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.

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

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[mbenitez]

The wind is the soul leaving my body as i learn Laplace Transformations

[presdent]

You can use a Fourier transform (special case of Laplace transform) to filter out the wind noise in the video.

[Warkip]

some say you can even hear the screams of the horrified students...

[devalon]

You are one of the few that made a proper series of the Laplace transform. Much appreciated. Keep up the good work!

[wunboonail]

The Wikipedia article on this topic freaked me out. It is so outstandingly presented and I like his style.

[brandonmohammed]

I was just starting my journey on laplace today and i love that you uploaded this today. Honestly on of the best yt channels there is. Keep doing great things sir because you make a great impact

[stevanmiletic]

Shout out to Pierre-Simon Laplace for this life hack

[JR-iuyl]

Cheers for these vids im currently doing Laplace Transforms for Maths Undergrad so this came at a perfect time.

[anonymouswolf]

The video becomes more exciting because he is happy to explain the topic.

[Defathomize]

How am I even supposed to understand something that's not fully explained (anywhere), like no one bothers to explain what even the purpose of laplace transforms is, you're just supposed to do it. Yet that's what I'm graded for and even if I get a good grade I would still have no clue what I'm actually doing. Kind of bizarre.

[BentHestad]

This is an excellent, little lecture. Thank you Sir, for this and other fine series in the field of mathematics!

[adeoladaniel]

Honestly.., been seeing commendable comments so far but as for me I rather feel ur not breaking this down enough and rather just jumping into solutions without even telling our it was brought about in the first place

[DRMath]

I remember solving these problems in undergrad!! Well explained
Happy Teaching!! ✌️✌️✅

[BoZhaoengineering]

Laplace transform is very important when you try to design a dynamic system.

[forrestgump]

Your enthusiasm makes your video much more interesting.

[brycewalker]

Love your content and I am doing my dissertation on the theory and applications of Laplace, this is a great help!

[kimhughes]

Kudos Trefor - great contribution to subject - much appreciated

[ZatoichiRCS]

Thank you for your effort on this video. You should start with the Fourier Transform. Even better is to start at the Taylor/McLauren Series. Can’t expect newbies to relate to this in depth material.

[kianvaziri]

Outstanding presentation! Incredible clarity. I never knew that the gamma function is the connection to the factorial, thank you so much for making this!

[nanahaha-yg]

I got 90 on my math systems exam. Hurrayy!!!