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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

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

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.

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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.

This is part of a 5-part series in Differential Equations:

What you'll learn

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.

Prerequisites

18.03.1x Introduction to Differential Equations

Meet your instructors

  • Featured image for Haynes Miller
    Professor of Mathematics, emeritus
  • Featured image for Jeremy Orloff
    Lecturer
  • Featured image for David Jerison
    Professor of Mathematics
  • Featured image for Jennifer French
    Lecturer in Mathematics

Who can take this course?

Because of U.S. Office of Foreign Assets Control (OFAC) restrictions and other U.S. federal regulations, learners residing in one or more of the following countries or regions will not be able to register for this course: Iran, Cuba, Syria, North Korea and the Crimea, Donetsk People's Republic and Luhansk People's Republic regions of Ukraine.