Syllabus ( MATH 676 )
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Basic information
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| Course title: |
Inverse Problems for the Hyperbolic-Type Equations |
| Course code: |
MATH 676 |
| Lecturer: |
Prof. Dr. Mansur İSGENDEROĞLU (İSMAİLOV)
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| ECTS credits: |
7.5 |
| GTU credits: |
3 (3+0+0) |
| Year, Semester: |
1/2/3/4, Fall and Spring |
| Level of course: |
Third Cycle (Doctoral) |
| Type of course: |
Area Elective
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| Language of instruction: |
Turkish
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| Mode of delivery: |
Face to face
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| Pre- and co-requisites: |
MATH 622 |
| Professional practice: |
No |
| Purpose of the course: |
Demonstration of the Existence, Uniqueness and Continuous Dependence of the Solution upon the data for the Hyperbolic Inverse Problems |
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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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Formulate the Hyperbolic Type Initial and Boundary Value Inverse Problems
Contribution to Program Outcomes
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Define and manipulate advanced concepts of Mathematics in a specialized way
Method of assessment
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Written exam
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Formulate the Hyperbolic Type Inverse Scattering Problems
Contribution to Program Outcomes
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Define and manipulate advanced concepts of Mathematics in a specialized way
Method of assessment
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Written exam
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Explain the concepts of Exitence, Uniqueness and Continuous Dependence Upon the Data for the Inverse Problems
Contribution to Program Outcomes
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Define and manipulate advanced concepts of Mathematics in a specialized way
Method of assessment
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Written exam
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Oral exam
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Contents
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| Week 1: |
Some properties of Fredholm and Volterra integral equations of the second kind |
| Week 2: |
Inverse problems with nonfocused initial data |
| Week 3: |
Inverse problems with a focused source of disturbance |
| Week 4: |
Reducing the problem with a focused source of disturbance to a linear integral equation: necessary and sufficient conditions for solvability of the inverse problem |
| Week 5: |
Relationship between the inverse problems for differential equations and Sturm-Liouville problem in a limited domain |
| Week 6: |
Systems of equations with a single spatial variable |
| Week 7: |
Midterm Exam. Inverse problems using focused sources of wave generation |
| Week 8: |
Problem of determining the right-hand part of a hyperbolic system |
| Week 9: |
Inverse scattering problems (ISP) for the one dimensional wave equation on the whole plane |
| Week 10: |
ISPs for the one dimensional wave equation on the half plane |
| Week 11: |
ISPs for two component Dirac equations on the whole plane |
| Week 12: |
ISPs for two component Dirac equations on the half plane |
| Week 13: |
ISPs for the first order strictly hyperbolic systems on the whole plane |
| Week 14: |
ISPs for the first order strictly hyperbolic systems on the half plane |
| Week 15*: |
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| Week 16*: |
Final Exam |
| Textbooks and materials: |
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| Recommended readings: |
V.G. Romanov, Inverse Problems of Mathematical Physics
A.L. Bukhgeim, Introduction to the Theory of Inverse Problems
L.P. Nizhnik, Inverse Scattering Problems for the Hyperbolic Equations |
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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: |
7 |
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: |
16 |
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: |
5 |
14 |
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| Practice, Recitation: |
0 |
0 |
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| Homework: |
0 |
0 |
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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: |
15 |
2 |
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| Mid-term: |
2 |
1 |
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| Personal studies for final exam: |
20 |
2 |
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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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