EE 303

Title:  MATHEMATICAL METHODS IN ELECTRICAL ENGINEERING

Credits: 3

Catalog Description: Vector spaces, subspaces. Linear dependence/independence, span, basis. Linear transformations, eigenstructure analysis. Matrix representations of linear transformations, change of coordinates. Analytic functions of complex variables. Contour integrals. Cauchy integral formula. Poles and residues. Partial derivatives. Total differential and total derivatives. Jacobean determinants.

Prerequisite: Math 201

Coordinator: Hakan Deliç, Professor of Electrical Engineering

Goals:   The calculus of complex numbers is studied. Areas of electrical engineering where the topics of this course are relevant are pointed out.

Learning Objectives:

At the end of this course, students will be able to:

1. Understand the fundamental concepts in complex calculus such as the modulus, conjugates, polar coordinates, roots of a complex number.
2. Carry out operations on complex functions such as taking limits, differentiation, contour integration and series expansion.
3. Perform mappings by elementary functions and understand their use in moving between different domains (e.g. the Laplace and z-domains).

Textbook:  J. W. Brown and R. V. Churchill, Complex Variables and Applications, 6th Edition, McGraw Hill, 1996.

Reference Texts: None.

Prerequisites by Topic:

• Matrix Theory

Topics:

Introduction to complex numbers. (1 week)

1. Analytic functions. (1 week)
2. Elementary functions. (1 weeks)
3. Integrals. Cauchy-Goursat Theorem. Cauchy integral formula (1.5 weeks)
4. Series (1.5 weeks)
5. Residues and poles (1.5 week)
6. Application of residues (1.5 weeks)
7. Mapping by elementary functions. Application to discrete-time filter design. (1 week)
8. Conformal mapping (1 week)
9. Applications of conformal mapping (1 week)

Course Structure: The class meets for two lectures a week, each consisting of two 50-minute sessions. One hour per week is dedicated to problem solving (problem session). 6 sets of homework problems are assigned per semester.  There are two in-class term exams and a final exam.

Computer Resources: Not applicable.

Laboratory Resources: None.

Grading:

1. Homework sets (20%)
2. Two term exams (25% each).
3. A final exam (30%).

Outcome Coverage:

• Apply math, science and engineering knowledge.  While this course is on the fundamentals of complex variables, certain applications of the theory are also presented. Examples from the signal processing and communications areas are furnished during the lectures. In particular, boundary value problems such as the electrostatic potential, and the linear fractional transformation-based discrete-time filter design are studied.

• Use the techniques, skills, and modern engineering tools necessary for engineering practice. Complex calculus is an essential mathematical tool for designing and analyzing modern communications and signal processing systems, among others.

Prepared by: Hakan Deliç

Last revised: Nov 6, 2003