Courses – Fakultet tehničkih nauka u Novom Sadu

Subject: Functional analysis 2 (17.D0M19Z)

Native organizations units: Department of Fundamentals Sciences

Type of studies	Title
Doctoral Academic Studies	Mathematics in Engineering (Godina: 2, Winter)

General information:

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

Educational goal:

To enable students to think abstractly and to acquire basic knowledge in the field of Functional Analysis (spaces, operators, distribution theory, short waves theory )

Educational outcome:

To utilize the acquired knowledge in further education and professional subjects, design and solve mathematical models in professional subjects using the subject content of Functional Analysis.

Course content:

Lectures: Local convex spaces: function spaces and their duals; measures, spaces; various operators classes; distribution theory, Fourier and Laplas transformation; Sobolev spaces; fundamentals of small waves theory. Study and research work includes active following of primary scientific sources, organization and conducting experiments and statistical data processing, numeric simulations, possiblem writing of scientific papers using functional analysis methods. Note: stated topics are very wide so the student will in cooperation with professors get appropriate literature that covers several topics from the list.

Teaching methods:

Lectures, independent study and research work, consultations. Lectures are held in combined way. Theoretical part is presented in lectures and it is followed by appropriate exampled contributing easier understanding of the subject content. Students expand knowledge through study and research work, studying of scientific journals and other literature. In cooperation with professor, student is enabled ot independently write scientific papers.

Literature:

Authors	Title	Year	Publisher	Language
J. Duoandikoetxea	Fourier Analysis	2001	AMS	English
M.Reed, B.Simon	Modern Mathematical Physics, Acad Press	1975	Acad.Press.	English
Kurepa, S.	Matematička analiza	1970	Školska knjiga, Zagreb	Serbian language
R.Adams	Sobolev Spaces	1975	Acad. Press.	English
F.Hirsh, G.Lacombe	Elements of Functional Analysis	1999	Springer	English
P.D.Hislop,L.M.Sigal	Introduction to Sprectal Theory	1996	Springer	English
V.Huston,J.S.Pym	Applications of Functional Analysis and Operator Theory	1980	Acad. Press.	English
P.S.Aleksandrov,B.A.Pasljnkov	Vvdenie v teorijo razmernosti	1973	Nauka, Moskkva	Russian language