Math 447 Fall 2016- A. FREIRE


PART I: Topology

Normed vector spaces
Continuity of maps
Spaces of continuous functions

Supplementary handouts (for advanced students):
(adapted from more advanced classes and not yet in final form)

Definitions and Theorems from General Topology
References: [D]= Topology, by James Dugundji; [R]=Functional Analysis, by W. Rudin

Locally compact Banach spaces are finite dimensional (includes 4 problems)

Spaces of Continuous Functions (outdated)

Stone-Weierstrass theorem-notes (includes 6 problems)

Ascoli-Arzela-Notes (final-included 7 exercises with solutions, and 11 extra problems.)

PART 2: Differentiable functions

Directional and partial derivatives
Differentiable functions
Functions of class C^k, Taylor's theorem
Relative extrema
Convex functions
Spaces of differentiable functions

PART 3: Differentiable maps and surfaces

Differentiable maps
Compositions and the Chain Rule
Inverse Function Theorem
Implicit Function Theorem
Surfaces in R^n
Constrained extrema (Lagrange multipliers)