FOURIER ANALYSIS

Course Code:

MATH 344

Course Type:

Area Elective

P:

3

Lab:

0

Laboratuvar Saati:

0

Credits:

3

ECTS:

7

Course Language:

English

Course Objectives:

To teach the basic principles of elementary Fourier analysis.

Course Content:

Functional sequences and series. Convergence. Cauchy-Schwarz inequality. Fourier series and its convergence. Orthogonal polynomials. Fourier series with respect to an orthogonal system. Bessel's inequality. Generalizations with weight. Completeness of orthogonal systems. Parseval's identity. Fourier integrals. Fourier transformations. Applications to boundary value problems,

Course Methodology:

1: Lecture, 2: Problem Solving, 3:Question-answer, 4: Homework

Course Evaluation Methods:

A: Written examination, B: Homework

Vertical Tabs

Course Learning Outcomes

Learning Outcomes	Program Learning Outcomes	Teaching Methods	Assessment Methods
1) Knows how to compute Fourier series of a function.	2,3	1,4	A
2) Knows the basic terminology and results of inner product spaces, Hilbert spaces, L^2 spaces.	2,3	1,4	A
3) Knows how to compute Fourier transform of a function.	2,3	1,4	A
4) Knows some applications of Fourier series and Fourier transform.	2,3,4	1,4	A

Course Flow

Week	Topics	Study Materials
1	Fourier Series	Textbook
2	Fourier Series (continued)	Textbook
3	Fourier Series (continued)	Textbook
4	Orthogonal Sets of Functions	Textbook
5	Orthogonal Sets of Functions (continued)	Textbook
6	Orthogonal Sets of Functions (continued)	Textbook
7	Orthogonal Polynomials	Textbook
8	Orthogonal Polynomials (continued)	Textbook
9	Orthogonal Polynomials (continued)	Textbook
10	The Fourier Transform	Textbook
11	The Fourier Transform (continued)	Textbook
12	The Fourier Transform (continued)	Textbook
13	Some Boundary Value Problems	Textbook
14	Some Boundary Value Problems (continued)	Textbook

Recommended Sources

Textbook	Fourier Analysis and Its Applications, by G. B. Folland
Additional Resources	Fourier Series and Boundary Value Problems, by J. W. Brown and R. V. Churchill.

Material Sharing

Documents
Assignments
Exams

Assessment

IN-TERM STUDIES	NUMBER	PERCENTAGE
Mid-terms	2	100
Quizzes	-	-
Assignments	-	-
Total		100
CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE		40
CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE		60
Total		100

COURSE CATEGORY

Expertise/Field Courses

Course’s Contribution to Program

No	Program Learning Outcomes	Contribution
No	Program Learning Outcomes	1	2	3	4	5
1	The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamenral research fields in mathematics (i.e., analysis, algebra, differential equations and geometry)	x
2	Acquiring fundamental knowledge on fundamental research fields in mathematics				x
3	Ability form and interpret the relations between research topics in mathematics				x
4	Ability to define, formulate and solve mathematical problems				x
5	Consciousness of professional ethics and responsibilty				x
6	Ability to communicate actively	x
7	Ability of self-development in fields of interest				x
8	Ability to learn, choose and use necessary information technologies	x
9	Lifelong education			x

ECTS

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
Activities	Quantity	Duration (Hour)	Total Workload (Hour)
Course Duration (14x Total course hours)	14	3	42
Hours for off-the-classroom study (Pre-study, practice)	14	5	70
Mid-terms (Including self study)	2	14	28
Quizzes	-	-	-
Assignments	7	3	21
Final examination (Including self study)	1	14	14
Total Work Load			175
Total Work Load / 25 (h)			7
ECTS Credit of the Course			7

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