Courses – Fakultet tehničkih nauka u Novom Sadu

Subject: Functional analysis 1 (17.D0M01L)

Native organizations units: Department of Fundamentals Sciences

Type of studies	Title
Doctoral Academic Studies	Mathematics in Engineering (Godina: 1, Summer)
Doctoral Academic Studies	Mathematics in Engineering (Godina: 1, Summer)

General information:

Category	Scientific-professional
Scientific or art field	Teorijska i primenjena matematika
Interdisciplinary	Yes
ECTS	10

Educational goal:

Enabling students to develop abstract thinking and acquire basic knowledge in the field of Functional Analysis:Topological properties (compactness,compactification paracompactness); measure and integration theory.

Educational outcome:

To use the acquired knowledge in further education and to postulate and solve mathematical models from functional analysis in engineering subjects.

Course content:

Theoretical aspects: Topological properties (compactness, compactification, paracompactness). Measure theory and integration (algebra of sets and measures on the algebra; Lebesgue and Lebesgue- Stieltjes measure; measurable functions;Lebesgque integral; convergence theorem; sets of measure zero, the L ^ p spaces, convergence in measure). Research work includes active monitoring of primary scientific sources possibly writing a paper applying the methods of functional analysis. Study and research work is based on primary scientific sources, organization and conduction of experiments and statistical data analysis, numerical simulations, and possible paper in the field of mathematics.

Teaching methods:

Lectures. Consultations. Lectures are organized in combined form. The presentation of the theoretical part is followed by the corresponding examples which contribute to better understanding of the theoretical part. In addition to lectures there are regular consultations. Through research and study work the student will, on the bases of scientific journals and other relevant literature that has been studied independently, develop further understanding of the material covered in lectures. Working with the course teacher the student develops the ability to independently work on a scientific paper.

Literature:

Authors	Title	Year	Publisher	Language
Sze- Tsen Hu	Introduction to general topology	1966	Holden-Day, Inc., San Francisko, London, Amsterdam,	English
Kurepa, S.	Matematička analiza	1970	Školska knjiga, Zagreb	Serbian language
Kovačević, I., Ralević, N.	Funkcionalna analiza	2004	Fakultet tehničkih nauka, Novi Sad	Serbian language
O.Hadžić	Fixed Point Theory in Topological Vector Spaces	1984	Univerzitet u Novom Sadu, Institut za matematiku ,Novi Sad	English
Rao,M.M.	Measure Theory and Integration	1987	John Wiley and Sons, New York	English