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Syllabus ( MATH 676 )


   Basic information
Course title: Inverse Problems for the Hyperbolic-Type 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 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
   Learning outcomes Up

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

  1. Formulate the Hyperbolic Type Initial and Boundary Value Inverse Problems

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics in a specialized way

    Method of assessment

    1. Written exam
  2. Formulate the Hyperbolic Type Inverse Scattering Problems

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics in a specialized way

    Method of assessment

    1. Written exam
  3. Explain the concepts of Exitence, Uniqueness and Continuous Dependence Upon the Data for the Inverse Problems

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics in a specialized way

    Method of assessment

    1. Written exam
    2. Oral exam
   Contents Up
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
Week 8: Inverse problems using focused sources of wave generation
Week 9: Problem of determining the right-hand 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 Up
Method of assessment Week number Weight (%)
Mid-terms: 7 40
Other in-term studies: 0
Project: 0
Homework: 0
Quiz: 0
Final exam: 16 60
  Total weight:
(%)
   Workload Up
Activity Duration (Hours per week) Total number of weeks Total hours in term
Courses (Face-to-face 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 mid-term exam: 15 2
Mid-term: 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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