Lectures in course MATH-105(b): Advanced analysis II

Covers extreme values of continuous functions on compact sets and differentiability.

Covers advanced optimization methods using Lagrange multipliers to find extrema of functions subject to constraints.

Covers the Implicit Functions Theorem, demonstrating the conditions under which a function can be expressed implicitly.

Covers the optimization of functions, focusing on finding the maximum and minimum values over a given domain.

Covers integrals doubles in compact domains with negligible borders and problematic cases.

Explores the consequences of double integrals, including compact sets and continuity.

Covers advanced integration techniques for double integrals, focusing on Fubini's Theorem.