# 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.

## There is one session available:

After a course session ends, it will be archived.
Estimated 10 weeks
3–6 hours per week
Self-paced
Free

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.

# What you'll learn

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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.

# Syllabus

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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