This course covers the learning outcomes and goals of understanding multivariable functions through topics such as partial derivatives, linear approximation, chain rule, directional derivatives, local extrema, Lagrange multipliers, and multivariable limits. Students will learn to apply these concepts to solve advanced problems involving multivariable functions. The teaching method includes visualization, examples, and theorems to enhance understanding. This course is intended for learners interested in advancing their knowledge of multivariable calculus and its applications.
Overview
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.
Taught by
Jonathan Walters
