Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits
7MATH453INTRODUCTION TO GENERALIZED FUNCTIONS3+036

Course Details
Language of Instruction English
Level of Course Unit First Cycle
Department / Program MATHEMATICS
Mode of Delivery Face to Face
Type of Course Unit Elective
Objectives of the Course This course is designed to develop the intuitive understanding, theory, and computational skills necessary for the concept of generalized functions. Upon completion of the course, students will have a working knowledge of the fundamental definitions and theorems of generalized functions.
Course Content Definition of test functions and generalized functions, Types of generalized functions, Operations on generalized functions, Weak solutions of PDE's, Fourier transform, Schwartz class, Tempered distributions, Order of a distribution, Bump functions, Smooth partition of unity, Support of a distribution, Compactly supported distributions, Convergence of sequence of distributions.
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers Dr.Öğr.Üyesi Ahmet Batal
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources Robert Strichartz, A Guide to Distribution Theory and Fourier Transform

Course Category

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Midterm exams 0 % 0
Quizzes 0 % 0
Homeworks 2 % 60
Other activities 0 % 0
Laboratory works 0 % 0
Projects 0 % 0
Final examination 1 % 40
Total
3
% 100

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 3 30 90
Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.) 2 30 60
Exams and Exam Preparations 1 30 30
Total Work Load   Number of ECTS Credits 6 180

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 To be able to make some operations on generalized functions
2 To be able to find weak solutions of PDE's
3 To be able to take Fourier transform of tempered distributions
4 To be able to compute the order of a distribution
5 To be able to find the support of a distribution
6 To be able to compute the limit of a sequence of distributions


Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Definitions of test and generalized functions
2 Operations on distributions
3 Weak solutions of PDE's
4 Fourier transform and its properties
5 Schwartz class functions and Fourier transform of tempered distributions
6 Midterm 1
7 Computing the Fourier transform of some special functions
8 Finding exact solutions of some PDE's using Fourier transform
9 Order of a distribution
10 Bump function and smooth partition of unity
11 Midterm 2
12 Support of a distribution
13 Compactly supported distributions
14 Convergence of sequence of distributions
15 Final


Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
C1
C2
C3
C4
C5
C6

Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant


https://obs.iyte.edu.tr/oibs/bologna/progCourseDetails.aspx?curCourse=163201&lang=en