Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | MAT567 | FOURİER ANALİZİ | Elective | 1 | 1 | 6 |
|
Level of Course Unit |
Second Cycle |
Objectives of the Course |
To introduce to the student applications of Laplace transformation. |
Name of Lecturer(s) |
Doç.Dr.Abdullah SÖNMEZOĞLU |
Learning Outcomes |
1 | To understand Laplace transformation | 2 | To apply Laplace transformation | 3 | Understanding between the relations of the Laplace transform with the inverse Laplace |
|
Mode of Delivery |
Formal Education |
Prerequisites and co-requisities |
None |
Recommended Optional Programme Components |
None |
Course Contents |
A brief outline of Lp spaces, density theorems in Lp spaces, Stone-Weierstrass density theorem, Fourier series, the relationship between differentiability and shrinkage of Fourier coefficients, Cesaro sum, Fejer kernel and convergent units, Fourier series absolute and point, uniform, L2- norm, L1-norm convergence, Fourier transform, L1 theory: convolution, convergent units, Schwartz space, L2 theory: Plancherel's theorem, Lp theory: Riesz-Thorin and Marcinkiewicz interpolation theorems, Young convolution theorem, Hausdorff-Young theorem, Band-bound theorem and Paley-Wiener spaces, Classical sampling theorem |
Weekly Detailed Course Contents |
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1 | Definition of Laplace transformation | | | 2 | Existence and uniqueness of the Laplace transformation | | | 3 | Laplace transforms of some functions | | | 4 | first-shift feature and its applications | | | 5 | second -shift feature and its applications | | | 6 | The properties of linear of Laplace transformation | | | 7 | Heaviside theorem | | | 8 | Midterm exam | | | 9 | Laplace transformation of derivatives | | | 10 | Laplace transformation of integrals | | | 11 | Product funcion with t | | | 12 | Split function with t | | | 13 | Laplace transformation of periodic functions | | | 14 | İnverse Laplace transformation and its applications | | | 15 | İnverse Laplace transformation and its applications | | | 16 | Final exam | | |
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Recommended or Required Reading |
Differential equations and their applications, Prof.Dr.İrfan Baki Yasar, political bookstore, Ankara, 2005.
Differantial equations, Dennis G. Zill, Michael R. Cullen, PWS Publishing Company, Boston, 1993. |
Planned Learning Activities and Teaching Methods |
|
Assessment Methods and Criteria | |
Midterm Examination | 1 | 100 | SUM | 100 | |
Final Examination | 1 | 100 | SUM | 100 | Term (or Year) Learning Activities | 40 | End Of Term (or Year) Learning Activities | 60 | SUM | 100 |
| Language of Instruction | | Work Placement(s) | None |
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Workload Calculation |
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Midterm Examination | 1 | 1 | 1 |
Final Examination | 1 | 1 | 1 |
Makeup Examination | 1 | 12 | 12 |
Attending Lectures | 14 | 3 | 42 |
Problem Solving | 14 | 2 | 28 |
Self Study | 14 | 2 | 28 |
Individual Study for Mid term Examination | 14 | 2 | 28 |
Individual Study for Final Examination | 14 | 2 | 28 |
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Contribution of Learning Outcomes to Programme Outcomes |
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* Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
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Yozgat Bozok University, Yozgat / TURKEY • Tel (pbx): +90 354 217 86 01 • e-mail: uo@bozok.edu.tr |