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COURSE INFORMATION
Course CodeCourse TitleL+P HourSemesterECTS
MAT 462FUNCTIONAL ANALYSIS3 + 08th Semester5,5

COURSE DESCRIPTION
Course Level Bachelor's Degree
Course Type Elective
Course Objective The aim of this course is to teach the theory of linear operator and inner product space.
Course Content Linear Operators, Dual Spaces, Hahn-Banach and Open Mapping Theorems, Closed Linear Operators and Closed Graph Theorem, Inner Product Space, Hilbert Space, Orthogonal Projection Operator, Hilbert-adjoint Operator, Self-Adjoint and Normal Operators.
Prerequisites No the prerequisite of lesson.
Corequisite No the corequisite of lesson.
Mode of Delivery Face to Face

COURSE LEARNING OUTCOMES
1Realizes the dfferences between the linear and nonlinear operators.
2Learns the cassifications of bounded operatrs, continuous operator and compact operators.
3Defines the dual spaces an proves the fundemental theorems.
4Expresses, proves and commens the fundemetal theorems in Functional Analysis.
5Compares the Banach ad Hilbert spaces.
6Compares the adjoint operators on normed spaces and Hilbert spaces.
7Realizes the advantages of the properties of Hilbert spaces for the operators on this space.
8classifies the operators as sef adjoint, normal and unitary.
9Realizes the soutions of operator equations.

COURSE'S CONTRIBUTION TO PROGRAM
PO 01PO 02PO 03PO 04PO 05PO 06PO 07PO 08PO 09PO 10
LO 001  4     4 
LO 002 54    55 
LO 003 45    45 
LO 004 44  5 33 
LO 005 54    4  
LO 006 44    5  
LO 007 54    45 
LO 008 45    54 
LO 009  4     5 
Sub Total 3138  5 3031 
Contribution0340010330

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
ActivitiesQuantityDuration (Hour)Total Work Load (Hour)
Course Duration (14 weeks/theoric+practical)14342
Mid-terms15151
Final examination15050
Total Work Load

ECTS Credit of the Course






143

5,5
COURSE DETAILS
 Select Year   


 Course TermNoInstructors
Details 2023-2024 Spring1ALP ARSLAN KIRAÇ
Details 2022-2023 Spring1İSMAİL YASLAN
Details 2021-2022 Spring1İSMAİL YASLAN
Details 2020-2021 Spring1İSMAİL YASLAN
Details 2019-2020 Spring1İSMAİL YASLAN
Details 2018-2019 Spring1İSMAİL YASLAN
Details 2017-2018 Spring1ALP ARSLAN KIRAÇ
Details 2016-2017 Spring1ALP ARSLAN KIRAÇ
Details 2015-2016 Spring1İSMAİL YASLAN


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Course Details
Course Code Course Title L+P Hour Course Code Language Of Instruction Course Semester
MAT 462 FUNCTIONAL ANALYSIS 3 + 0 1 Turkish 2023-2024 Spring
Course Coordinator  E-Mail  Phone Number  Course Location Attendance
Prof. Dr. ALP ARSLAN KIRAÇ aakirac@pau.edu.tr FEN A0312 %
Goals The aim of this course is to teach the theory of linear operator and inner product space.
Content Linear Operators, Dual Spaces, Hahn-Banach and Open Mapping Theorems, Closed Linear Operators and Closed Graph Theorem, Inner Product Space, Hilbert Space, Orthogonal Projection Operator, Hilbert-adjoint Operator, Self-Adjoint and Normal Operators.
Topics
WeeksTopics
1 Linear Operator, Kernel of a Linear Operator, Isomorphism
2 Bounded and Continuous Linear Operators
3 Bounded and Continuous Linear Operators
4 Bounded Linear Extensions, Linear Functionals and Dual Space
5 Algebraic Dual Space, Linear Operators and Functionals on Finite Dimensional Spaces
6 Hahn-Banach Theorem, Hahn-Banach Theorem for Complex Linear Spaces and Normed Spaces, Baire Theorem
7 Open Mapping Theorem, Closed Linear Operators and Closed Graph Theorem
8 Banach-Steinhouse Theorem, Adjoint Operator for Normed Spaces
9 Midterm Exam
10 Inner Product Space, Parallelogram Equality, Orthogonality, Pythagorean Theorem
11 Hilbert Space, Orthogonal Complement and Direct Sum
12 Closed Subspace, Minimizing Vector Theorem, Orthogonal Projection Operator
13 Riesz’s Theorem, Hilbert-adjoint Operator
14 Self-Adjoint and Normal Operators
Materials
Materials are not specified.
Resources
ResourcesResources Language
FONKSİYONEL ANALİZ,Prof.Dr.Mustafa BAYRAKTARTürkçe
Course Assessment
Assesment MethodsPercentage (%)Assesment Methods Title
Final Exam50Final Exam
Midterm Exam50Midterm Exam
L+P: Lecture and Practice
PQ: Program Learning Outcomes
LO: Course Learning Outcomes