Why Exponential Growth?? Intro to Separable Differential Equations

Epidemics initially have exponential growth. So does money invested in a bank account compounded continuously. Why? In this introduction to differential equations we study the ODE y'=ky. This is an example of a separable differential equation, and it's solution is exponential growth. This equation is reasonable for a simple model of things like the early days of an epidemic because the growth rate is proportional to the current size, y'=ky. After solving this equation by the method of separation of variables we turn to the general procedure for separable equations.

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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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[irenepadre]

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[Algo]

I'm a Lawyer in a family of Engineers and I didn't follow that path because I knew this would be in my way.
Guess 10 years made the difference, or you're an excellent teacher or both because I'm understanding this pretty easily, instant subscribe.

[FrancisBacontherd]

Seriously good explanation. I'm taking Diff Eq this semester and have been going through the paces of memorizing all the rules and methods without having a firm grasp on what any of it means. Thank you so much!!!

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[fernanmontevista]

Thanks doc for wonderful explanation !!!

[sinaasadiyan]

After watching this video, I wonder why university professors mostly skip this kind of enlightening examples and explanations.

[sergekamga]

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[pipertripp]

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[wcemkfd]

Colors are very helpful. Superb exposing style!!!

[UHmurrayClass]

Very nicely done! Out of curiosity, what video software do you use that allows you to super-impose the formulas on the background while you talk? It appears you can monitor it as you present, and I noticed the controller in your left hand. Would love to be able to do that for my online classes.

[joyanbhathena]

Can somebody explain (dy/dt)*dt --> dy? 04:20

[ItsMe-dtgr]

Hi sir, will u please tell me how do i solve a differential equation like
dy/dx + p(x)y = Q(x), where p and Q are the function of x or constants by laplace transform. Please sir, reply

[BoZhaoengineering]

It is like where the differential equations start. A Classic example, it is the compound interest and where the Euler e comes from.

[therealctoo]

It's a shame that most of the people who really need to understand this stuff in order to not be manipulated will not watch this.