California State University, Northridge - Spring 2018

College of Engineering & Computer Science

Department of Electrical & Computer Engineering

ECE 455 – Mathematical Models in Electrical Engineering

Course Units: 3.00 Design Units: 0.5

Professor: Dr. Mahmoud Youssef

http://www.fusion.ucla.edu ,

Course website: http://www.seas.ucla.edu/~myoussef/ECE455-S18

Office: JD 3338

ECE Phone: (818) 677-2190

ECE Fax: (818) 677-7062

EMAIL: ,

Class Schedule: TR 3:30 p.m. – 4:45 p.m. JD2203

Office Hours: TR 2:30 p.m. – 3:30 p.m. JD3338

Additional Office Hours: By Appointment

I - COURSE DESCRIPTION

The advanced topics in mathematics in the areas of Complex Variables, Linear Algebra, and Partial Differential Equations are discussed. These mathematical tools are used to model and solve Electrical Engineering related problems in the areas of Circuits, Control, Electromagnetic, Solid State and Communication Theory.

II - TEXTBOOK (Recommended)

“Advanced Engineering Mathematics”, Erwin Kreyszig, 10th ed., Wiley,

ISBN 978-0-470-45836-5

“Mathematical Models in Electrical Engineering-Complex Variables, Linear Algebra, Partial Differential Equation”, Ali Amini, May 2016

III – SOFTWARE

MATLAB

IV - PREREQUISITE

ECE 350 (Linear System Theory)

V - GRADING POLICY (Minimum Passing Grade = Class Avg. – 0.5 x Std. Dev.) Exam 1 30%

Exam 2 30%

Final 35%

Submitting class notes+HW+

HW-solutions+Mids-Exams and

their solutions for ABET 5% + / - Grading is used in this course

VI – CLASS POLICIES AND PROCEDURES

Attendance: Each student is required to attend every lecture. Students are responsible for arriving before class begins, and remaining for the duration of the course meeting. If a student misses a class, it is his or her responsibility to find out what was discussed in class, any homework assigned or exam scheduled.
Make-Up Exam and Homework: No examination can be made up.

Homework:

Homework will be assigned every week and students are responsible to know all the homework problems for the exams. Homework solutions will be provided at the same time homework problems are assigned. Homework problems are important part of this course and they enhance the understanding of the subjects. Everyone is required to keep an organized set of notes, a binder, or folder of his/her homework problems.

However homework problems are not collected or graded.

MATLAB will be used to enhance the understanding of the materials covered and become familiar with this important software package.

Examinations (JD1553):

Midterm I will be administered during week 5 or 6.

Midterm II will be administered during week 10 or 11.

Final Examination: Tuesday, May 15, 2018 3:00 p.m. –6:00 p.m.???

All Exams are closed book & closed notes. One 3"x 5" card allowed on exams 1 & 2.

One Sheet of 8.5ʺx11ʺ allowed on the final exam. No calculator allowed.

Academic Integrity:

Ideas and learning form the core of the academic community. In all centers of education, learning is valued and honored. No learning institution can thrive if its members counterfeit their achievement and seek to establish an unfair advantage over their fellow students. The Academic Integrity is designed to foster a fair and impartial set of standards. All students are required to adhere to these standards. Any dishonest act such as copying, plagiarism, lying, unauthorized collaboration, alteration of records, bribery, and misrepresentation for the purpose of enhancing one’s academic standing results in a failing grade for the entire course and will be reported to the College as well as the Dean of Students.

VII - COURSE MATERIAL (Based on Lecture Notes of Ali Amini)

Week Material

2, 3, 4 Chapter 4 – Linear Algebra – Matrix Theory

4.1 – Matrices and Basic Operations (Covered in ECE309)

4.2 – Determinants (Covered in ECE309)

4.3 – Systems of Linear Equations (Covered in ECE309)

4.4 – Linear Independence and Dependence and Rank of a Matrix

4.5 – Inverse of a Matrix

4.6 – Solving Linear System of Equations Using Inverse of a

Matrix and Cramer’s Rule

4.7 – Orthogonal Matrices

5, 6, 7 Chapter 5 – Linear Algebra, Eigenvalue-Eigenvector, State

Variable Equations

5.1 – Eigenvalues, Eigenvectors

5.2 – Similarity Transformation and Diagonalization

5.3 – Bilinear and Quadratic Forms

5.4 – State Variable Equations

5.5 – Solution of State Variable Equations – Time Domain

5.6 – Solution of State Variable Equations – S Domain

5.7 – Linear Transformation and Diagonalization

8, 9 Chapter 1 – Complex Variables

1.1 – Complex Numbers and Basic Operations

1.2 – Polar Form of Complex Numbers and Basic Operations

1.3 – Complex Set, Functions, Domain, and Range

1.4 – Limit, Continuity, Derivative, and Analytic Function

1.5 – Cauchy-Riemann Equations and Harmonic Functions

1.6 – Exponential and Logarithmic Functions

1.7 – Trigonometric and Inverse Trigonometric Functions.

1.8 – Hyperbolic and Inverse Hyperbolic Functions.

10 Chapter 2 – Integral of Complex Functions

2.1 – Line Integration

2.2 – Cauchy-Goursat Integral Theorem

2.3 – Some Applications of Cauchy-Goursat Theorem

2.4 – Cauchy’s Integral Formulas

11, 12, 13 Chapter 3 – Complex Series and Residue Theorem

3.1 – Sequences and Series of Complex Values

3.2 – Geometric and Power Series

3.3 – Taylor and Maclaurin Series

3.4 – Laurent Series and Residue

3.5 – Poles and Zeros

3.6 – Evaluation of Residue

3.7 – Residue Theorem

3.8 – Application of Residue Theorem to Real Integrals

14, 15 Chapter 6 – Partial Differential Equations

6.1 – Introduction

6.2 – Solving PDE Using ODE

6.3 – Wave Equation

6.4 – Diffusion or Heat Equation

6.5 – Laplace’s Equation

The Content of the Course Syllabus is Subject to Change with Appropriate Notice to the Students

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ECE 455 Spring 2018