Differential equations | Faculty of Technical Sciences

Subject: Differential equations (17.0M518)

Native organizations units: Department of Fundamentals Sciences

Type of studies	Title
Master Academic Studies	Mathematics in Engineering (Year: 1, Semester: Winter)

General information:

Category	Academic-general educative
Scientific or art field	Teorijska i primenjena matematika
ECTS	5

Acquiring fundamental methods for solution of differential equations and enabling students to use the acquired knowledge in other general and engineering subjects. Developing ability for independent analysis and solving of various problems that involve differentail equations.

Students are competent to use methods of solution of mathematical models in practice and in their further education in engineering subjects.

Introduction. Existence and uniqueness.Different methods solution of differential equations. Systems of differential equations (Sturm theorems,Sturm-Liouville systems,problems oscillations,eigenvalues) Boundary problems. Some problems of the qualitative analysis(Linear and nonlinear problems), Stability of solutions of ordinary differential equations((The stability of linear systems,The stability of solutions of nonlinear systems,Analysis of the autonomous system in phase space).

Lectures, computing practice, consultations. The presentation of the theoretical part during the lectures is followed by the characteristic examples which contribute to better understanding of the subject matter. The practice classes which follow the lectures are devoted to practical tasks which contribute to better understanding of the material. In addition to lectures and practices there are regular consultations.

Authors	Title	Year	Publisher	Language
Rubinstein, Z.	A Course in Ordinary and Partial Differential Equations	1969	Academic Press, New York	English
Reid, W.T.	Ordinary Differential Equations	1971	John Wiley & Sons, New York	English
Mackelvey, R.	Lectures on ordinary differential equations	1970	Academic Press, New York	English
Boyce, W.,E., Diprina ,R.C.	Elementary Differential Equations and Boundary Value Problems	1997	John Wilye$ Sons, Inc.	English

Course activity	Pre-examination	Obligations	Number of points
Test	Yes	Yes	10.00
Test	Yes	Yes	10.00
Practical part of the exam - tasks	No	Yes	60.00
Oral part of the exam	No	Yes	10.00
Exercise attendance	Yes	Yes	5.00
Lecture attendance	Yes	Yes	5.00