Laplace Transform Basics & Examples 📊

Welcome to a new series on the Laplace Transform. This remarkable tool in mathematics will let us convert differential equations to algebraic equations we can solve, and then convert back. In this first video we will define the Laplace Transform as an improper integral. We will see three examples: exponential functions, the step function aka Heaviside function, and the Laplace Transform of polynomials. The latter examples will make use of something called the Gamma Function and we will see it has nice properties related to factorials.

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0:00 Laplace Transforms Help Solve Differential Equations
1:37 Definition of the Laplace Transform
2:46 Laplace Transform of Exponentials
5:21 Laplace Transform of Step Functions
7:21 Properties of the Gamma Function
10:31 Laplace Transform of the Gamma Function

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