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