Engineering mathematics

Course title

Code

F18L2W104

Study programme

—

Organizer of the study programme (unit, institute, department)

Faculty of Computer Science and Engineering

Degree level (first, second, third cycle)

First cycle

Academic year / semester

3 / Winter

Number of ECTS credits

Teacher

—

Prerequisites for enrolling in the course

Калкулус 2 или Калкулус

10.

Course objectives (competences)

The course covers methods for numerical solving of many mathematical problems and application of some significant mathematical transformations in engineering.

11.

Course content

Numerical mathematics: Approximate numbers: presentation of numbers and operations. Analysis of errors (absolute and relative errors). Rounding an approximate number: exact and significant digits, Approximation of functions, Some examples of errors obtained from elementary functions, Approximately solving nonlinear equations, Numerical methods for solving systems of linear equations, Calculating schemas for polynomials and their applications, Interval of real polynomial roots (Criteria of Lagrange, Newton and Descartes);
Mathematical transformations - Complex numbers: definition, properties, modul, argument, Practical applications, Complex functions: types, derivatives. Cauchy -Riemann conditions, Laplace transformation (definition, existence, properties), Inverse Laplace transformation, Practical examples for solving ordinary differential equations with Laplace transformation, Fourier transformations, Fourier series, Fourier integral, Inverse Fourier transformation, Practical examples for finding Fourier transformations of functions.

12.

Learning methods

Lectures, exercises, independent work, project assignments, seminar papers

13.

Total available time

6 ECTS x 30 hours = 180 hours

14.

Distribution of the available time

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

15.

Forms of teaching activities

15.1.	Lectures – theoretical teaching	30 hours
15.2.	Exercises (laboratory, auditory), seminars, team work	45 hours

16.

Other forms of activities

16.1.	Project assignments	15 hours
16.2.	Individual assignments	15 hours
16.3.	Home study	75 hours

17.

Grading

17.1.	Tests	10 points
17.2.	Seminar paper / project (presentation: written and oral)	15 points
17.3.	Activity and participation	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.

Requirements for signature and taking the final exam

completed 15 and 16

20.

Language of instruction

Macedonian and English

21.

Method of monitoring teaching quality

Internal Evaluation and Survey Mechanism

22.

Literature

22.1.	Required literature No. Author Title Publisher Year
22.2.	Additional literature No. Author Title Publisher Year