EECS 600 Syllabus

This is a tentative syllabus for EECS 600.
The actual order will probably be different, but
this reflects the topics that I would *like* to cover.

Introduction 1.1-1.4
Linear spaces 2.1
Vector spaces 2.2-2.5
Normed linear spaces 2.6
Topology 2.7-2.9, 2.13, 2.15
lp and Lp spaces 2.10
Banach spaces 2.11-2.12

Method of successive approximations 10.1-10.2
(preview of the applications)

Hilbert spaces 3.1
Projection theorem 3.2-3.3
Orthogonality and the Gram-Schmidt procedure 3.4-3.5
Normal equations and Fourier series 3.6-3.9
Minimum norm problems 3.10-3.12

Linear operators 6.1
Space of bounded linear operators 6.2
Inverse linear operators 6.3

Dual spaces 5.1
Spaces of linear functionals 5.2-5.3
Hahn-Banach theorem (Extension form) 5.4
Riez-Representation theorem 5.5
Second dual spaces and weak convergence 5.6,5.10
Alignment and orthogonal complements 5.7
Minimum norm problem and its applications 5.8-5.9
Hahn-Banach theorem (Geometric form) and its applications 5.11-5.12

Optimization of functionals 7.1
Gateaux and Frechet derivatives 7.3
Conditions for an optimum 7.4
Application to the calculus of variations 7.5
Conjugate duality (if time permits)
Convex functionals and their properties 7.8-7.9
Conjugate functionals 7.10
Fenchel duality 7.12

Newton's Method 10.3 (requires Frechet derivatives)

POCS?