In Calculus IV on Thursday, February 8th, we covered the derivation of tangent planes. We also showed how the tangent plane for functions of 2 variables generalizes to functions of several variables, a process we call linearization.
We also used this concept of linearization to define differentiability for functions of several variables. We also covered the concept of differentials.
I know that in this day and age, with technology so available, I should be utilizing some tools on the computer to draw these pictures that help us visualize these concept. Honestly, I just really enjoy drawing the pictures by hand. Having taught this course for several years now, I think I’m getting pretty good at it. I’d post a picture, but I wouldn’t want anyone to disagree with me and hurt my feelings. 
Next time, we cover the chain rule and will start directional derivatives.
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