not in the time domain, where we normally observe behavior of systems, but rather in the “frequency domain.” We need a device for moving from the time domain to the frequency domain; this is the Laplace transform.

We will illustrate these principles using concrete mechanical and electrical systems such as tuned mass dampers and RLC circuits.

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

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Please note: edX Inc. has recently entered into an agreement to transfer the edX platform to 2U, Inc., which will continue to run the platform thereafter. The sale will not affect your course enrollment, course fees or change your course experience for this offering. It is possible that the closing of the sale and the transfer of the edX platform may be effectuated sometime in the Fall while this course is running. Please be aware that there could be changes to the edX platform Privacy Policy or Terms of Service after the closing of the sale. However, 2U has committed to preserving robust privacy of individual data for all learners who use the platform. For more information see the edX Help Center.

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Lo que aprenderás

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You’ll learn how to:

  • Pass back and forth between the time domain and the frequency domain using the Laplace Transform and its inverse.
  • Use a toolbox for computing with the Laplace Transform.
  • Describe the behavior of systems using the pole diagram of the transfer function.
  • Model for systems that have feedback loops.
  • Model sudden changes with delta functions and other generalized functions.

Plan de estudios

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  • Review of differential equations
  • System function and frequency response
  • Laplace Transform
  • Rules and applications
  • Impulses and impulse response
  • Convolution
  • Feedback and filters

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.

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