Courses – Fakultet tehničkih nauka u Novom Sadu

Subject: Fixed point theory (17.DOM59L)

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 fixed point theory.

Educational outcome:

Student is enabled to develop and solve mathematical models in fixed point theorz in further education and professional subjects.

Course content:

Metric and Banach spaces, Differentiation and integration in Banach spaces , Contraction principles, the Brouwer fixed-point theorem , Kakutani’s fixed-point theorem and applications , The Jordan curve theorem, The Leray–Schauder mapping degree, Compact operators, The Leray–Schauder mapping degree ,The Leray–Schauder principle and the Schauder fixed-point theorem ,Applications to integral and differential equations . .

Teaching methods:

Lectures, Consultations. The presentation of the theoretical part is followed by the corresponding examples for easier understanding of subject content. 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. In cooperation with professors, student is enabled to independently write scientific paper.

Literature:

Authors	Title	Year	Publisher	Language
Kim Border	Fixed point theorems with applications to economics and game theory	1985	Cambridge Univ.Press	English
Olga Hadžić	Osnovi teorije nepokretne tačke	1987	Institut za matematiku, Novi Sad	English