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: [ Ссылка ]
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
****************************************************
Other Course Playlists:
►CALCULUS I: [ Ссылка ]
► CALCULUS II: [ Ссылка ]
►Full Multivariable Calculus Playlist: [ Ссылка ]
►DISCRETE MATH: [ Ссылка ]
►LINEAR ALGEBRA: [ Ссылка ]
***************************************************
► Want to learn math effectively? Check out my "Learning Math" Series:
[ Ссылка ]
►Want some cool math? Check out my "Cool Math" Series:
[ Ссылка ]
****************************************************
►X/Twitter: [ Ссылка ]
►TikTok: [ Ссылка ]
*****************************************************
This video was created by Dr. Trefor Bazett. I'm an Assistant Teaching Professor at the University of Victoria.
BECOME A MEMBER:
►Join: [ Ссылка ]
MATH BOOKS & MERCH I LOVE:
► My Amazon Affiliate Shop: [ Ссылка ]
