درس ریاضی مهندسی پیشرفته، ارائه شده توسط محمد فتحی

مشخصات درس

عنوان

ریاضی مهندسی پیشرفته

شماره

مقطع

کارشناسی ارشد

پیش‌نیاز

توضیحات

Advanced ٍEngineering Mathematics

ریاضیات مهندسی پیشرفته

Instructor:

M. Fathi, Department of Electrical Engineering, University of Kurdistan, Sanandaj, Iran.

Course description:

This course aims to provide the students with mathematical optimization useful for graduate level thesis and projects. The course starts with a review of Linear Algebra including properties and operations on vectors and matrices, eigenvalues and eigenvectors. It then switches to recognition and formulation of convex optimization problems; most commonly used decision making problems in the field of Electrical Engineering.

Text books:

Edwin K. P. Chong, Stanislaw H. Zak, An Introduction to Optimization, ۳rd Edition , ۲۰۰۱ (Text for Linear Algebra).
S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, Cambridge Univ. Press, ۲۰۰۴ (Text for Optimization)
D. Luenberger, Yinyu Ye, Linear and Nonlinear Programming, Springer, ۳rd edition, ۲۰۰۸. (Chapters ۷ and ۱۱).

Grading:

Final exam: ۵۰%
Midterm exam: ۲۰%
Project: ۲۰%
Homework: ۱۰%

Schedule (time table):

Week	Topic
#۱	Linear algebra: vectors and matrices
#۲	Linear algebra: eigenvalues and eigenvectors, quadratic forms
#۳	Linear algebra: gradient and hessian
#۴	Linear algebra: level sets, directional derivative
#۵	Unconstrained optimization: introduction
#۶	Unconstrained optimization: optimality conditions
#۷	Unconstrained optimization: genaral optimization algorithms
#۸	Unconstrained optimization: steepest descent and Newton's methods
#۹	Convex programming: convex set
#۱۰	Convex programming: convex function
#۱۱	Convex programming: convex problem
#۱۲	Duality: introduction
#۱۳	Duality: Lagrangian, dual function and dual problem
#۱۴	CVX: optimization tool
#۱۵	Optimization applications in Electrical Engineering
#۱۶	Optimization applications in Electrical Engineering