Courses – Fakultet tehničkih nauka u Novom Sadu

Subject: Mathematical analysis 1 (17.E212)

Native organizations units: Department of Fundamentals Sciences

Type of studies	Title
Undergraduate Academic Studies	Computing and Control Engineering (Godina: 1, Winter)

General information:

Category	Academic-general educative
Scientific or art field	Teorijska i primenjena matematika
Interdisciplinary	Yes
ECTS	9

Educational goal:

Enabling students to think abstractly and gain basic knowledge in the field of Mathematical analysis (limiting processes, differential and integral calculus, ordinary differential equations). The goal is to develop the capability to connect complex notions from mathematical analysis and to perceive the possibilities for the application of the acquired knowledge.

Educational outcome:

Acquired knowledge is used in further education and student designs and solves mathematical models in professional courses using the knowledge from Mathematical Analysis 1. The student is encouraged to use appropriate software tools (Matlab, Mathematica).

Course content:

Theoretical lectures: Field of real and complex numbers. Metric space. Series (convergence of series, real and complex sequences, complete metric space). Limits, continuity and uniform continuity of functions. Real functions of a real variable (limit, continuity, uniform continuity, differential calculus and application, indefinite integral; definite integral and application; improper integral). Real functions of several real variables (limits, continuity, uniform continuity, differential calculus and application). Ordinary differential equations of first and higher order. Linear differential equations of n-th order. Practice (Exercises): Corresponding examples from theoretical lectures are done in exercises, thus practicing the taught lectures and understanding them better.

Teaching methods:

Lectures; Numeric computing practice. Consultations. Lectures are combined. Theoretical part of the lectures is accompanied by typical examples in order to better understand the matter taught in lectures. In practice, which accompanies lectures, typical problems are solved and the knowledge from the lectures is deepened. Besides lectures and practice, consultations are held on a regular basis. Part of the lectures, which presents one logical whole, can be passed during the teaching process in the form of the following 5 modules (the first module: limiting processes; the second module: differential calculus of real functions of a real variable, the third module: differential calculus of real functions of several variables; the fourth module: integral calculus: the fifth module: ordinary differential equations).

Literature:

Authors	Title	Year	Publisher	Language
Novković, M., i dr	Zbirka rešenih zadataka iz Matematičke analize 1	2012	Fakultet tehničkih nauka, Novi Sad	Serbian language
Grupa autora	Testovi sa ispita iz Matematičke analize 1	2012	Fakultet tehničkih nauka, Novi Sad	Serbian language
Kovačević, I. i dr.	Matematička analiza 1 : uvodni pojmovi i granični procesi	2012	Fakultet tehničkih nauka, Novi Sad	Serbian language
Kovačević, I. i dr.	Matematička analiza 1 : diferencijalni i integralni račun, obične diferencijalne jednačine	2012	Fakultet tehničkih nauka, Novi Sad	Serbian language

Knowledge evaluation:

Course activity	Pre-examination	Obligations	Number of points
Lecture attendance	Yes	Yes	2.00
Exercise attendance	Yes	Yes	3.00
Final exam - part one	No	No	50.00
Written part of the exam - tasks and theory	No	Yes	70.00
Homework	Yes	Yes	5.00
Test	Yes	Yes	10.00
Test	Yes	Yes	10.00
Final exam - part two	No	No	50.00