Course Name Code Semester T+U Hours Credit ECTS
Functional Analysis and Its Applications MAT 548 0 3 + 0 3 6
 Precondition Courses Recommended Optional Courses Course Language Turkish Course Level yuksek_lisans Course Type Optional Course Coordinator Prof.Dr. MUSTAFA ERÖZ Course Lecturers Prof.Dr. MUSTAFA ERÖZ, Course Assistants Course Category Course Objective The importance of tecniques of functional analysis in the fields of applied mathematics and engineering is gettting The aim of this course is to learn these tecniques which are powerful tools in problem solving and use them efficiently. Course Content Metric spaces, Banach and Hilbert spaces,Fundamental theorems for normed spaces,Banach fixed point theorem,Contraction mapping principle in metric spaces,Some applications of contraction mapping pr. Application of fixed point theorem to linear equations, Application of fixed point theorem to linear equations,Application of fixed point theorem to integral equations, Differentiation of nonlinear operators, Gateaux derivative, Frechet derivative, Newton method for nonlinear operator equations, Application of Newton method to nonlinear algebraic equations, Application of Newton method to integral equations.
# Course Learning Outcomes Teaching Methods Assessment Methods
1 Students will have explained Banach fixed point theorem. Lecture, Question-Answer, Drilland Practice, Testing, Homework,
2 Students will have applied fixed point theorem to linear equations. Lecture, Question-Answer, Drilland Practice, Testing, Homework,
3 Students will have applied fixed point theorem to differential equations. Lecture, Question-Answer, Drilland Practice, Testing, Homework,
4 Students will have applied fixed point theorem to integral equations. Lecture, Question-Answer, Drilland Practice, Testing, Homework,
5 Students will have defined Gateaux and Frechet derivatives of nonlinear operators. Lecture, Question-Answer, Drilland Practice, Testing, Homework,
6 Students will have explained how to use Newton method in solving nonlinear operator equations. Lecture, Question-Answer, Drilland Practice, Testing, Homework,
Week Course Topics Preliminary Preparation
1 Metric spaces, Banach and Hilbert spaces
2 Fundamental theorems for normed spaces
3 Banach fixed point theorem
4 Contraction mapping principle in metric spaces
5 Some applications of contraction mapping pr.
6 Application of fixed point theorem to linear equations
7 Application of fixed point theorem to linear equations
8 Application of fixed point theorem to integral equations
9 Differentiation of nonlinear operators
10 Gateaux derivative
11 Frechet derivative
12 Newton method for nonlinear operator equations
13 Application of Newton method to nonlinear algebraic equations
14 Application of Newton method to integral equations
Resources
Course Notes
Course Resources
Order Program Outcomes Level of Contribution
1 2 3 4 5
0 Develop strategic, political and practice plans and evaluate the results by taking into account the quality process in his/her area of expertise
2 Student follows the current journals in his/her field and puts forward problems. X
3 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
4 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field.
5 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
6 Student determines the problems to be solved within his/her field and if necessary takes the lead.
7 Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field.
8 Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters X
9 Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research.
10 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. X
11 Student considers the scientific and cultural ethical values in the phases of gathering and conveying data or writing articles.
Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 50
1. Ödev 50
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100