ECE 7030 Advanced Mathematics for Engineers

Fall 2011

3:30 – 5:20 M W 289 Manoogian

I General Information

Instructor Ivan Avrutsky, Associate Professor

Office Room 3142, Engineering Building, tel.: 577-4801

Office hours 1:30–3:30 p.m. Mondays

1:30–3:30 p.m. Wednesdays (except for days reserved for faculty meetings

and seminars – call to check)

Text book Modern Advanced Mathematics for Engineers

by V. V. Mitin, D. A. Romanov, M. P. Polis

Wiley, New York, 2001

Lecture notes from a previous semester are available online

Updated lecture notes will be posted shortly after a lecture is delivered

II Course Summary

Chapters 1-11 of the textbook, including

- Basic Set Theory

- Relations and Mapping

- Math Logic

- Algebraic structures

- Linear Mappings and Matrices

- Metrics and Topological Properties

- Banach and Hilbert Spaces

- Orthonormal Bases and Fourier Series

- Operator Equations

- Fourier and Laplace Transforms

- Partial Differential equations

III Grading Policy 1. Weighting: 2 Quizzes 30% (15% each)

Midterm 30%

Final 40%

2. Final Course Grades: 85 – 90 – 100% A– A

70 – 75 – 80 – 85% B– B B+

55 – 60 – 65 – 70% C– C C+

0 – 55 F

IV Expectations

It is expected that students will acquire knowledge necessary to solve the problems similar to the

exercises considered in the textbook. Students are expected to attend all lectures.

V Testing Policy

All quizzes and the exams will be open books and open notes. Use this freedom wisely. The final

exam may include problems from any topic studied in the course. No make-up quizzes will be

administrated. Adjustment for one missed quiz will be made based on average student’s

performance on all other assignments.

VI Academic Honesty

Your work on quizzes and exams must be absolutely independent, no help from anybody in any

form. Also, it is your responsibility to protect your work from unauthorized copying.

VII Withdrawal Policy

General University policies applied.

ECE 7030 FALL 2011 SCHEDULE 3:30-5:20 289 Manoogian

Date Lecture

Number

Lecture Subject Chapter

W Aug 31 # 1 Subject of ECE 7030. -

M Sept 5 Holyday, University closed -

W Sept 7 # 2 Basic Set Theory 1

M Sept 12 # 3 Relations and Mappings 2

W Sept 14 # 4 Math Logic 3

M Sept 19 # 5 Algebraic structures I 4

W Sept 21 # 6 Algebraic structures II 4

M Sept 26 # 7 Linear Mappings and Matrices I 5

W Sept 28 # 8 Linear Mappings and Matrices II 5

M Oct 3 # 9 Sample problems for Quiz #1 -

W Oct 5 # 10 Quiz #1 -

M Oct 10 # 11 Analysis of Quiz #1 -

W Oct 12 # 12 Sample problems for Midterm Exam -

M Oct 17 # 13 Midterm Exam -

W Oct 19 # 14 Analysis of Midterm Exam. Metrics and Topological Properties I 6

M Oct 24 # 15 Metrics and Topological Properties II 6

W Oct 26 # 16 Banach and Hilbert Spaces I 7

M Oct 31 # 17 Banach and Hilbert Spaces II 7

W Nov 2 # 18 Orthonormal Bases 8

M Nov 7 # 19 Complete Orthonormal Sequences and Fourier Series 8

W Nov 9 # 20 Operator Equations I 9

M Nov 14 # 21 Operator Equations II 9

W Nov 16 # 22 The Fourier Transforms 10

M Nov 21 # 23 The Laplace Transform 10

W Nov 23 No Classes. Thanksgiving recess -

M Nov 28 # 24 Partial Differential Equations 11

W Nov 30 # 25 Sample problems for Q #2 -

M Dec 5 # 26 Quiz #2 -

W Dec 7 # 27 Analysis of Quiz #2 -

M Dec 12 # 28 Sample problems for Final Exam -

W Dec 14 # 29 Final Exam -