Using Laplace Transform to Solve ODEs with Discontinuous Inputs
In this lesson, the instructor explains how to use Laplace Transform to solve ODEs with discontinuous inputs. He introduces the unit step function and the unit box function, which handle jump discontinuities in functions very nicely. He then goes on to calculate the Laplace transform of the unit step function, which leads to a discussion of the inverse Laplace transform and the uniqueness of the solution. Finally, he derives a translation formula for the Laplace transform of a function, which is useful in solving differential equations.
Using Laplace Transform to Solve ODEs with Discontinuous Inputs -- Lecture 22. The last lecture using the Laplace Transform to solve ODEs.
Arthur Mattuck, 18.03 Differential Equations, Spring 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 27, 2008). License: Creative Commons BY-NC-SA.
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- Lecture Notes - Lecture Notes
- Input-Response Models - Input-Response Models
- Supplementary Notes - Chapter 18 Supplementary Notes written by Prof. Miller
- Recitation Problems - Recitation Problems and classwork exercises
- Recitation Solutions - Recitation problem solutions
- What are jump discontinuities?
- How can you use the Laplace Transform to solve differential equations with discrete inputs?
- How do you use the Laplace Transform?
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Staff Review
In this final lecture using the Laplace Transform; this lecture solves several differential equations with discrete inputs using the transform. You will also learn what a jump discontinuity is and what it means in problems. More good problems using this useful technique.
