Course Description:
This course aims at introducing and laying down the fundamental of advanced mathematic: Perturbation, Interval Analysis, Optimization, The Calculus of Variations, Sloving Polynomial System of Equation. The course is established in such a way that includes readings, 2 homework and two projects. There will be have quizzes, one in-class midterm and a final examination. These examinations will be close book. Lectures will be based mainly, but not exclusively, on material in the textbook given below. Students are asked to show they abilities in applying theoretical concepts into practical problems for which three practical projects are envisaged for this end. To provide the essential materials for practical projects several workshops are considered which are given by the TA listed below.
Time: Saturday 7:30--9:00 and Monday 7:30 --9:00
Room: A11
Instructor: Mehdi Tale Masouleh
Teaching Assistant: Monday 14:30 -- 15:30
Mohamad Sharifzadeh
Office Hours: 9:00-11:00 Saturday
Prerequisites:
- LATEX2e (Words typeset are not accepted)
- Matlab
- Maple
- Last but not least: Patience
Course Outline:
| Polynomial, Calc of Variation -- 9 weeks | |
|---|---|
| Chapter 3 (The Calculus of Variations) | approx 2 weeks |
| Chapter 4 (The Euler-Lagrange equation) | approx 1 week |
| Quiz I | |
| Chapter 6 (Further theoretical developments ) | approx 1 week |
| Chapter 9 (Parametric Functionals) | approx 1 week |
| Quiz II | |
| Chapter 10 (Variable end points) | approx 1 week |
| Chapter 11 (Conditional stationary points) | Left To be Read By Students |
| Chapter 12 (Constrained Variational Problems) | approx 1 week |
| Quiz III | |
| Linear Polynomial Systems Equations By MAPLE | approx 1 week |
| High Degree polynomial System Equations By MAPLE | |
| Final Exam | 4 hours |
Files to Download:
- "Introduction to interval analysis" by Moore, Kearfoot, Cloud (Chapter 1 to 5)
- "Convex Optimization" by Stephen P.Boyd, Leiven Vandenberghe
- Polynomial System
Projects: Works done by students are of two sorts:
- Two Homeworks: Homeworks are essentially based on theoretical concepts and are designated to get familiar students with basic issue of Advance Mathematic problem.
- Two Practical Projects:
Report: Homeworks should be done individually, unless otherwise is stated, and plagiarism is not tolerated. In the case of plagiarism, the note of the corresponding work would be marked as zero. All the reports should be typeset in LATEX, upon following the class proposed by IEEE. The report should follows the the instruction given by IEEE and includes:
- Abstract
- Introduction
- Main body (each section should corresponds to a problem)
- Conclusion
- Reference
Academic Honesty: As a University of Tehran student, you have agreed to abide by the University's academic honesty policy. A Lack of knowledge of the academic honesty policy is not a reasonable explanation for a violation. Questions related to course assignments and the academic honesty policy should be directed to the instructor..
| In this regard, we invite you to see the following clip in order to have a better understanding in how we are able to find out whether your homework is done by yourself or one of your classmate. |  |
Extra Help: Dot not hesitate to come to my office or contact me during office hours or by appointment to discuss a homework problem or any aspect of the course. Moreover, TA considered for each part are also at your total disposal for helping you in your homework, projects and exams.
Important Dates and Grades: Quiz (1% each) and Exams (10% each) are scheduled based on the calender provided in the course outline and have flexible date.
Homeworks (7% each)
| First Homework |
||
| Second Homework |
Projects (11% each)
| First Project | |
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| Second Project |