Syllabus ( MATH 676 )

Basic information


Course title: 
Inverse Problems for the HyperbolicType Equations 
Course code: 
MATH 676 
Lecturer: 
Prof. Dr. Mansur İSGENDEROĞLU (İSMAİLOV)

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

Language of instruction: 
Turkish

Mode of delivery: 
Face to face

Pre and corequisites: 
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 



Learning outcomes


Upon successful completion of this course, students will be able to:

Formulate the Hyperbolic Type Initial and Boundary Value Inverse Problems
Contribution to Program Outcomes

Define and manipulate advanced concepts of Mathematics in a specialized way
Method of assessment

Written exam

Formulate the Hyperbolic Type Inverse Scattering Problems
Contribution to Program Outcomes

Define and manipulate advanced concepts of Mathematics in a specialized way
Method of assessment

Written exam

Explain the concepts of Exitence, Uniqueness and Continuous Dependence Upon the Data for the Inverse Problems
Contribution to Program Outcomes

Define and manipulate advanced concepts of Mathematics in a specialized way
Method of assessment

Written exam

Oral exam


Contents


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 SturmLiouville problem in a limited domain 
Week 6: 
Systems of equations with a single spatial variable 
Week 7: 
Midterm Exam 
Week 8: 
Inverse problems using focused sources of wave generation 
Week 9: 
Problem of determining the righthand part of a hyperbolic system 
Week 10: 
Inverse scattering problems (ISP) for the one dimensional wave equation on the whole plane 
Week 11: 
ISPs for the one dimensional wave equation on the half plane 
Week 12: 
ISPs for two component Dirac equations on the whole plane 
Week 13: 
ISPs for two component Dirac equations on the half plane 
Week 14: 
ISPs for the first order strictly hyperbolic systems on the whole plane 
Week 15*: 
ISPs for the first order strictly hyperbolic systems on the half plane 
Week 16*: 
Final Exam 
Textbooks and materials: 

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 

* Between 15th and 16th weeks is there a free week for students to prepare for final exam.




Assessment



Method of assessment 
Week number 
Weight (%) 

Midterms: 
7 
40 
Other interm studies: 

0 
Project: 

0 
Homework: 

0 
Quiz: 

0 
Final exam: 
16 
60 

Total weight: 
(%) 



Workload



Activity 
Duration (Hours per week) 
Total number of weeks 
Total hours in term 

Courses (Facetoface teaching): 
3 
14 

Own studies outside class: 
5 
14 

Practice, Recitation: 
0 
0 

Homework: 
0 
0 

Term project: 
0 
0 

Term project presentation: 
0 
0 

Quiz: 
0 
0 

Own study for midterm exam: 
15 
2 

Midterm: 
2 
1 

Personal studies for final exam: 
20 
2 

Final exam: 
2 
1 



Total workload: 



Total ECTS credits: 
* 

* ECTS credit is calculated by dividing total workload by 25. (1 ECTS = 25 work hours)



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