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Advanced ٍEngineering Mathematics 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, 3rd Edition , 2001 (Text for Linear Algebra).
- S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, Cambridge Univ. Press, 2004 (Text for Optimization)
- D. Luenberger, Yinyu Ye, Linear and Nonlinear Programming, Springer, 3rd edition, 2008. (Chapters 7 and 11).
Grading: - Final exam: 50%
- Midterm exam: 20%
- Project: 20%
- Homework: 10%
Schedule (time table): | Week | Topic |
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| #1 | Linear algebra: vectors and matrices | | #2 | Linear algebra: eigenvalues and eigenvectors, quadratic forms | | #3 | Linear algebra: gradient and hessian | | #4 | Linear algebra: level sets, directional derivative | | #5 | Unconstrained optimization: introduction | | #6 | Unconstrained optimization: optimality conditions | | #7 | Unconstrained optimization: genaral optimization algorithms | | #8 | Unconstrained optimization: steepest descent and Newton's methods | | #9 | Convex programming: convex set | | #10 | Convex programming: convex function | | #11 | Convex programming: convex problem | | #12 | Duality: introduction | | #13 | Duality: Lagrangian, dual function and dual problem | | #14 | CVX: optimization tool | | #15 | Optimization applications in Electrical Engineering | | #16 | Optimization applications in Electrical Engineering |
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