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| MATL5060 | Applied Mathematical Methods | 3+0+0 | ECTS:7.5 | | Year / Semester | Fall Semester | | Level of Course | Second Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Prof. Dr. Erhan COŞKUN | | Co-Lecturer | | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The course aims to provide students with a general framework of equilibrium equations, both discrete and continium, with applications in various disiplines. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | analyse discrete equilibrium equations | 3,4,6,7 | 1, | | PO - 2 : | analyse equilibrium equations in continuous case | 3,4,6,7 | 1,3, | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), PO : Learning Outcome | | |
| Symmetric Linear Systems(Gauss Elimination, Positive definite matrices, Eigenvalues and dynamical systems), Discrete Equilibrium equations(A framework for applications, Constraints and Lagrange multipliers, Electrical networks, structures in equlibrium, least square estimation), Equilibrium in continuous case(Differential equations of equilibrium, Laplace equation and potantial flow, Vector calculus in three dimensions, Equilibrium of fluids and solids, Calculus of variations) |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Gaussian Elimination | | | Week 2 | Positive Definite matrices | | | Week 3 | Eigenvalues and dynamical ssytems | | | Week 4 | Ayrık denge denklemleri | | | Week 5 | Applications in elctrical networks and structures | | | Week 6 | Least squares method | | | Week 7 | Overview | | | Week 8 | Midterm | | | Week 9 | Equilibrium in the continuous case | | | Week 10 | Differential equations of equilibrium | | | Week 11 | Laplace equation and potential flow | | | Week 12 | Vector calculus in three dimensions | | | Week 13 | Equilibrium of fluids | | | Week 14 | Equilibrium of solids | | | Week 15 | Calculus of variations | | | Week 16 | Calculus of variations | | | |
| 1 | Strang, Gilbert, 1986, Introduction to applied mathematics, Wellesley-Cambridge Press. USA | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 8 | | 2 | 30 | | End-of-term exam | 16 | | | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 3 | 14 | 42 | | Sınıf dışı çalışma | 6 | 14 | 84 | | Ödev | 7 | 6 | 42 | | Dönem sonu sınavı için hazırlık | 20 | 1 | 20 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 190 |
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