Subject

Engineering Mathematics

Course Title

Engineering Mathematics
Mathematics for engineers

Code

F23L2W104

Study Programme

—

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

Faculty of Computer Science and Engineering

Degree level (first, second, third cycle)

First Cycle

Academic year / semester

3 / Winter

Number of ECTS credits

Teacher

Vesna Dimitrova

Prerequisites for enrolling in the course

Calculus 1 or Mathematics 1

10.

Objectives of the course programme (competences)

The subject covers methods for the numerical solution of various mathematical problems, as well as the application of some.
The most significant mathematical transformations in engineering.

11.

Course content

Lectures:
1. Numerical Mathematics - Approximate Numbers: Representation and Operations, Types of Errors (Absolute and Relative Error).
2. Numerical Mathematics - Rounding of approximate numbers: significant and correct digits.
3. Numerical Mathematics - Errors in computing the values of functions of a single independent variable.
4. Numerical Mathematics - Approximate solution of nonlinear equations, numerical methods for solving systems of linear equations.
5. Numerical Mathematics - Computational schemes for polynomials and their practical application.
6. Numerical Mathematics - Interval bounds for the real roots of polynomials
equations.
7. Mathematical Transformations - Complex Numbers: definition, properties, modulus, argument,
8. Mathematical Transformations - Complex Functions, Types of Complex Functions, Derivative 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 using the Laplace transform.
11. Mathematical Transformations - Fourier Transforms, Fourier Series.
12. Mathematical Transformations - Fourier Integral, Inverse Fourier Transform.

Practical Classes:
1. Practical problems with approximate numbers.
2. Examples of significant figures.
3. Examples of elementary function errors.
4. Problems and examples with various numerical methods.
5. Practical examples with computational schemes for polynomials.
6. Practical problems with Lagrange, Newton, and Cartesian criteria.
7. Practical examples and tasks.
8. Examples of complex functions.
9. Problems applying the Laplace transform and the inverse Laplace transform.
10. Practical examples for solving ordinary differential equations using the Laplace transform.
11. Practical problems for determining the Fourier transforms of functions.
12. Practical problems for determining Inverse Fourier Transforms for 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 available time

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

15.

Forms of teaching activities

15.1.	Lectures - theoretical instruction	30 hours
15.2.	Exercises (laboratory, auditory), seminars, teamwork	45 hours

16.

Other forms of activities

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

17.

Assessment method

17.1.	Tests	10 points
17.2.	Seminar paper / 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.

Requirement for obtaining a signature and taking the final exam

completed 15 and 16

20.

Language of instruction

Macedonian and English

21.

Method for monitoring the quality of teaching

Internal Evaluation and Survey Mechanism

22.

Literature

22.1.	Required literature 1. Glyn James \| Mathematics for Modern Engineering \| Macedonian Edition (Ars Lamina) \| 2009 2. H. Anton, I. Bivens, S. Davis \| Calculus \| John Wiley & Sons, Inc. \| 2002
22.2.	Additional literature No. Author Title Publisher Year