Stewart Calculus - Multivariable Functions

This course develops core techniques for multivariable functions, including partial derivatives, linear approximation, differentials, the chain rule, directional derivatives, limits, and local extrema. It also uses Lagrange multipliers to find maximum and minimum values.

Syllabus

What The Heck are Partial Derivatives?? With Visualization, Examples and Clairaut's Theorem!!.
Partial Derivative Examples Advanced (Including Derivative of an Integral).
Find the Linear Approximation of f(x,y) = 1-xycos(pi y) at the Point (1,1).
Use Differentials to Estimate the Amount of Metal in a Cylindrical Can.
Use the Chain Rule to find the Partial Derivatives.
Use the Chain Rule to Find the Partial Derivatives of z = tan(u/v), u-2s+3t, v=3s-2t.
Find all points at which the direction of fastest change of the function is i+j.
Find the Directional Derivative of f(x,y,z) = xy+yz+xz at (1,-1,3) in the direction of (2,4,5).
Local Extrema and Saddle Points of a Multivariable Function. 2nd Derivative Test.
Use Lagrange Multipliers to Find the Maximum and Minimum Values of f(x,y) = x^3y^5.
Multivariable Limit Using the Definition.