Courses – Fakultet tehničkih nauka u Novom Sadu

Subject: Nonlinear equations with applications (17.D0M38Z)

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:

Enabling students to develop abstract thinking and acquire knowledge about non-linear equations.

Educational outcome:

To use the acquired knowledge in engineering subjects and in practice, postulate and solve mathematical models in engineering subjects using the knowledge of non-linear equations.

Course content:

Theoretical part (Lectures): Non-linear operator equations – introduction to basic notions. Numerical solutions of differential equations. Functional equations. Differential equations. Delay differential equations. Integral equations. Integro differential equations. Stochastic differential equations. Geometry and differential equations. Part of the course is organized in the form of independent study and research work in the field of mathematics. The study and research work involves active study of primary scientific sources, organization and conduction of experiments and statistical data analysis, numerical simulations, and possibly writing a paper in the filed 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. The students can also take partial exams (covering one module) during the course. In consultation with the course teacher a student gives an oral presentation (covering one module) and writes a seminar paper. The oral part of the final examination is eliminatory. 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
Dodd, R.K. et al.	Solitons and Nonlinear Wave Equations	1984	Academic Press, London	English
A. Kufner, S. Fučik	Nonlinear Differential Equations	1980	Amsterdam-Oxford-New York	English
Saaty, T. L.	Modern Nonlinear Equations	1981	Dover Publications, Inc., New York	English
M. Kuczma	An introduction to the Theory of Functional Equations and Inequalities	1985	Universytet Slaski, Warszava-Krakow-Katowice	English

Knowledge evaluation:

Course activity	Pre-examination	Obligations	Number of points
Project defence	Yes	Yes	10.00
Lecture attendance	Yes	Yes	5.00
Practical part of the exam - tasks	No	Yes	25.00
Term paper	Yes	Yes	20.00
Theoretical part of the exam	No	Yes	40.00