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COURSE INFORMATION
Course CodeCourse TitleL+P HourSemesterECTS
MAT 540FUNCTIONAL ANALYSIS I3 + 01st Semester7,5

COURSE DESCRIPTION
Course Level Master's Degree
Course Type Elective
Course Objective The aim of this course is to teach concepts of metric space, norm space, Banach space, Hilbert space and basic theorems on Banach Space.
Course Content Metric Spaces, Normed Spaces, Banach Spaces, Inner Product Spaces, Hilbert Spaces, Fundamental Theorems on Normed and Banach Spaces, Advanced Application, Banach Fixed Point Theorem, Approach Theory.
Prerequisites No the prerequisite of lesson.
Corequisite No the corequisite of lesson.
Mode of Delivery Face to Face

COURSE LEARNING OUTCOMES
1Learns the structures of Metric Spaces, Normed Spaces, Banach Spaces, Inner Product Spaces, Hilbert Spaces.
2Knows the expression and proof of the Fundamental Theorems on Normed and Banach Spaces.
3States and proves the Banach fixed point theorem.
4Have information on Approximation Theory.

COURSE'S CONTRIBUTION TO PROGRAM
PO 01PO 02PO 03PO 04PO 05PO 06PO 07PO 08
LO 001     5  
LO 002  44    
LO 0035 45    
LO 004  44    
Sub Total5 1213 5  
Contribution10330100

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
ActivitiesQuantityDuration (Hour)Total Work Load (Hour)
Course Duration (14 weeks/theoric+practical)14342
Hours for off-the-classroom study (Pre-study, practice)14798
Assignments155
Mid-terms11515
Final examination13535
Total Work Load

ECTS Credit of the Course






195

7,5
COURSE DETAILS
 Select Year   


 Course TermNoInstructors
Details 2017-2018 Spring1İSMAİL YASLAN
Details 2017-2018 Fall1ALP ARSLAN KIRAÇ
Details 2016-2017 Spring1ALP ARSLAN KIRAÇ
Details 2016-2017 Fall1ALP ARSLAN KIRAÇ
Details 2015-2016 Fall1ALP ARSLAN KIRAÇ
Details 2013-2014 Spring1ALP ARSLAN KIRAÇ
Details 2012-2013 Fall1ALP ARSLAN KIRAÇ
Details 2011-2012 Spring1ALP ARSLAN KIRAÇ
Details 2010-2011 Spring1ALP ARSLAN KIRAÇ
Details 2009-2010 Fall1ALP ARSLAN KIRAÇ


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Course Details
Course Code Course Title L+P Hour Course Code Language Of Instruction Course Semester
MAT 540 FUNCTIONAL ANALYSIS I 3 + 0 1 Turkish 2017-2018 Spring
Course Coordinator  E-Mail  Phone Number  Course Location Attendance
Prof. Dr. İSMAİL YASLAN iyaslan@pau.edu.tr FEN A0391 %90
Goals The aim of this course is to teach concepts of metric space, norm space, Banach space, Hilbert space and basic theorems on Banach Space.
Content Metric Spaces, Normed Spaces, Banach Spaces, Inner Product Spaces, Hilbert Spaces, Fundamental Theorems on Normed and Banach Spaces, Advanced Application, Banach Fixed Point Theorem, Approach Theory.
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