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Online Course

Transfer Functions and the Laplace Transform

Massachusetts Institute of Technology via edX

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Overview

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 Equations XSeries Program Page to learn more and to enroll in the modules.

Syllabus

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

Taught by

Haynes Miller and Jeremy Orloff

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