Khan Academy
Khan Academy: Differential Equations: Dirac Delta Function
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...
Khan Academy
Khan Academy: Differential Equations: Inverse Laplace Examples
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...
Khan Academy
Khan Academy: Differential Equations: Laplace Transform 4
Video continues the lesson from the previous video finding a Laplace transform table value which involves integration by parts twice. [9:13]
Khan Academy
Khan Academy: Differential Equations: Laplace Transform 5
Video proves properties of the Laplace transform including showing it is a linear operator and showing the Laplace tranform of the derivative of a function. [11:36]
Khan Academy
Khan Academy: Differential Equations: Laplace Transform 6
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...
Khan Academy
Khan Academy: Differential Equations: Laplace Transform 3 (L{sin(at)})
Video first reviews integration by parts then shows finding a Laplace transform table value using integration by parts twice. Problem is continued in next video. [10:44]
Khan Academy
Khan Academy: Differential Equations: Introduction to Convolution
Video first defines convolution, then gives an example of the convolution of two trig functions. [18:59]
Khan Academy
Khan Academy: Differential Equations: Laplace Transform 1
Video explains what the Laplace transform is, shows its notation and gives an example of using the Laplace transform. [8:01]
Khan Academy
Khan Academy: Differential Equations: Laplace Transform of T^n: L{t^n}
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]
Khan Academy
Khan Academy: Differential Equations: Laplace Transform of : L{t}
Video first reviews the Laplace transform of L{1} then uses it to help determine the Laplace transform of L{t}. [9:06]
Khan Academy
Khan Academy: Differential Equations: The Convolution and the Laplace Transform
Video gives the convolution theorem showing how the convolution and Laplace transform are related, then shows an example applying the convolution theorem. [13:46]
Khan Academy
Khan Academy: Differential Equations: Laplace Transform of Dirac Delta Function
Video first reviews what the Dirac delta function is, then shows how to determine the Laplace transform of the product of the Dirac delta function and another function. [12:13]
Khan Academy
Khan Academy: Intro to Differential Equations: Simple Differential Equations
In this video lesson students are provided an introduction to differential equations by exploring 3 basic differential equations that can be solved by taking the antiderivatives of both sides.
Khan Academy
Khan Academy: Properties of the Laplace Transform: Inverse Laplace Examples
This video uses the properties and inverse Laplace transforms to find the Laplace transform of more difficult functions.
Khan Academy
Khan Academy: Laplace as Linear Operator and Laplace of Derivatives
Video proves properties of the Laplace transform including showing it is a linear operator and showing the Laplace tranform of the derivative of a function.
Khan Academy
Khan Academy: Laplace Transform Solves an Equation 2
This vidio is part two to show how to use the Laplace transform to solve a differential equation.
Khan Academy
Khan Academy: Exact Equations and Integrating Factors: Exact Equations Example 3
In this video lesson students explore an exact equation example.
Khan Academy
Khan Academy: Laplace Transform of Cos T and Polynomials
Video uses the properties of the Laplace transform and extends them to show how they can be used to simplify and help find values for the Laplace transform table faster.
Khan Academy
Khan Academy: Laplace Transform: L{sin(at)}) Transform of Sin(at)
This video first reviews integration by parts then shows finding a Laplace transform table value using integration by parts twice.
Khan Academy
Khan Academy: Method of Undetermined Coefficients: Undetermined Coefficients 3
Video shows an example of solving a second order linear nonhomogeneous differential equation involving a polynomial function using undetermined coefficients.
Khan Academy
Khan Academy: Exact Equations and Integrating Factors: Exact Equations
In this video lesson students explore the chain rule using partial derivatives.
Khan Academy
Khan Academy: The Convolution Integral: Introduction to the Convolution
Introduction to the Convolution. Video first defines convolution, then gives an example of the convolution of two trig functions.
Khan Academy
Khan Academy: Exact Equations and Integrating Factors: Integrating Factors 1
In this video lesson students learn about using an integrating factor to make a differential equation exact.
Khan Academy
Khan Academy: Laplace Transform: Laplace Transform 1
A video introducing the Laplace Transform.