Syllabus ( MATH 545 )
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Basic information
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Course title: |
Numerical Analysis I |
Course code: |
MATH 545 |
Lecturer: |
Assoc. Prof. Dr. Hülya ÖZTÜRK
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ECTS credits: |
7.5 |
GTU credits: |
3 (3+0+0) |
Year, Semester: |
1/2, Fall and Spring |
Level of course: |
Second Cycle (Master's) |
Type of course: |
Area Elective
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Language of instruction: |
English
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Mode of delivery: |
Face to face
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Pre- and co-requisites: |
none |
Professional practice: |
No |
Purpose of the course: |
To teach the fundamental principles of numerical analysis |
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Learning outcomes
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Upon successful completion of this course, students will be able to:
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Explain the fundamental principles of numerical analysis
Contribution to Program Outcomes
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Acquire scientific knowledge and work independently
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Develop mathematical, communicative, problem-solving, brainstorming skills.
Method of assessment
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Written exam
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Grasp applications of differential equations
Contribution to Program Outcomes
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Define and manipulate advanced concepts of Mathematics
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Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
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Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results
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Acquire scientific knowledge and work independently
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Work effectively in multi-disciplinary research teams
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Continuously develop their knowledge and skills in order to adapt to a rapidly developing technological environment
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Develop mathematical, communicative, problem-solving, brainstorming skills.
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Effectively express his/her research ideas and findings both orally and in writing
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Demonstrating professional and ethical responsibility.
Method of assessment
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Written exam
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Homework assignment
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Seminar/presentation
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Solve differential equations numerically
Contribution to Program Outcomes
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Define and manipulate advanced concepts of Mathematics
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Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
-
Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results
-
Acquire scientific knowledge and work independently
-
Work effectively in multi-disciplinary research teams
-
Continuously develop their knowledge and skills in order to adapt to a rapidly developing technological environment
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Develop mathematical, communicative, problem-solving, brainstorming skills.
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Demonstrating professional and ethical responsibility.
Method of assessment
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Written exam
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Homework assignment
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Contents
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Week 1: |
Numerical Solution of Initial-Value problems Euler's Method |
Week 2: |
Runge Kutta methods |
Week 3: |
Predictor-Corrector methods: Adams-Moulton Adams-Bashforth Milne's and Simpson's methods |
Week 4: |
Extrapolation methods |
Week 5: |
Adaptive techniques |
Week 6: |
Methods for systems of equations |
Week 7: |
Stiff Differential Equations |
Week 8: |
Boundary-value problems for ordinary differential equations: Linear Shooting method |
Week 9: |
Boundary-value problems for ordinary differential equations: Linear Shooting method |
Week 10: |
Linear Finite Difference |
Week 11: |
Non-linear Shooting method |
Week 12: |
Non-linear Finite Difference |
Week 13: |
Variational techniques |
Week 14: |
Rayleigh-Ritz method |
Week 15*: |
Matlab applications |
Week 16*: |
Final exam |
Textbooks and materials: |
Numerical Methods, Faires and Burden, 2013 Numerical Methods and Analysis, Buchanan and Turner, 1992 |
Recommended readings: |
Numerical Methods, Faires and Burden, 2013 Numerical Methods and Analysis, Buchanan and Turner, 1992 |
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* Between 15th and 16th weeks is there a free week for students to prepare for final exam.
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Assessment
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Method of assessment |
Week number |
Weight (%) |
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Mid-terms: |
8 |
40 |
Other in-term studies: |
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0 |
Project: |
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0 |
Homework: |
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0 |
Quiz: |
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0 |
Final exam: |
14 |
60 |
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Total weight: |
(%) |
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Workload
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Activity |
Duration (Hours per week) |
Total number of weeks |
Total hours in term |
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Courses (Face-to-face teaching): |
3 |
14 |
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Own studies outside class: |
3 |
14 |
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Practice, Recitation: |
0 |
0 |
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Homework: |
6 |
10 |
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Term project: |
10 |
2 |
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Term project presentation: |
1 |
1 |
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Quiz: |
0 |
0 |
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Own study for mid-term exam: |
10 |
1 |
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Mid-term: |
1 |
1 |
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Personal studies for final exam: |
10 |
1 |
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Final exam: |
2 |
1 |
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Total workload: |
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Total ECTS credits: |
* |
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* ECTS credit is calculated by dividing total workload by 25. (1 ECTS = 25 work hours)
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