Mathematics 1

1.

Subject title

Mathematics 1

Математика 1

2.

Code

F23L2W002

3.

Study program

Софтверско инженерство и информациски системи, Интернет, мрежи и безбедност, Информатичка едукација, Software engineering and information systems, Софтверско инженерство и информациски системи, Интернет, мрежи и безбедност, Software engineering and information systems,

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

1 / Зимски

7. Number of ECTS credits

6.0

8.

Instructor

проф. д-р Александра Поповска Митровиќ проф. д-р Билјана Тојтовска Рибарски доц. д-р Емил Станков ворн. проф. д-р Методија Јанчески проф. д-р Верица Бакева проф. д-р Весна Димитриевска Ристовска проф. д-р Весна Димитрова

9.

Prerequisites for enrollment

10.

Subject goals and competencies:

The subject is of support and is necessary to introduce the concepts of function, limes, derivative and integrals which are necessary in almost all subjects of higher years.

11.

Subject content:

1. Definition of a function. Properties of functions. Root functions. Functions defined by parts. Operations with functions (sum, difference, product, quotient and composition). 2. Stretching, compression, translation and reflection of a graph of a function. Even and odd functions. Lines (equation of a line through two points, direction coefficient). Families of functions (power functions). 3. Polynomials, rational functions, trigonometric functions (definition, period, graph, domain). Inverse functions (domain, rank, determination of an inverse function, conditions for the existence of an inverse function). 4. Exponential and logarithmic functions (definition, graph, domain, rank, exponential and logarithmic growth). Limes (intuitive definition, determination of one-sided and two-sided limes from the graph of a function). 5. Infinite limes and limes in infinity. Vertical and horizontal asymptote. Calculation of limes (basic limes, limes of sum, difference, product, quotient, limes of functions defined by parts). 6. Continuity of functions. Limes and continuity of trigonometric functions. 7. Definition of derivative. The tangent. Differentiability. Techniques of differentiation (derivative of a constant, power function, sum, difference, product, quotient). 8. Derivatives of trigonometric functions. Chain rule for the derivative of a composition of functions. Derivatives of exponential and logarithmic functions. Local linear approximation. 9. Lopital`s rule. Application of derivatives: monotonicity of functions. 10. Application of derivatives: convexity and concavity of functions, local extrema. Examining properties and sketching the graph of a function. 11. Integrating (area problem, method of rectangles and antiderivative method). Indefinite integral. Integrating with Substitution. 12. Definite integral. Fundamental theorem in calculus. Partial integration. Improper integrals (only with infinite limits)

12.

Learning methods:

Предавања со користење на презентации, интерактивни предавања, вежби (користење на опрема и софтверски

13.

Total available time fund

6.0 ECTS x 30 hours = 180 hours

14.

Time distribution

45 + 45 + 10 + 0 + 80 = 180 hours

15.

Forms of teaching activities

15.1.

Lectures - theoretical teaching

45 hours

15.2.

Exercises (laboratory, classroom), seminars, team work

45 hours

16.

Other forms of activities

16.1.

Project tasks

0 hours

16.2.

Independent tasks

10 hours

16.3.

Homework

80 hours

17.

Grading method

17.1.

Tests

points

17.2.

Seminar work / project (presentation: written and oral)

0 points

17.3.

Activities and learning

points

17.4.

Final exam

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

20.

Language of instruction

Македонски

21.

Quality assurance method

механизам на интерна евалуација и анкети

22.

Literature

22.1.

Mandatory literature

22.2.

Additional literature