# ECE501B

Advanced Linear Systems Theory
Fall
Catalog Data:

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ECE 501B - Advanced linear system theory

Credits:  3.00

Course Website: www.ece.arizona.edu/~gehm/501

UA Catalog Description:  http://catalog.arizona.edu/allcats.html

Course Assessment:

Homework:  6 assignments

Project:  1 team project

Exams:  2 Midterm Exams, 1 Final Exam

Typically: 50% Midterms,

30% Final Exam,

10% Homework,

10% Project.

Course Summary:

Mathematical fundamentals for analysis of linear systems. Maps and operators in finite and infinite dimensional linear vector spaces, metric spaces, and inner-product spaces. Introduction to representation theory. Eigensystems. Spectral theorems and singular value decomposition. Continuity, convergence, and separability. Sturm-Louisville theory.

Prerequisite(s):
Graduate Standing or Permission of the Instructor
Textbook(s):

Required: Linear Algebra Done Right, 2nd Ed., by Sheldon Axler w

Required: Signal Theory, Revised Ed., by L.E. Franks (Provided)

Suggested: How to Read and Do Proofs, 4th Ed., by Daniel Solow

Course Learning Outcomes:

At the end of the course, Students will be able to apply these concepts to real-world application problems in science and engineering.

Course Topics:

1) Vector space

2) Subspace

3) Subspace sum and direct sum

4) Span and linear independence

5) Bases

6) Dimension

7) Linear maps and operators

8) Null space and range

9) Matrix representation of a map

10) Invertability

11) Invariant subspaces (especially eigenvalues/vectors)

12) Inner products and norms

13) Orthonormal bases

14) Linear functionals and adjoints

15) “Special” operator forms (self-adjoint, normal, positive, isometries, etc.)

16) Real and complex spectral theorems

17) Polar and singular value decompositions

18) Trace and determinant

19) Function spaces

20) Continuity, convergence, and separabilty

21) Equivalence classes

22) Eigenfunctions

Class/Laboratory Schedule:

Lecture:  150 minutes/week

Prepared by:
Michael E. Gehm
Prepared Date:
April 2013

University of Arizona College of Engineering