Mathematics II

COURSE CURRICULUM 

1.

Course title

MATHEMATICS II

2.

Code

HM-20M

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/II

7.

ECTS points

8

8.

Lecturer

Petar Sokoloski, Assistant professor

9.

Prerequisites

Signature of Mathematics I

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:
Definite integral: Definition of definite integral and its properties; Relationship between the indefinite and definite integral; Change of variable and partial integration in the definite integral; Newton-Leibniz formula and area of curvilinear trapezoids; Mean value theorem in the definite integral; Definite integral with variable upper bound and with infinite upper bound; Approximate computation of definite integral; Application of definite integral. Series: Definition and some basic concepts of series; Some theorems for convergent series; Comparison theorems and some criteria for convergence of series with positive terms; Alternating series; Functional power series; Taylor's and Maclaurin's series for functions. Elements of linear and vector algebra: Determinants of second and third order and their application for solving systems of linear equations; Chemical mixtures with two and three components; Concept of matrices and operations with matrices; Inverse matrix; Hamilton-Cayley theorem; Matrix equations and application of matrices for solving systems of linear equations; Gaussian method for solving systems of linear equations; Concept of vector and operations with vectors in space; Coordinates of vectors and points in space; Division of a segment in a given ratio; Scalar, vector, and mixed product of vectors; Equations of planes; Equations of lines in space. Functions of several variables: Concept of real function of several real independent variables; Surfaces of second order; Concept of partial derivatives; Total differential; Equations of tangent plane and normal to surface; Partial derivatives and differentials of higher order; Local extrema; Partial derivatives of composite functions. Curvilinear integrals of first and second type. Double and triple integrals.

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 (Chapter V)

UKIM

2011

2.

Borko Ilievski 

Математика 2 (internal script)

/

/

22.2.

Additional

No.

Author

Title

Publisher

Year

1.

Boro M. Piperevski

Математичка анализа II

ETF

2004

2.

Gj..Chupona, B. Trpenovski and N. Celakoski

Предавања по виша математика

ETF

1971

3.

Dr. I. Shapkarev

Задачи за вежбање по математика II

UKIM

1979