Intro to the Laplace Transform & Three 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.

►Laplace Transforms (and more ODE topics) Playlist:    • Intro to the Laplace Transform & Thre...  

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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Other Course Playlists:

►CALCULUS I:    • Calculus I (Limits, Derivative, Integ...  

► CALCULUS II:    • Calculus II (Integration Methods, Ser...  

►Full Multivariable Calculus Playlist:    • Calculus III: Multivariable Calculus ...  

►DISCRETE MATH:    • Discrete Math (Full Course: Sets, Log...  

►LINEAR ALGEBRA:    • Linear Algebra (Full Course)  

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This video was created by Dr. Trefor Bazett. I'm an Assistant Teaching Professor at the University of Victoria.

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