Laplace Transform Basics & Examples đ
Discover the Laplace Transform, a powerful tool to convert differential equations into algebraic form with three illustrative examples.
Dr. Trefor Bazett
1.2M views âą Mar 15, 2020
About this video
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.
âșLaplace Transforms (and more ODE topics) Playlist: https://www.youtube.com/watch?v=KqokoYr_h1A&list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1
âĄâĄâĄSUPPORT THE CHANNELâĄâĄâĄ
âșSupport on PATREON: https://patreon.com/DrTrefor
âșCURIOSITY BOX: https://www.CuriosityBox.com/DrTrefor use CODE drtrefor for 25% off awesome STEM merch boxes
âșMATH BOOKS I LOVE (affiliate link): https://www.amazon.com/shop/treforbazett
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
COURSE PLAYLISTS:
âșDISCRETE MATH: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS
âșLINEAR ALGEBRA: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6
âșCALCULUS I: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m
âșCALCULUS II: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n
âșMULTIVARIABLE CALCULUS (Calc III): https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd
âșVECTOR CALCULUS (Calc IV) https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa
âșDIFFERENTIAL EQUATIONS: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw
âșLAPLACE TRANSFORM: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1
âșGAME THEORY: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlX
OTHER PLAYLISTS:
âșCool Math Series:
https://www.youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpiho
âș Learning Math Series
https://www.youtube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw
SOCIALS:
âșX/Twitter: http://X.com/treforbazett
âșTikTok: http://tiktok.com/@drtrefor
âșInstagram (photography based): http://instagram.com/treforphotography
âșLaplace Transforms (and more ODE topics) Playlist: https://www.youtube.com/watch?v=KqokoYr_h1A&list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1
âĄâĄâĄSUPPORT THE CHANNELâĄâĄâĄ
âșSupport on PATREON: https://patreon.com/DrTrefor
âșCURIOSITY BOX: https://www.CuriosityBox.com/DrTrefor use CODE drtrefor for 25% off awesome STEM merch boxes
âșMATH BOOKS I LOVE (affiliate link): https://www.amazon.com/shop/treforbazett
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
COURSE PLAYLISTS:
âșDISCRETE MATH: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS
âșLINEAR ALGEBRA: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6
âșCALCULUS I: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m
âșCALCULUS II: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n
âșMULTIVARIABLE CALCULUS (Calc III): https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd
âșVECTOR CALCULUS (Calc IV) https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa
âșDIFFERENTIAL EQUATIONS: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw
âșLAPLACE TRANSFORM: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1
âșGAME THEORY: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlX
OTHER PLAYLISTS:
âșCool Math Series:
https://www.youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpiho
âș Learning Math Series
https://www.youtube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw
SOCIALS:
âșX/Twitter: http://X.com/treforbazett
âșTikTok: http://tiktok.com/@drtrefor
âșInstagram (photography based): http://instagram.com/treforphotography
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Video Information
Views
1.2M
Likes
17.6K
Duration
12:05
Published
Mar 15, 2020
User Reviews
4.8
(234)