Harmonic Analysis and Applications
Mathematics
Institute of Natural and Applied Sciences
Third Cycle (Doctorate Degree)
| Course Unit Title | Course Unit Code | Type of Course Unit | Level of Course Unit | Year of Study | Semester | ECTS Credits |
|---|---|---|---|---|---|---|
| Harmonic Analysis and Applications | MAT610 | Elective | Doctorate degree | 1 | Fall | 8 |
Name of Lecturer(s)
Prof. Dr. İrem BAĞLAN
Prof. Dr. Ali DEMİR
Associate Prof. Dr. Hülya KODAL SEVİNDİR
Learning Outcomes of the Course Unit
1) Explain Basic Concepts of Harmonic Analysis.
2) Explain Fourier Theory.
3) Explain Fourier Integrals ve Complex Function Theory.
4) Explain Fourier Transformations.
5) Explain Bessel ve Parseval inequalities.
Program Competencies-Learning Outcomes Relation
| Program Competencies | ||||||||
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | ||
| Learning Outcomes | ||||||||
| 1 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 2 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 3 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 4 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 5 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
Mode of Delivery
Face to Face
Prerequisites and Co-Requisites
None
Recommended Optional Programme Components
no recommended course
Course Contents
Periodic Functions, Odd and Even Functions, Orthogonal Functions, Partial Fourier Series, Dirichlet Conditions, Fourier Series, Harmonic Definition, Finding Fourier Coefficients, Fourier Series of an Odd Function, Fourier Series of an Even Function, Fourier Series of 2?-Periodic Functions, Fourier Series of 2L-Periodic Functions,Fourier Series of Periodic Functions on the interval [a, b],Complex Fourier Series, Fourier Integral, Trigonometric Form of Fourier Integral,Fourier Transform, Fourier Cosine Transform, Fourier Sine Transform,Linearity Property, Shifting Property,Explain Fourier Transformations..
Weekly Schedule
1) Periodic Functions, Add and even functions, orthogonal functions, piecewise continous functions2) Dirichlet conditions, Fourier theorem
3) Fourier sequence, defination of Harmonic, find to Fourier coefficient
4) Fourier sequence of add functions, Fourier sequence of even functions
5) Fourier sequence of Periodic functions with 2 pi
6) Fourier Sequence of periodic functions with 2L
7) Fourier sequence of periodic functions on [a,b]
8) Complex Fourier Sequence
9) midterm
10) Fourier Integral and trigonometric impression
11) Fourier transformation
12) Fourier cosinüs transformations, Fourier sinüs transformations
13) Convergence of Fourier series
14) Bessel ve Parseval Inequalities
15) Final
Recommended or Required Reading
1- W. A. Strauss: Partial Differential Equations: An Introduction, 2nd Ed., Chap. 10 & 11, John Wiley & Sons, 2008.
2- Hutson, V. and Pym, J. S. Applications of Functional Analysis and Operator Theory. New York: Academic Press, 1980.
3- R. Courant and D. Hilbert: Methods of Mathematical Physics, Vol.I, Chap. V, VI, & VII, Wiley-Interscience, 1953.
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Planned Learning Activities and Teaching Methods
1) Lecture
2) Question-Answer
3) Discussion
4) Drill and Practice
5) Demonstration
6) Modelling
7) Role Playing
8) Group Study
9) Problem Solving
Assessment Methods and Criteria
Contribution of Presentation/Seminar to Course Grade |
40% |
|---|---|
Contribution of Final Examination to Course Grade |
60% |
Total |
100% |
Language of Instruction
Turkish
Work Placement(s)
Not Required