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  • Course Information
    • Course Title Code Semester Laboratory+Practice (Hour) Pool Type ECTS
    Fourier Transforms MAT569 FALL-SPRING 3+0 E 6
    Learning Outcomes
    1-Defines L_{p} spaces, Schwartz space and Fourier transform.
    2- Investigates the Fourier transforms of the sine and cosine function, continuity and differential properties of the Fourier transform.
    3-Interprets the Riemann-Lebesgue theorems, essential properties of direct and inverse Fourier transforms in the L_{1} space.
    4-Interprets the Plancherel theory in the L_{2} space, generalized functions and their Fourier transform
  • ECTS / WORKLOAD
    • ActivityPercentage

    (100)

    		NumberTime (Hours)Total Workload (hours)
    Course Duration (Weeks x Course Hours)14342
    Classroom study (Pre-study, practice)14570
    Assignments2021632
    Short-Term Exams (exam + preparation) 0000
    Midterm exams (exam + preparation)3011818
    Project0000
    Laboratory 0000
    Final exam (exam + preparation) 5012020
    0000
    Total Workload (hours)   182
    Total Workload (hours) / 30 (s)     6,07 ---- (6)
    ECTS Credit   6
  • Course Content
    • Week Topics Study Metarials
    1 L_{p} spaces R1. Section 1.1
    2 Schwartz space R1. Section 2.1
    3 Definition of Fourier transform R1. Section 3.1
    4 Fourier transforms of the sine and cosine function R1. Section 3.2
    5 Continuity and differential properties of the Fourier transform R1. Section 3.3
    6 Differential properties of the Fourier transform R1. Section 3.4
    7 Riemann-Lebesgue theorems R1. Section 4.1
    8 Essential properties of direct Fourier transforms in the L_{1} space R1. Section 5.1
    9 Essential properties of inverse Fourier transforms in the L_{1} space R1. Section 5.2
    10 Essential properties of direct and inverse Fourier transforms in the L_{1} space R1. Section 5.3
    11 Plancherel theory in the L_{2} space R1. Section 6.1
    12 Generalized functions R1. Section 6.2
    13 Generalized functions and their Fourier transform. R1. Section 6.3
    14 Properties of generalized functions and their Fourier transform. R1. Section 6.4
    Prerequisites -
    Language of Instruction Turkish
    Responsible Prof. Dr. Hüseyin IRMAK
    Instructors

    1-)10143 10143 10143
    Assistants -
    Resources K1. Lecture notes
    Supplementary Book YK1. Stein, E. M., & Shakarchi, R. (2011). Fourier analysis: an introduction (Vol. 1). Princeton University Press. YK2. Butzer, P. L., & Nessel, R. J. (1971). Fourier analysis and approximation, Vol. 1. Reviews in Group Representation Theory, Part A (Pure and Applied Mathematics Series, Vol. 7).
    Goals The aim of the course is to learn L_{p} spaces and Schwartz spaces, Definition of Fourier transform, Fourier transforms of the sine and cosine function, continuity and differential properties of the Fourier transform are investigated. Furthermore, the aim is to obtain Riemann-Lebesgue theorems, essential properties of direct and inverse Fourier transforms in the L_{1} space, Plancherel theory in the L_{2} space.
    Content L_{p} spaces and Schwartz space, definition of Fourier transform, Fourier transforms of the sine and cosine function, continuity and differential properties of the Fourier transform, Riemann-Lebesgue theorems, essential properties of direct and inverse Fourier transforms in the L_{1} space, Plancherel theory in the L_{2} space, generalized functions and their Fourier transform.
  • Program Learning Outcomes
    • Program Learning Outcomes Level of Contribution
    1 Improve and deepen the gained knowledge in Mathematics in the speciality level 3
    2 Use gained speciality level theoretical and applied knowledge in mathematics 4
    3 Perform interdisciplinary studies by relating the gained knowledge in Mathematics with other fields. 3
    4 Analyze mathematical problems by using the gained research methods -
    5 Conduct independently a study requiring speciliaty in Mathematics -
    6 Develop different approaches and produce solutions by taking responsibility to problems encountered in applications -
    7 Evaluate the gained speciality level knowledge and skills with a critical approach and guide the process of learning -
    8 Transfer recent and own research related to mathematics to the expert and non-expert shareholders written, verbally and visually -
    9 Uses computer software and information technologies related to the field of mathematics at an advanced level. -
    10 Have the awareness of acting compatible with social, scientific, cultural and ethical values during the process of collecting, interpreting, applying and informing data related to Mathematics -
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