ECE 69500 - Introduction to Mathematical Fundamentals for Systems and Control Theory

Lecture Hours: 3 Credits: 1

Areas of Specialization(s):

Automatic Control

Counts as:
CMPE Special Content Elective
EE Elective - Special Content

Normally Offered: Each Spring

Requisites:
ECE 30200; MA 26500 and 26600 (or MA 26200)

Requisites by Topic:
Undergraduate linear algebra, differential equations, and probability

Catalog Description:
This course serves as background for ECE 602 Lumped System Theory, ECE 595/695 Epidemic Processes over Networks, and ECE 695 Structure and Dynamics of Large-Scale Networks, and other similar courses. The course will make the necessary mathematical background for the aforementioned courses accessible by decomposing and illustrating difficult concepts with a number of real world examples and problems for students to work out. Namely, the course consists of five modules: 1) Linear Algebra, 2) Basic Graph Theory, 3) Basic Control Theory, 4) Probability, and 5) Optimization.

Supplementary Information:
This is a 1-credit, 5-week course that runs weeks 1-5 of the semester. For more information on this course and subsequent courses, please go to https://sites.google.com/view/philpare/teaching.

Required Text(s): None.

Recommended Text(s):
  1. A First Course in Probability, S. Ross, Pearson, 2018, ISBN No. 978-0134753119.
  2. Convex Optimization, L. Vandenberghe, S. Boyd and S. P. Boyd, 2004, ISBN No. 9780521833783.
  3. Convex Optimization, L. Vandenberghe, S. Boyd and S. P. Boyd, 2004, ISBN No. 9780521833783.
  4. Feedback Systems: An Introduction for Scientists and Engineers, K. J. Astrom and R. M. Murray, 2009, ISBN No. 9780691135762.
  5. Introduction to Graph Theory, D. B. West, Pearson, 2012, ISBN No. 9780131437371.
  6. Matrix Analysis, R. A. Horn and C. R. Johnson, Cambridge University Press, 2012, ISBN No. 978-0521548236.

Lecture Outline:

Week Topic
1 Linear Algebra Review
2 Basic Graph Theory
3 Basic Control Theory
3 Basic Probability
4 Basic Optimization