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Course Code: 
MATH 344
Course Type: 
Area Elective
P: 
3
Lab: 
0
Laboratuvar Saati: 
0
Credits: 
3
ECTS: 
6
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

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

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

3

42

Mid-terms (Including self study)

2

20

40

Quizzes

-

-

-

Assignments

-

-

-

Final examination (Including self study)

1

26

26

Total Work Load

 

 

150

Total Work Load / 25 (h)

 

 

6

ECTS Credit of the Course

 

 

6