Study program:
Environmental Engineering (IX semester -MsC)
Geology of oil and gas (IX semester -MsC)
Petroleum Engineering (IX semester -MsC) |
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Name of subject: Selected Topics in Mathematics |
Instructors:
Prof. Dejan Ćebić |
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Status: Compulsory |
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ECTS: 6 |
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Prerequisites: Completed undergraduate studies of mining engineering |
Course Objectives:
Getting acquainted with the theory and practice of basic methods in selected fields of Mathematics of interest for future masters in mining engineering |
Learning Outcomes:
Enabling students to use methods from various areas of mathematics in engineering practice at the master level |
Content:
Theory teaching
Numerical Analysis. Methods for approximate solving of ordinary equations. Approximate solution of ordinary differential equations and partial differential equations. Functions of more variables and partial derivatives. Polynomials and interpolation. Numerical integration. Splines. Probability. Random events and basic concepts of probability. Discrete random variables, individual distributions. Moments of discrete random variables and variance. Chebyshev inequality and Central boundary theorem of probability. Continuous random variables, individual distributions, moments. Distribution of two-dimensional random variables. Discrete and continuous Markov chains. Statistics. Basic statistical values. Some distributions of statistics. Intervals of trust. Testing statistical hypotheses. Variance analysis. Correlation and regression. Harmonic analysis. Fourier series and Fourier transformations. Characteristic functions and moment generating functions Integral transformations. Laplace transformation and application. Solving differential equations using Laplace transformation and using sums. Numerical analysis. Interpolation. Methods of numerical differentiation and numerical integration. Calculation and approximation of functions. Approximate solution of ordinary equations, ordinary differential equations and partial differential equations. Practical teaching
Solving problems related to the material in the lectures. |
Suggested Reading List:
- Milan Merkle, Verovatnoća i statistika za inženjere i studente tehnike, Akademska misao, Beograd, 2006.
- Biljana Popović i Miroslav Ristić, Statistika za geografe, Niš, 2006.
- Vesna Jevremović, Verovatnoća i statistika (Matematika III), Građevinski fakultet i KRUG, Beograd, 1999.
- Slobodan Vujić i Aleksandar Ivić, Matematičke metode u rudarstvu i geologiji, RGF, Univerzitet u Beogradu, 1991.
- Sheldon M. Ross, Introduction to Probability and Statistics for Engineers and Scientists, 3rd edition, Elsevier Academic Press, 2004.
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Conduct of the Course:
The standard method using the blackboard; for some parts of the course there are lecture notes by A. Ivić that the students are free to use. |
Fund hours:
| Lectures |
Exercises |
Other forms of teaching |
Study research |
| 2 |
2 |
0 |
0 |
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Assessment:
| Final Exam |
ECTS |
| Oral Exam | 25 | | Written exam | 25 |
| Classwork Assessment |
ECTS |
| Class Participationа | 30 | | Seminars | 20 |
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Additional Assessment Criteria: - |
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