Partial Derivatives

Explore the intricacies of partial derivatives in this comprehensive 3.5-hour lecture series. Delve into topics such as polar and spherical limits, the chain rule, Clairaut's theorem, implicit differentiation, tangent planes, and linear approximations. Master practical applications including surface area and volume optimization, the second derivative test, and Lagrange multipliers. Gain a deeper understanding of calculus concepts like the arithmetic-geometric mean inequality and distance calculations between points and planes.

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.