What is differentiability for multivariable functions??

Published: 17 June 2020
on channel: Dr. Trefor Bazett

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How should we define differentiability of multivaraible functions? We saw in the previous video of our Calc III playlist that partial derivatives is not enough because we saw an example of a discontinuous function whose partials didn't exist, violating our intuition from Calculus I. In this video we will dive back into Calc 1 and rephrase the normal limit definition of the derivative in terms of errors. That formulation of the derivative concept extends nicely to the multivariable case and gives us a nice definition. Finally we note the theorem that if the partials exist and are continuous then we have existence of the derivative.

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COURSE PLAYLISTS:

►CALCULUS I:    • Calculus I (Limits, Derivative, Integ...

► CALCULUS II:    • Calculus II (Integration Methods, Ser...

►MULTIVARIABLE CALCULUS (Calc III):    • Calculus III: Multivariable Calculus ...

►DIFFERENTIAL EQUATIONS (Calc IV):    • How to solve ODEs with infinite serie...

►DISCRETE MATH:    • Discrete Math (Full Course: Sets, Log...

►LINEAR ALGEBRA:    • Linear Algebra (Full Course)

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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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