Partial Derivatives

This course develops partial derivatives through limits, the chain rule, implicit differentiation, tangent planes, linear approximations, and second derivative tests. It also applies multivariable calculus to optimization problems using Lagrange multipliers.

Syllabus

Polar coordinate limit.
Spherical Limit.
What is a Partial Derivative ?.
Chain Rule Surprise.
Clairaut Counterexample.
Clever Clairaut Proof.
Implicit Differentiation.
Tangent Planes.
Linear Approximations and Differentials.
My favorite calculus problem.
Surface area of box max/min.
Volume of box Lagrange.
The true second derivative test.
The arithmetic-geometric mean inequality.
Distance point and plane the Lagrange way.
Lagrange multiplier two constraints.