Math: Partial Differential Eqn. - Ch.1: Introduction (14 of 42) Understanding the Laplacian Operator

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In this video I will explain what is a Laplacian operator by simplifying the function to a single dimension where f(x,y,z)=x^3.

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Excellent explanation. Thank you Professor.

valeriereid

Michel, It would be really nice if you could do GRE and if possible MCAT videos. Furthermore if you ever are able to have time, one key thing that would be nice is to incorporate interactivity somehow so perhaps someone could work out problems related to each lecture video or at the end of each subject. There is a lot of value in learning from doing. You are changing lives for the better, I thank you again.

Jarrod_C

I thought the second derivative actually tells us the curvature of the function. In 3D it means that out gradient field is curved up or down. So we can understand where things are accumulating and where things are draining. Right?

masoudjafary

Hard to wrap your head around this, but you did a very good job of explaining it.

Would your consider it similar to first and second derivatives of position, which are velocity and acceleration?

schifoso

What is the use of knowing the average of change in the slope. Where v use this function

sainathreddyvarikuti

So, I conclude that the Laplacian is kind of acceleration.

davidkwon

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