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