Khan Academy: Differential Equations: Introduction to Convolution

Video gives an introduction to what differential equations are and shows how they are different from regular equations. Shows an example of a differential equation and how to check if a given answer is a correct solution to a...

Video first gives an intuition of and defines the Dirac delta function. Includes graphing notation of the Dirac delta function and shows how to shift the Dirac delta function. Gives example of relating a real world scenario to...

Watch a video to explore an introduction to improper integrals.

Video gives the convolution theorem showing how the convolution and Laplace transform are related, then shows an example applying the convolution theorem. [13:46]

Video shows how to extend the derivative property of the Laplace transform to write the Laplace transform of higher order derivatives in terms of their original function. Shows an alternate notation of the Laplace transform and an...

Video gives another example of using the Laplace transform to find Laplace transform table values. Includes an example of what it means for the Laplace transformation when the improper integral diverges and shows the connection between...

Video first defines and shows a visualization of the unit step function and explains where it is useful in the real world. Shows how linear combinations of the unit step function can be used to created functions that model other...

Video first reviews properties of the Laplace transform that were shown in previous videos as well as Laplace transform table values that have been shown in previous videos. Then uses the properties and inverse Laplace transforms to find...

Video uses the properties of the Laplace transform shown in the previous video and extends them to show how they can be used to simplify problems and help find values for the Laplace transform table more quickly. Examples include trig...

Video demonstrates finding the Laplace transform of t^n using integration by parts and using a pattern of values to develop a general formula. [10:16]