Syllabus ( MATH 434 )
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Basic information
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| Course title: |
Boundary Value Problems |
| Course code: |
MATH 434 |
| Lecturer: |
Assoc. Prof. Dr. Gülden GÜN POLAT
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| ECTS credits: |
6 |
| GTU credits: |
3 (3+0+0) |
| Year, Semester: |
4, Spring |
| Level of course: |
First Cycle (Undergraduate) |
| Type of course: |
Departmental 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: |
Math 203 |
| Professional practice: |
No |
| Purpose of the course: |
The objective of this course is to introduce elemantary methods regarding the solution of the problem including differential equations and boundary conditions. |
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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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Perceive the methods regarding the solution of the boundary-value problems
Contribution to Program Outcomes
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Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
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Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.
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Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.
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Exhibiting professional and ethical responsibility.
Method of assessment
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Written exam
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Transfer the mathematical applications to engineering and other applied sciences
Contribution to Program Outcomes
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Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
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Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.
Method of assessment
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Homework assignment
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Gain the capability of mathematical modeling
Contribution to Program Outcomes
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Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
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Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
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Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.
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: |
Mathematical models of physical problems. Standart equations of mathematical physics |
| Week 2: |
Existence and uniqueness of the solution of boundary-value problems |
| Week 3: |
The D'Alambert and seperation of variables solutions |
| Week 4: |
Fourier series and Fourier transforms |
| Week 5: |
Applications of Fourier transforms |
| Week 6: |
Greens Function Method |
| Week 7: |
Strum-Liouville eigenvalue problem |
| Week 8: |
Theorems on expansion and completeness |
| Week 9: |
Midterm exam and Solutions |
| Week 10: |
Boundary-value problems in cartesian coordinates |
| Week 11: |
Boundary-value problems in cartesian coordinates |
| Week 12: |
Bessel functions and Legandre polinomials |
| Week 13: |
Boundary-value problems in cylindrical coordinates |
| Week 14: |
Boundary-value problems in spherical coordinates |
| Week 15*: |
- |
| Week 16*: |
Final Exam |
| Textbooks and materials: |
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| Recommended readings: |
Partial Differential Equations and Boundary - Value Problems with Applications (Mark A. Pinsky)
Boundary Value Problems (Chy Y. Lo) |
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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: |
9 |
40 |
| Other in-term studies: |
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0 |
| Project: |
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0 |
| Homework: |
1, 2, 3, 5, 6, 7, 10, 11, 12, 13 |
10 |
| Quiz: |
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0 |
| Final exam: |
16 |
50 |
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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: |
5 |
14 |
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| Practice, Recitation: |
0 |
0 |
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| Homework: |
2 |
10 |
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| Term project: |
0 |
0 |
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| Term project presentation: |
0 |
0 |
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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: |
2 |
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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