Mathematics I

COURSE CURRICULUM 

1.

Course title

MATHEMATICS I

2.

Code

HM-10М

3.

Study curriculum

All chemistry study programs

4.

Organizer of the curriculum (institute, department)

Faculty of Natural Sciences and Mathematics,
Institute of Chemistry

5.

Degree (BSc, MSc, PhD)

BSc

6.

Academic year/semester

I/I

7.

ECTS points

8

8.

Lecturer

Petar Sokoloski, Assistant professor

9.

Prerequisites

/

10.

Course objectives (competences):
The students are expected to acquire the fundamentals of modern mathematical disciplines necessary for successfully mastering the content of other teaching-scientific disciplines in chemistry. Additionally, one of the objectives of the course is to develop the student's ability to independently and logically connect concepts.

11.

Course content:
Sets: Concept of sets; Countable sets; Extended set of real numbers; Intervals and neighborhoods; Mathematical induction; Binomial formula; Ratio, proportion, and their application in chemical problems. Series of real sequences: Concept of sequences; Convergent and divergent sequences; Monotonic and bounded sequences; Some theorems for convergent sequences; Arithmetic sequence; Geometric sequence; Natural sequences and the number e; Decimal measurement of segments and introduction of real number; Measurement of masses. Real functions: Concept of real function of one real independent variable; Monotonic, bounded, even and odd, inverse, periodic (trigonometric), cyclometrical, and composite functions; Limit values of functions; Asymptotes of functions; Some important limit values; Continuity of functions. Differential calculus: Concept of derivative; Derivative of sum, difference, product, and quotient of two functions; Derivative of inverse functions; Table of basic derivatives; Derivative of composite functions; Derivative of implicit and parametric functions; Geometric, physical, and chemical meaning of derivative; Some basic theorems of differential calculus (Rolle's, Lagrange's, and Cauchy's theorems); First differential of function; Higher-order derivatives and differentials; Monotonicity of functions using derivatives; Local extrema and Fermat's theorem; Taylor's and Maclaurin's formula; Indeterminate expressions and L'Hôpital's rules; Examination of the behavior of a function and construction of a graph. Indefinite integral: Concept of indefinite integral and its properties; Table of basic integrals; Change of variable and partial integration in indefinite integral; Some recursive formulas; Some types of indefinite integrals containing quadratic trinomial; Indefinite integrals of rational, irrational, and trigonometric functions; Application of indefinite integral in some chemical reactions (mono, bi, and polymolecular reactions).

12.

Teaching methods: lectures, exercises and assignments for independent work

13.

Total available time

240

14.

Time distribution

4+3+0 (lectures 60 hours, numerical exercises 45 hours)

15.

Teaching methods distribution

15.1.

Teaching - lectures

60

15.2.

Practicals (laboratory, problem solving), seminars, team work

45

16.

Other activities

16.1.

Projects

0

16.2.

Independent work

45

16.3.

Homework

90

17.

Grading methods

17.1.

Tests

90

17.2.

Seminars/projects (written/oral presentation)

0

17.3.

Activity

10

18.

Grading scale (points/mark)

< 50 points

5 (five) (F)

51 to 60 points

6 (six) (E)

61 to 70 points

7 (seven) (D)

71 to 80 points

8 (eight) (C)

81 to 90 points

9 (nine) (B)

91 to 100 points

10 (ten) (A)

19.

Criteria for taking the final exam

Realized activity 17.3.

20.

Course language

Macedonian

21.

Teaching quality control

Survey

22.

Literature

22.1.

Compulsory

No.

Author

Title

Publisher

Year

1.

Borko Ilievski                         

Математика 1

UKIM

2011

22.2.

Additional

No.

Author

Title

Publisher

Year

1.

Boro Piperevski

Математичка анализа I

ETF

2001

2.

Novak Ivanovski

Математичка анализа I

ETF

1991

3.

D. Bitrakov and

Dr. I. Shapkarev

Задачи за вежбање по математика I

UKIM

1972