8.1.5-PDEs: Derivation of the Laplace Equation

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These videos were created to accompany a university course, Numerical Methods for Engineers, taught Spring 2013. The text used in the course was "Numerical Methods for Engineers, 6th ed." by Steven Chapra and Raymond Canale.
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Thank you! But I have a few questions..
1. What equation is that qi=-kρc(∂T/∂i) you used?
2. I'm currently taking a Hydrodynamics class. Is it okay to submit this method as a test answer in this class? Because this seems to be a thermodynamic method, given that you mentioned heat and temperature. I have never learned thermodynamics so I'm very confusing..

SJ-zntu
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I'm actually looking for the explanation for flow equation of underground water but this is also adaptable. Thank you so much

KorawichKavee
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Could you add an anotation for the missing delta z, because I paused the video and tried to find why it wasn't there and wasted some time on that (so nobody else will do that ;))

MrMytubevidmaker
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what is the wesbite/program used to write the equations or formulas?

amuri
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I have deleted my first comment as I can see it now as rough and unfair for I did not appreciate the effort you had put to make this tutorial which is still very good. Thanks a lot Jacob for helping others to learn and for being a sensitive human being. If we have met in reality, we would be very close friends. Thanks!

simple
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Just read section 3.4 of Volume II of Feynman's Lectures on Physics.

MathsatBondiBeach
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Please what the k and c and T and q and p ?

gigihiza