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Course Code: 
MATH 452
Semester: 
Spring
Course Type: 
Core
P: 
3
Lab: 
0
Laboratuvar Saati: 
0
Credits: 
3
ECTS: 
8
Course Language: 
English
Course Objectives: 
Functional analysis, is a subject that has many applications. We can count the theory of differential equations and applications in physics among them.
Course Content: 

Topological dual. Compact, closed and adjoint operators. Inner product spaces. Orthonormal sets and Fourier series. Linear operators on Hilbert spaces. Resolvent and spectrum of an operator. Spectra of continuous and compact linear operators. Spectral analysis on Hilbert spaces. Derivations of operators.

Course Methodology: 
1: Lecture, 2: Problem Solving
Course Evaluation Methods: 
A: Written examination, B: Homework

Vertical Tabs

Course Learning Outcomes

Learning Outcomes

Teaching Methods

Assessment Methods

1) Learns inner product and Hilbert Spaces

1,2

A

2) Computes the Fourier Coefficients with respect to an orthonormal basis

1,2

A

3) Learns dual spaces and to utilize of Hahn-Banach theorem

1,2

A

4) Learns Riesz Representation Theorem

1,2

A

5) Learns the spectrum of linear operators

1,2

A

6) Learns compact operators and how to apply them

1,2

A

Course Flow

Week

Topics

Study Materials

1

Inner  Product  Spaces, Hilbert Spaces ,Orthogonality

 

2

Orthonormal Bases in Infinite Dimensions ,Fourier Series

 

3

Continuous Linear Transformations

 

4

Hahn–Banach  Theorem

 

5

Dual Spaces

 

6

The Second Dual, Reflexive Spaces and Dual Operators

 

7

Projections and Complementary Subspaces

 

8

Linear Operators on Hilbert Spaces, Riesz Theorem

 

9

The Adjoint of an Operator

 

10

Normal, Self-adjoint and Unitary  Operators

 

11

The Spectrum of an Operator

 

12

Positive Operators and Projections

 

13

Compact Operators

 

14

Spectral Theory of Compact Operators

 

Recommended Sources

Textbook

Linear Functional Analysis, Bryan Rynne, M.A. Youngson

Additional Resources

 

Material Sharing

Documents

 

Assignments

 

Exams

 

Assessment

IN-TERM STUDIES

NUMBER

PERCENTAGE

Mid-terms

2

100

Quizzes

0

0

Assignments

0

0

Total

 

100

CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE

 

60

CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE

 

40

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

6

84

Mid-terms (Including self study)

2

20

40

Quizzes

-

   

Assignments

-

   

Final examination (Including self study)

1

30

30

Total Work Load

   

196

Total Work Load / 25 (h)

   

7,84

ECTS Credit of the Course

   

8