Course Code:
MATH 456
Semester:
Spring
Course Type:
Core
P:
2
Lab:
2
Laboratuvar Saati:
0
Credits:
3
ECTS:
9
Prerequisite Courses:
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

 ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION Activities Quantity Duration (Hour) Total Workload (Hour) Course Duration (14x Total course hours) 14 4 56 Hours for off-the-classroom study (Pre-study, practice) 14 7 98 Mid-terms (Including self study) 2 23 46 Quizzes - Assignments - Final examination (Including self study) 1 25 25 Total Work Load 225 Total Work Load / 25 (h) 9 ECTS Credit of the Course 9