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Differential Equations and Numerical Analysis

Study program:
Geotechnics (I semester -PhD)
Mining Engineering (I semester -PhD)
Name of subject: Differential Equations and Numerical Analysis
Instructors:
Prof. Dragan Stankov, Prof. Dejan Ćebić
Status: Optional
ECTS: 10
Prerequisites: Completed basic and master studies of mining
Course Objectives:
Getting acquainted with the theory and practice of basic methods in different areas of Differential equations and Numerical analysis for the needs of future doctors of mining.
Learning Outcomes:
The enabling of students to use in engineering practice the methods of different areas of Mathematics at the level of a doctor of sciences.
Content:

Theory teaching
Differential equations. The forming and types of ordinary differential equations. The existence of solutions. Some types of first order differential equations. The general linear euqation of order n. Sustems of ordinary differential equations. The solutions of equations by series and the Laplace transform. Partial differential equations, types and their forming. Some properties of partial differential equations of the first and second order. Numerical analysis. The methods of approximate solutions of equations. Approximate solutions of ordinary differential equations and partial differential equations. Polynomials and interpolation. Approximate solutions of systems of differential equations. Numerical differentiation and ingegration. Splines.

Practical teaching
The working out of problems or seminars which correspond to the material that is being taught in class.

Suggested Reading List:
  1. I.S. Sokolnikoff and R.M. Redheffer, Mathematics of physics and modern engineering, McGraw Hill, New York etc, 2nd. ed., 1966.
  2. Miloš Miličić, Nada Miličić, Dragan Stankov, Elementi Numeričke analize, Rudarsko-geološki fakultet u Beogradu, 2003
  3. D. Kuzmanović, A. Sedmak, I. Obradović, D. Nikolić, Matematička Fizika, RGF, Univerzitet u Beogradu, 2003
  4. Slobodan Vujić i Aleksandar Ivić, Matematičke metode u rudarstvu i geologiji, RGF, Univerzitet u Beogradu, 1991.
  5. G.V. Milovanović, Numerička Analiza I deo (1985), II deo (1985), III deo(1988), Naučna Knjiga, Beograd,
Conduct of the Course:
A classic method over the table, for some parts of the course there are script A. Ivić that students can take.
Fund hours:
Lectures Exercises Other forms of teaching Study research
4 0 0 0
Assessment:
Final Exam ECTS
Oral Exam25
Written exam25

Classwork Assessment ECTS
Class Participationа30
Seminars20
Additional Assessment Criteria: -


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