Workshop in Analysis

This course is meant to discuss problems and provide examples in the following topics. Close coordination with the parallel course Geometric Calculus 1 is recommended.

1. Topology of $\mathbb{R}^n$: open, closed, compact and connected sets.
2. Continuity and differentiability of functions from $\mathbb{R}^m$ to $\mathbb{R}^n$, including the basic geometric properties of directional derivatives and the gradient. Curves in $\mathbb{R}^n$.
3. Implicit and inverse function theorems
4. Taylor’s theorem for multivariable functions and the Hessian
5. Extrema for multivariable functions, with and without constraints
6. Fubini’s theorem and the change of variables formula