Mathematics 4

Објавено: June 28, 2022
1. Course Title Mathematics 4
2. Code 4ФЕИТ08Л010
3. Study program ТКИИ,КХИЕ,КСИАР,ЕЕС,ЕЕПМ,ЕАОИЕ
4. Organizer of the study program (unit, institute, department) Faculty of Electrical Engineering and Information Technologies
5. Degree (first, second, third cycle) First cycle
6. Academic year/semester II/4 7. Number of ECTS credits 6
8. Lecturer D-r Katerina Hadji-Velkova Saneva, D-r Biljana Jolevska-Tuneska
9. Course Prerequisites Passed: Mathematics 1 and Mathematics 2

10. Course Goals (acquired competencies): To adopt the basic concepts and methods of complex analysis and probability. Developing analytical thinking, critical skills, problem solving, ability for analysis and synthesis. Upon completion of the course, the student is able to:

• perform calculations with complex numbers and solve equations in the set of complex numbers,

• work with complex functions,

• understand the concept of complex function analyticity,

• solve integrals of complex functions by applying residue theory,

• calculate the probability of random events,

• understand the concept of random variable and random vector,

• apply different types of random variable distributions to real problems,

• interpret and apply the central boundary theorem,

• to solve problems of electrical engineering and information technologies by applying methods of complex analysis and probability theory,

• to study engineering courses in the higher study years.

11. Course Syllabus: Complex numbers. Algebra of complex numbers. Sets in a complex plane. Functions with complex variable. Analyticity. Cauchy-Riemann equations. Elementary functions. Integral of a complex function by contour. Cauchy’s integral formula. Taylor an Laurent series. Zeros and singularities. Residue theory.

Basic concepts of probability theory. Classical and geometric definitions of probability. Conditional probability. Independence of events. Total probability formula and Bayes formula. Random variable, numerical characteristics of a random variable, some important distributions. Function of one random variable. Random vectors. Independence of random variables. Conditional distributions of random variables. Numerous characteristics of a random vector. Boundary theorems.
12. Learning methods: Lectures, presentations, auditory exercises
13. Total number of course hours 3 + 3 + 0 + 0
14. Distribution of course hours 180
15. Forms of teaching 15.1. Lectures-theoretical teaching 45
15.2. Exercises (laboratory, practice classes), seminars, teamwork 45
16. Other course activities 16.1. Projects, seminar papers 35
16.2. Individual tasks 10
16.3. Homework and self-learning 45
17. Grading 17.1. Exams 30
17.2. Seminar work/project (presentation: written and oral) 0
17.3. Activity and participation 0
17.4. Final exam 70
18. Grading criteria (points) up to 50 points 5 (five) (F)
from 51to 60 points 6 (six) (E)
from 61to 70 points 7 (seven) (D)
from 71to 80 points 8 (eight) (C)
from 81to 90 points 9 (nine) (B)
from 91to 100 points 10 (ten) (A)
19. Conditions for acquiring teacher’s signature and for taking final exam Аttend classes regularly and take tests
20. Forms of assessment

During the semester, two partial exams are planed (in the 8th and 15th week of the semester, lasting a maximum of 90 minutes), and tests can be conducted during the class. In the planned exam sessions, a written exam is taken (duration up to 135 minutes). For students who have passed the partial exams, i.e. the written exam, a final oral exam can be conducted (duration up to 60 minutes).

The final grade includes the points from the partial exams, that is the written exam, as well as the points from the tests and the final oral exam.
21. Language Macedonian and English
22. Method of monitoring of teaching quality Self-evaluation and surveys
23. Literature
23.1. Required Literature
No. Author Title Publisher Year
1 К. Хаџи-Велкова Санева, С. Атанасова, А. Бучковска Збирка решени задачи од веројатност УКИМ 2016
2 А. Бучковска, К. Хаџи-Велкова Санева, С. Атанасова Вовед во веројатност за инженери ФЕИТ/УКИМ 2018
3 Е.Б.Саф, А.Д.Снајдер Основи на комплексната анализа со примени во инженерството и науката Арс-Ламина-публикации (превод на дело) 2014
4 Џејмс Браун и Руел Черчил Комплексна анализа и примени МекГро-Хил 2004