State university

Faculty, Skopje, macedonia

State university

Faculty, Skopje, macedonia

The aim of the course is for the student to acquire basic knowledge of some mathematical concepts, including differential and integral calculus, without which a large number of modern architectural buildings could not be realized. The course aims to introduce the student to the aesthetic values ​​of mathematics as well as the philosophical-mathematical meaning of the idea of ​​symmetry. The student will be introduced to the development of mathematical thought and its contribution and significance for modern society.

Elements of number theory. Real numbers. Sequences of real numbers. Functions of one real variable. Limit of a function at a point. Continuity of a function. Elementary functions. Concept of derivative and differential, basic properties. Basic theorems of differential calculus. L'Hôpital's rule. Application of derivatives for constructing a graph of a function. Concept of primitive function and indefinite integral. Integration with change of variables. Partial integration. Definite integral, basic properties. Application of definite integral for calculating areas of plane figures, arc length of a curve, volume of a solid of revolution. Proportions. Golden ratio. Fibonacci numbers. Concept of symmetry. Relationship between group theory and geometry. Mathematics as an instrument for understanding and interpreting nature and for creating new forms and concepts.

Lecture: 2 hours

Exercise: 2 hours

Consultation: 1 hour

The course is delivered in lectures, tutorials, and information. Students are encouraged to ask questions and participate in discussions.

Examinations and grades

The system of assessment is based on three elements:

1. In the presence of the lecture: 10%

2. Homework: 40%

3. Examination: 50%

Students must have a minimum of 70% attendance in lectures and tutorials for you to get it right on the test.

Examination: written and oral

Homework: 40%

Colloquium: 30%

Examination: 30%

Colloquium (1)

Colloquium (2)

Exam (final)

Lectures: 30 hours

Tutorials: 30 hours

Project: 30 hours

Working in groups

Individual work

In the presence of the lecture: 10%

Homework: 40%

Examination: 50%

Grading (points/grade)

From 61 to 70 points (7)

From 71 to 80 points (8)

From 81 to 90 points (9)

From 91 to 100 units (10)

Up to 60 points (6) – lack of

From 61 to 70 points (7) – enough

From 71 to 80 points (8) – a good

From 81 to 90 points (9) – very good

From 91 to 100 points (10) – excellent

1. Mary Orovcanec, Mathematics-Skopje, University “Ss. Cyril and Methodius university in 2001

2. This Colleague, The Orb Georgievska, Game 1-Skopje, University “Ss.The first and the Last

3. This Colleague, The Orb Georgievska Game 2-Skopje, University “Ss. Cyril and Methodius university in the year 2002;

4. Nikita Шекуткоски, Mathematical analysis, 1, Просветно act of 1996

5. Герман Вейл, Симетрия, Издательство “Science”, The 1968 Moscow.

6. C. C. Дужин B. D. Чеботаревски, The орнаментов to дифференциальных уравнени, Издательство Вышэјшая school, 1988, Minsk

7. Morris Клайн, Game-поиск истины, Издательство “Mir” 1988 in Moscow

Students must attend a minimum of 70% of the course for, to be able to be tested.

All assignments will be given, and to be a part of your final grade.

Prof. in the republic of Macedonia Ѓастовски