Mathematics 1

ID: 1463
Course type: theoretical and methodological
Course coordinator: Tomanović D. Jelena
Lecturers: Đukić Lj. Dušan, Jandrlić R. Davorka, Mutavdžić-Đukić M. Rada, Pejčev V. Aleksandar, Spalević M. Miodrag, Tomanović D. Jelena
Contact: Tomanović D. Jelena
Level of studies: B.Sc. (undergraduate) Academic Studies – Mechanical Engineering
ECTS: 6
Final exam type: written+oral
Department: Department of Mathematics

Lectures

Semester 1, position 1

Goal

Learning the basics of linear algebra with analytical geometry and one variable differential calculus in a theoretical and practical sense.

Outcome

Upon completion of the course, the student is expected to: 1. know the concepts and properties of vectors and matrices and methods for solving systems of linear equations; 2. know to represent basic geometric objects in a rectangular coordinate system and work with them; 3. understand the concept of function with basic properties and be familiar with elementary functions; 4. know the differential calculus of one variable functions, including the determination of asymptotes, extrema, turning points, and Taylor polynomials; 5. be familiar with the curves represented аs vector functions and with the concept of curvature and torsion.

Theoretical teaching

- Matrix calculus - Systems of linear equations - Vectors in geometry and in coordinates - Lines and planes in the coordinate system - Curves and surfaces of the second order - Concept of function and elementary functions - Limits, properties and applications - Derivatives and applications of differential calculus - Taylor polynomial - Parametric given curves

Practical teaching

In accordance with theoretical teaching.

Attendance requirement

Defined by the curriculum of the study program/module.

Resources

I. Aranđelović, A. Pejčev, D. Đukić, D. Jandrlić, J. Tomanović, R. Mutavdžić Đukić, M. Vučić, Mathematics 1: textbook and problem collection, 2020, University of Belgrade - Faculty of Mechanical Engineering, ISBN: 978-86-6060-057-0 (in Serbian).

Assigned hours

Total assigned hours: 75

Active teaching (theoretical)

New material: 18
Elaboration and examples (recapitulation): 12

Active teaching (practical)

Auditory exercises: 25
Laboratory exercises: 0
Calculation tasks: 5
Seminar paper: 0
Project: 0
Consultations: 0
Discussion/workshop: 0
Research study work: 0

Knowledge test

Review and grading of calculation tasks: 0
Review and grading of lab reports: 0
Review and grading of seminar papers: 0
Review and grading of the project: 0
Test: 10
Test: 0
Final exam: 5

Knowledge test (100 points total)

Activity during lectures: 0
Test/test: 50
Laboratory practice: 0
Calculation tasks: 0
Seminar paper: 0
Project: 0
Final exam: 50
Requirement for taking the exam (required number of points): 25

Literature

I. Aranđelović, A. Pejčev, D. Đukić, D. Jandrlić, J. Tomanović, R. Mutavdžić Đukić, M. Vučić, Mathematics 1, 2020, University of Belgrade - FME, ISBN: 978-86-6060-057-0 (in Serbian).