Course code:
001A2		 Course name:
Mathematics

Academic year:

2024/2025.

Attendance requirements:

There are no requirements.

ECTS:

8

Study level:

basic academic studies, integrated basic and graduate academic studies

Study programs:

Chemistry: 1. year, winter semester, compulsory course

Biochemistry: 1. year, winter semester, compulsory course

Environmental Chemistry: 1. year, winter semester, compulsory course

Chemical Education: 1. year, winter semester, compulsory course

Teachers:

Aleksandar B. Vučić, Ph.D.
assistant professor, Faculty of Mathematics, Studentski trg 16, Beograd

Vladimir N. Grujić, Ph.D.
associate professor, Faculty of Mathematics, Studentski trg 16, Beograd

Assistants:

Milica D. Jovanović
teaching assistant, Faculty of Mathematics, Studentski trg 16, Beograd

Kristina D. Kostić
teaching assistant, Faculty of Mathematics, Studentski trg 16, Beograd

Dušan G. Bogojević

Aleksandar M. Miladinović

Hours of instruction:

Weekly: four hours of lectures + four hours of exercises (4+4+0)

Goals:

The goal of the course is to help students gain the basic knowledge of mathematics which they need in order to understand the subject matter of other courses they will take during their studies.

Outcome:

Students will gain the basic knowledge of mathematics which will make it possible for them to understand the subject matter of other courses they will take during their studies.

Teaching methods:

Lectures, practical classes, revision.

Extracurricular activities:

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Coursebooks:
  • D. Adnađević, A. Vučić: Matematika 1 za studente hemije
  • D. Adnađević, A. Vučić: Matematika 2 za studente hemije
  • M. Miličić, P. Uščumlić: Zbirka zadataka iz više matematike

Additional material:

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  Course activities and grading method

Lectures:

0 points (4 hours a week)

Syllabus:

  1. The introductory part: Sets. Natural, whole, rational, real and complex numbers. Sequences. Convergence of sequences. Properties of limits. Number Ő. Series. Criteria for convergence of series with positive terms. The Leibniz series. Geometric and harmonic series.
  2. Functions: Domain. Basic properties of functions. Limits and continuity of functions. Derivative. Properties and the table of derivatives. Differential of a function. Derivatives and higher-order differentials. Basic theorems of differential calculus. Analyzing and sketching a graph of a function. Power series. Taylor series.
  3. Integrals: Definite integral. Indefinite integral. The Newton-Leibniz formula. Partial integration. Shift in integrals. Table of integrals. Integration of rational trigonometric functions. Application of integrals in geometry. Curvilinear integrals. Improper integral.
  4. Differential equations: First-order differential equation. Equations with separated variables. Homogenous and linear differential equation, the Bernoulli differential equation and the Riccati differential equation. Higher-order homogenous and non-homogenous linear differential equations with constant coefficients. Application.
  5. Probability: Chance events. Definition and properties of probability. The formula of total probability and the Bayes’ rule. Distribution and density function. Mathematical expectation and dispersion. Binominal, Poisson, uniform and normal distribution.

Exercises:

10 points (4 hours a week)

Syllabus:

The practical classes accompany the lectures and the syllabus of the practical classes is the same as the syllabus of the lectures.

Colloquia:

30 points

Remarks:

Working out problems from the lectures and workshops. There are two colloquia. First one is after first half of the lectures and includes the first part of integrals. The second is after the classes are done and starts with application of integrals till the end.

Written exam:

60 points