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| MATL7913 | Fourier Analysis | 3+0+0 | ECTS:7.5 | | Year / Semester | Fall Semester | | Level of Course | Third Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Dr. Öğr. Üyesi Ayşe KABATAŞ | | Co-Lecturer | Assoc. Prof. Dr. Elif BAŞKAYA | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | Derivation of Fourier Series Formulas, Defining the Trigonometric Fourier Series, Using the Fourier Sine and Cosine Series over Finite Intervals, Derivation of the Complex Exponential Fourier Series, Calculating the differentiation of Fourier Series, Calculating the integral of Fourier Series, Derivation of the Classical Fourier Transform
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| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | can derive trigonometric Fourier series. | 1 | 1,3, | | PO - 2 : | can derive complex exponential Fourier series. | 1 | 1,3, | | PO - 3 : | can calculate the derivatives and integrals of Fourier series. | 1 | 1,3, | | PO - 4 : | can solve heat flow problem and vibrating string problem. | 1 | 1,3, | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), PO : Learning Outcome | | |
| History of Fourier; Continuity and Smoothness; Symmetry and Periodicity; Elementary Complex Analysis; Derivation of the Fourier Series Formulas; Trigonometric Fourier Series; Fourier Series over Finite Intervals (Sine and Cosine Series); Inner Products, Norms, and Orthogonality; Complex Exponential Fourier Series; Convergence and Fourier?s Conjecture; Derivatives and Integrals of Fourier Series; Applications (Heat Flow Problem, Vibrating String Problem, Sturm-Liouville Problems, etc.); Derivation of the Classical Fourier Transform; Fourier Integral Transforms |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | History of Fourier and Mathematical Preliminaries | | | Week 2 | Continuity and Smoothness, Symmetry and Periodicity | | | Week 3 | Elementary Complex Analysis | | | Week 4 | Derivation of the Fourier Series Formulas, Trigonometric Fourier Series | | | Week 5 | Fourier Series over Finite Intervals (Sine and Cosine Series) | | | Week 6 | Inner Products, Norms, and Orthogonality | | | Week 7 | Complex Exponential Fourier Series | | | Week 8 | Convergence and Fourier?s Conjecture | | | Week 9 | Quiz | | | Week 10 | Derivatives and Integrals of Fourier Series | | | Week 11 | Applications (Heat Flow Problem, Vibrating String Problem, Sturm-Liouville Problems, etc.) | | | Week 12 | Applications (Heat Flow Problem, Vibrating String Problem, Sturm-Liouville Problems, etc.) | | | Week 13 | Derivation of the Classical Fourier Transform | | | Week 14 | Fourier Integral Transforms | | | Week 15 | Fourier Integral Transforms | | | Week 16 | Final Exam | | | |
| 1 | Howell, Kenneth. 2001; Principles of Fourier Analysis, Chapman & Hall/CRC, USA. | | | |
| 1 | Gonzalez-Velasco, Enrique A. 1996; Fourier Analysis and Boundary Value Problems, Elsevier Science & Technology Books, Dunstable, Massachusetts. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | | 3 | 20 | | Quiz | 12 | | 1 | 10 | | Homework/Assignment/Term-paper | 4 | | 144 | 20 | | End-of-term exam | 16 | | 3 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 3 | 14 | 42 | | Sınıf dışı çalışma | 5 | 14 | 70 | | Arasınav için hazırlık | 3 | 1 | 3 | | Arasınav | 3 | 1 | 3 | | Ödev | 144 | 1 | 144 | | Kısa sınav | 3 | 1 | 3 | | Dönem sonu sınavı için hazırlık | 3 | 1 | 3 | | Dönem sonu sınavı | 3 | 1 | 3 | | Total work load | | | 271 |
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