Math 447 Fall 2016- A. FREIRE
TOPICS
PART I: Topology
Normed vector spaces
Continuity of maps
Compactness
Connectedness
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Spaces of Continuous Functions (outdated)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)