EE436

Mathematical Foundations of Signal Processing and Control

Meeting times : Friday; 14:30, 15:30, 16:30

Instructor : Bilge Karaçalı, PhD

Office : EEE Building Room 209

Phone : 6719

E-mail : bilgekaracali@iyte.edu.tr

Summary

Introduction to set theory. Metric spaces. Neighborhood and continuity. Convergence of sequences. Normed vector spaces. Completeness, Banach spaces. Linear operators and functionals. Inner product spaces, Hilbert spaces.

Syllabus

Grading

Homework 30%

Midterm 30%

Final 40%

Text

N. Kolmogorov, S. V. Fomin, “Introductory real analysis,” Dover, New York, 1975

E. Kreyszig, “Introductory functional analysis with applications,” John Wiley & Sons, New York, 1989

Weekly schedule

Week 1: Introduction to set theory: Basics and definitions

Week 2: Decomposition of a set into classes

Week 3: Ordered sets and set systems

Week 4: Metric spaces

Week 5: Neighborhood and continuity

Week 6: Convergence, Cauchy sequences and completeness

Week 7: Midterm

Week 8: Completion of metric spaces

Week 9: Vector spaces, normed spaces

Week 10: Banach spaces

Week 11: Finite dimensional normed spaces

Week 12: Linear operators

Week 13: Inner product spaces, Hilbert spaces

Week 14: Orthogonal complements and direct sums