Mathematics for engineers

1.

Subject title

Mathematics for engineers

Инженерска математика

2.

Code

F23L2W104

3.

Study program

Примена на информациски технологии, Примена на информациски технологии, Софтверско инженерство и информациски системи, Компјутерски науки, Компјутерско инженерство, Интернет, мрежи и безбедност, Software engineering and information systems, Софтверско инженерство и информациски системи, Компјутерски науки, Компјутерско инженерство, Интернет, мрежи и безбедност, Информатичка едукација, Software engineering and information systems, Стручни студии за програмирање, Стручни студии за програмирање,

4.

Organizer of the study program (unit, institute, department, division)

Faculty of Information Sciences and Computer Engineering

5.

Study cycle (first, second, third)

Прв циклус

6.

Academic year / semester

2 / Зимски

7. Number of ECTS credits

6.0

8.

Instructor

проф. д-р Весна Димитрова

9.

Prerequisites for enrollment

Калкулус 1 или Математика 1

10.

Subject goals and competencies:

The subject includes methods for the numerical solution of several mathematical problems, as well as the application of some more significant mathematical transformations in engineering.

11.

Subject content:

Lectures: 1. Numerical Mathematics - Approximate numbers: representation and operations, Types of errors (absolute and relative error). 2. Numerical Mathematics - Rounding Approximate Numbers: Exact and Significant Figures. 3. Numerical mathematics - Errors when calculating values of functions from one independent variable. 4. Numerical mathematics - Approximate solution of nonlinear equations, Numerical methods for solving systems of linear equations. 5. Numerical mathematics - Calculation schemes for polynomials and their practical application. 6. Numerical mathematics - Limits of an interval in which the real roots of polynomials are located equations. 7. Mathematical transformations - Complex numbers: definition, properties, modulus, argument, 8. Mathematical transformations - Complex functions, Types of complex functions, Derivation of complex functions, Cauchy-Riemann conditions 9. Mathematical transformations - Laplace transform (definition, existence, properties), Inverse Laplace transform, 10. Mathematical transformations - Methods for solving ordinary differential equations with Laplace transformation. 11. Mathematical transformations - Fourier transformations, Fourier series. 12. Mathematical transformations - Fourier integral, Inverse Fourier transformation. Exercises: 1. Practical problems with approximate numbers. 2. Examples of exact and significant figures. 3. Examples of elementary function errors. 4. Problems and examples with different numerical methods. 5. Practical examples with calculation schemes for polynomials. 6. Practical tasks with criteria of Lagrange, Nutn, Descartes. 7. Practical examples and tasks. 8. Examples of complex functions. 9. Tasks using Laplace transform and Inverse Laplace transform. 10. Practical examples for solving ordinary differential equations with Laplace transform. 11. Practical tasks for determining Fourier transforms for functions. 12. Practical tasks for determining Inverse Fourier transforms for functions.

12.

Learning methods:

Предавања, вежби, самостојна работа, проектни задачи, семинарски работи

13.

Total available time fund

6.0 ECTS x 30 hours = 180 hours

14.

Time distribution

30 + 45 + 15 + 15 + 75 = 180 hours

15.

Forms of teaching activities

15.1.

Lectures - theoretical teaching

30 hours

15.2.

Exercises (laboratory, classroom), seminars, team work

45 hours

16.

Other forms of activities

16.1.

Project tasks

15 hours

16.2.

Independent tasks

15 hours

16.3.

Homework

75 hours

17.

Grading method

17.1.

Tests

10 points

17.2.

Seminar work / project (presentation: written and oral)

15 points

17.3.

Activities and learning

10 points

17.4.

Final exam

70 points

18.

Grading criteria (points / grade)

up to 50 points

5 (five) (F)

from 51 to 60 points

6 (six) (E)

from 61 to 70 points

7 (seven) (D)

from 71 to 80 points

8 (eight) (C)

from 81 to 90 points

9 (nine) (B)

from 91 to 100 points

10 (ten) (A)

19.

Condition for signature and taking final exam

реализирани 15 и 16

20.

Language of instruction

македонски и англиски

21.

Quality assurance method

Механизам за интерна евалуација и анкети

22.

Literature

22.1.

Mandatory literature

22.2.

Additional literature