Differentiation in multivariable function, partial derivative and more

Differentiation in multivariable function, partial derivative, and more

0:00 start
4:12 definition of Differentiation in multivariable function
9:00 definition of partial derivative
10:19 connect Differentiation in multivariable function to the partial derivative

15:39 gradient
20:00 bound derivative and convex: generalization to mean value theorem
25:00 continuously differentiable
29:00 prove a function is continuously differentiable iff all its partial derivatives are continuously differentiable

Mathematical analysis
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Advanced mathematics list:

Group representation for finite group
https://www.youtube.com/playlist?list=PLg9w7tItBlZvxk4eus_gi2Wp3yYAEXF9-

exact sequences
https://www.youtube.com/playlist?list=PLg9w7tItBlZuI7n7notRRA2jol69e9mc9

Ring theory lecture
https://www.youtube.com/playlist?list=PLg9w7tItBlZtfPKHWGlU55kqafEgUu45u

group theory lecture
https://www.youtube.com/playlist?list=PLg9w7tItBlZtSHrTTVjEzAsUcO69YXY7v

Category theory
https://www.youtube.com/playlist?app=desktop&list=PLg9w7tItBlZtI1njDjtXt_0Hkqbn9RVvi

Field theory in abstract algebra
https://www.youtube.com/playlist?list=PLg9w7tItBlZtA6XhMIgIPkgj_SDKChbN-

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