| School/Faculty/Institute | Faculty of Engineering | ||||
| Course Code | IE 437 | ||||
| Course Title in English | Numerical Methods and Optimization | ||||
| Course Title in Turkish | Sayısal Yöntemler ve Optimizasyon | ||||
| Language of Instruction | EN | ||||
| Type of Course | Ters-yüz öğrenme | ||||
| Level of Course | Orta | ||||
| Semester | Fall | ||||
| Contact Hours per Week |
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| Estimated Student Workload | 150 hours per semester | ||||
| Number of Credits | 6 ECTS | ||||
| Grading Mode | Standard Letter Grade | ||||
| Pre-requisites |
MATH 211 - Linear Algebra COMP 109 - Computer Programming (JAVA) |
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| Co-requisites | None | ||||
| Expected Prior Knowledge | Prior knowledge in linear algebra and computer programming | ||||
| Registration Restrictions | - | ||||
| Overall Educational Objective | To learn and apply theoretical and algorithmic concepts related to systems of equations and continuous optimization | ||||
| Course Description | This course presents theoretical and algorithmic aspects related to systems of equations and continuous optimization problems. The ideas behind the numerical methods developed to solve such systems and problems, their connection to the theoretical results and optimality conditions, as well as their convergence behavior are covered. The following topics will be included in the course: solving systems of linear equations by direct and iterative methods; solution of nonlinear equations by iterative methods; approximating functions; fundamental concepts of optimization; theory of unconstrained optimization; line search methods for unconstrained optimization; theory of constrained optimization; effect of equality constraints; effect of inequality constraints; general formulation of nonlinear programming, solving the KKT system. |
Course Learning Outcomes and CompetencesUpon successful completion of the course, the learner is expected to be able to:1) understand systems of linear equations and apply solution methods for them; 2) understand systems of nonlinear equations and apply solution methods for them; 3) apply theoretical results on optimality conditions and solution methods for unconstrained optimization; 4) understand and apply theoretical results on optimality conditions for constrained optimization; 5) implement algorithms for systems of equations and unconstrained optimization. |
| Program Learning Outcomes/Course Learning Outcomes | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| 1) An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics | |||||
| 2) An ability to apply engineering design to produce solutions that meet specified needs with consideration of public health, safety, and welfare, as well as global, cultural, social, environmental, and economic factors | |||||
| 3) An ability to communicate effectively with a range of audiences | |||||
| 4) An ability to recognize ethical and professional responsibilities in engineering situations and make informed judgments, which must consider the impact of engineering solutions in global, economic, environmental, and societal contexts | |||||
| 5) An ability to function effectively on a team whose members together provide leadership, create a collaborative and inclusive environment, establish goals, plan tasks, and meet objectives | |||||
| 6) An ability to develop and conduct appropriate experimentation, analyze and interpret data, and use engineering judgment to draw conclusions | |||||
| 7) An ability to acquire and apply new knowledge as needed, using appropriate learning strategies |
| N None | S Supportive | H Highly Related |
| Program Outcomes and Competences | Level | Assessed by | |
| 1) | An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics | H | Exam,Homework,Derse Katılım |
| 2) | An ability to apply engineering design to produce solutions that meet specified needs with consideration of public health, safety, and welfare, as well as global, cultural, social, environmental, and economic factors | S | Exam,Derse Katılım |
| 3) | An ability to communicate effectively with a range of audiences | N | |
| 4) | An ability to recognize ethical and professional responsibilities in engineering situations and make informed judgments, which must consider the impact of engineering solutions in global, economic, environmental, and societal contexts | N | |
| 5) | An ability to function effectively on a team whose members together provide leadership, create a collaborative and inclusive environment, establish goals, plan tasks, and meet objectives | N | |
| 6) | An ability to develop and conduct appropriate experimentation, analyze and interpret data, and use engineering judgment to draw conclusions | N | |
| 7) | An ability to acquire and apply new knowledge as needed, using appropriate learning strategies | N |
| Prepared by and Date | FİLİZ GÜRTUNA , December 2023 |
| Course Coordinator | FİLİZ GÜRTUNA |
| Semester | Fall |
| Name of Instructor | Asst. Prof. Dr. FİLİZ GÜRTUNA |
| Week | Subject |
| 1) | Systems of Equations and Types of Optimization Problems |
| 2) | Solving Systems of Linear Equations: LU and Cholesky Factorizations |
| 3) | Solution of Linear Equations: Iterative Methods |
| 4) | Solution of Nonlinear Equations: Bisection and Newton’s Methods |
| 5) | Solution of Nonlinear Equations: Secant Method |
| 6) | Solution of Nonlinear Equations: Fixed Points |
| 7) | Solution of Nonlinear Equations: Roots of Polynomials |
| 8) | Approximating Functions: Polynomial Interpolation |
| 9) | Approximating Functions: Least Squares Problems |
| 10) | Theory of Unconstrained Optimization |
| 11) | Unconstrained Optimization: Line Search Methods (Steepest Descent) |
| 12) | Unconstrained Optimization: Line Search Methods (Newton’s Method, Quasi-Newton Methods) |
| 13) | Theory of Constrained Optimization: Equality and Inequality Constraints |
| 14) | Theory of Constrained Optimization: Solving Optimality Conditions |
| 15) | Final Exam/Project/Presentation period |
| 16) | Final Exam/Project/Presentation period |
| Required/Recommended Readings | • Lecture Notes • Kincaid, D., Cheney, W., (2002). Numerical Analysis (3rd Edition). American Mathematical Society | ||||||||||||||||||
| Teaching Methods | Lectures/contact hours using “flipped classroom” as an active learning technique | ||||||||||||||||||
| Homework and Projects | Homework involves computer programming | ||||||||||||||||||
| Laboratory Work | - | ||||||||||||||||||
| Computer Use | Yes | ||||||||||||||||||
| Other Activities | - | ||||||||||||||||||
| Assessment Methods |
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| Course Administration |
gurtunaf@mef.edu.tr - Exams and quizzes: Closed book and closed notes. Rules for attendance: YÖK regulations. You are responsible for the announcements made in class. Rules for late submission of assignments: Homework deadlines are always extendable up to 72 hours, with submissions late for (0,24] hours receive 70% of the credit they get, (24,48] hours receive 35% , and (48,72] receive 10%. Missing a quiz: NA Missing a project: NA Missing a midterm: You are expected to be present without exception and to plan any travel around these dates accordingly. Medical emergencies are of course excluded if accompanied by a doctor’s note. A note indicating that you were seen at the health center on the day of the exam is not a sufficient documentation of medically excused absence from the exam. The note must say that you were medically unable to take the exam. Provided that proper documents of excuse are presented, a make-up exam will be given for each missed midterm. If you fail to take the exam on the assigned day and do not have a valid excuse, you will be given zero (0) on the exam. Employment interviews, employer events, weddings, vacations, etc. are not excused absences. Eligibility to take the final exam: YÖK regulations. Missing a final: Faculty regulations. Improper behavior, academic dishonesty and plagiarism : YÖK Disciplinary Regulation |
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| Activity | No/Weeks | Hours | Calculation | ||||
| No/Weeks per Semester | Preparing for the Activity | Spent in the Activity Itself | Completing the Activity Requirements | ||||
| Course Hours | 14 | 1 | 3 | 56 | |||
| Homework Assignments | 3 | 10 | 10 | 60 | |||
| Midterm(s) | 1 | 15 | 2 | 17 | |||
| Final Examination | 1 | 15 | 2 | 17 | |||
| Total Workload | 150 | ||||||
| Total Workload/25 | 6.0 | ||||||
| ECTS | 6 | ||||||