Faculty of Mechanical Engineering

Dušan Lj. Đukić

Dušan Lj. Đukić, Ph.D., associate professor
Department of Mathematics
Office: 440
Email: ddjukic@mas.bg.ac.rs
Phone: extension 340; direct 3302-340

Student consultation hours

By email, unless arranged otherwise

Courses

Calculus
Probability and statistics
Advanced course in mathematics
Discrete mathematics
Mathematics 1
Mathematics 2
Mathematics 3
Numerical methods

Research area

numerical analysis

Education, qualifications

BSc in Mathematics: University of Belgrade, 2003 PhD in Mathematics (numerical analysis): University of Kragujevac, 2018

Publications, recognitions, awards

Co-authored 4 textbooks at Faculty of Mechanical Engineering, Univ. of Belgrade Also co-authored several books focused on mathematical olympiads, including "The IMO Compendium", Springer 2006,2011

Membership in scientific and professional organizations

Serbian mathematical society, mathematical competition committee in Serbia (2003-2022)

Bibliography

Papers in journals indexed in the SCI and SCIe lists

Đukić Dušan, Mutavdžić Đukić Rada, Pejčev Aleksandar, Reichel Lothar, Spalević Miodrag, Spalević Stefan (2025). Internality of Two-Measure-Based Generalized Gauss Quadrature Rules for Modified Chebyshev Measures II, Mathematics, 13(3).
MDPI, ISSN: 2227-7390, 10.3390/math13030513, M21a+.

Đukić Dušan, Mutavdžić Đukić Rada, Reichel Lothar, Spalević Miodrag (2025). Generalized Averaged Gaussian Quadrature Rules: A Survey, Mathematics, 13(19).
MDPI, ISSN: 2227-7390, 10.3390/math13193145, M21a+.

Đukić Dušan, Mutavdžić Đukić Rada, Reichel Lothar, Spalević Miodrag (2023). Internality of averaged Gauss quadrature rules for certain modification of Jacobi measures, Applied and Computational Mathematics, 22(4), 426-442.
Ministry of Communications and Information Technology (Azerbaijan), Azerbaijan National Academy of Sciences and Institute of Applied Mathematics of Baku State University, ISSN: 1683-3511, 10.30546/1683-6154.22.4.2023.426, M21a+.

Đukić Dušan, Kadelburg Zoran, Radenović Stojan (2011). Fixed Points of Geraghty-Type Mappings in Various Generalized Metric Spaces, Abstract and Applied Analysis.
Hindawi Ltd, London, ISSN: 1085-3375, 10.1155/2011/561245, M21a+.

Đukić Dušan, Mutavdžić Đukić Rada, Reichel Lothar, Spalević Miodrag (2024). Decompositions of optimal averaged Gauss quadrature rules, Journal of Computational and Applied Mathematics, 438(Art. 115586).
Elsevier, ISSN: 0377-0427, 10.1016/j.cam.2023.115586, M21a.

Alqahtani H, Borges CF, Đukić Dušan, Mutavdžić Đukić Rada, Reichel Lothar, Spalević Miodrag (2024). Computation of pairs of related Gauss-type quadrature rules, Applied Numerical Mathematics.
Elsevier, ISSN: 0168-9274, 10.1016/j.apnum.2024.03.003, M21a.

Đukić Dušan, Fermo Luisa, Mutavdžić Đukić Rada (2023). Averaged cubature schemes on the real positive semiaxis, Numerical Algorithms, 92, 545–569.
Springer, ISSN: 1572-9265e, 10.1007/s11075-022-01408-6, M21a.

Đukić Dušan, Mutavdžić Đukić Rada, Reichel Lothar, Spalević Miodrag (2023). Internality of generalized averaged Gauss quadrature rules and truncated variants for modified Chebyshev measures of the third and fourth kinds, Numerical Algorithms, 92, 523-544.
Springer, ISSN: 1017-1398, 10.1007/s11075-022-01385-w, M21a.

Đukić Dušan, Mutavdžić Đukić Rada, Reichel Lothar, Spalević Miodrag (2023). Weighted averaged Gaussian quadrature rules for modified Chebyshev measures, Applied Numerical Mathematics.
Elsevier, ISSN: 0168-9274, 10.1016/j.apnum.2023.05.014, M21a.

Đukić Dušan, Mutavdžić Đukić Rada, Reichel Lothar, Spalević Miodrag (2021). Internality of generalized averaged Gauss quadrature rules and truncated variants for modified Chebyshev measures of the first kind, Journal of Computational and Applied Mathematics, 398.
Elsevier, Amsterdam, ISSN: 0377-0427, 10.1016/j.cam.2021.113696, M21a.

Đukić Dušan, Pejčev Aleksandar, Spalević Miodrag (2018). The error bounds of Gauss-Kronrod quadrature formulae for weight functions of Bernstein-SzegoIi type, Numerical Algorithms, 77(4), 1003-1028.
Springer, Dordrecht, ISSN: 1017-1398, 10.1007/s11075-017-0351-8, M21a.

Đukić Dušan, Mutavdžić Đukić Rada, Pejčev Aleksandar, Spalević Miodrag (2020). Error estimates of gaussian-type quadrature formulae for analytic functions on ellipses-a survey of recent results, Electronic Transactions on Numerical Analysis, 53, 352-382.
Kent State University, Kent, ISSN: 1068-9613, 10.1553/etna_vol53s352, M21.

Đukić Dušan, Reichel Lothar, Spalević Miodrag (2019). Internality of generalized averaged Gaussian quadrature rules and truncated variants for measures induced by Chebyshev polynomials, Applied Numerical Mathematics, 142, 190-205.
Elsevier Science Bv, Amsterdam, ISSN: 0168-9274, 10.1016/j.apnum.2019.03.008, M21.

Đukić Dušan, Reichel Lothar, Spalević Miodrag, Tomanović Jelena (2019). Internality of generalized averaged Gaussian quadrature rules and truncated variants for modified Chebyshev measures of the second kind, Journal of Computational and Applied Mathematics, 345, 70-85.
Elsevier Science Bv, Amsterdam, ISSN: 0377-0427, 10.1016/j.cam.2018.06.017, M21.

Đukić Dušan, Reichel Lothar, Spalević Miodrag, Tomanović Jelena (2016). Internality of generalized averaged gauss rules and their truncations for bernstein-szego weights, Electronic Transactions on Numerical Analysis, 45, 405-419.
Kent State University, ISSN: 1068-9613, M21.

Đukić Dušan, Reichel Lothar, Spalević Miodrag (2016). Truncated generalized averaged Gauss quadrature rules, Journal of Computational and Applied Mathematics, 308, 408-418.
Elsevier Science Bv, Amsterdam, ISSN: 0377-0427, 10.1016/j.cam.2016.06.016, M21.

Đukić Dušan, Mutavdžić Đukić Rada, Pejčev Aleksandar, Reichel Lothar, Spalević Miodrag, Spalević Stefan (2024). Internality of two-measure-based generalized Gauss quadrature rules for modified Chebyshev measures, Electronic Transactions on Numerical Analysis (ETNA), 61, 157-172.
ISSN: 1068-9613, 10.1553/etna_vol61s157, M22.

Đukić Dušan, Mutavdžić Đukić Rada, Reichel Lothar, Spalević Miodrag (2023). Optimal Averaged Pade-Type Approximants, ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS, 59, 145-156.
the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM), ISSN: 1068-9613, 10.1553/etna_vol59s145, M22.

Papers in journals not indexed in the SCI and SCIe lists

Đukić Dušan, Paunović Ljiljana, Radenović Stojan (2011). Convergence of iterates with errors of uniformly quasi-Lipschitzian mappings in cone metric spaces, Kragujevac Journal of Mathematics, 35(3), 399-410.
Univerzitet u Kragujevcu - Prirodno-matematički fakultet, Kragujevac, ISSN: 1450-9628, M51.

Conference papers

Đukić Dušan, Mutavdžić Đukić Rada, Reichel Lothar, Spalević Miodrag (2023). On Internality of Generalized Averaged Gaussian Quadrature Rules and Their Truncations, International Mathematical Conference Analysis, Approximations and Applications (AAA2023), Vrnjačka Banja.
Prirodno-matematički fakultet Kragujevac, M34.

Đukić Dušan, Mutavdžić Đukić Rada, Reichel Lothar, Spalević Miodrag (2023). Internality of Averaged Gaussian Quadrature Rules, 6TH INTERNATIONAL CONFERENCE ON MATHEMATICAL AND RELATED SCIENCES BOOK OF ABSTRACTS.
ISBN: 978-605-70978-8-0, M34.

Đukić Dušan, Mutavdžić Đukić Rada, Reichel Lothar, Spalević Miodrag (2022). Internality of averaged Gaussian quadrature rules for modified Jacobi measures, FAATNA 2020>22 conference, Book of abstracts.
M34.

Đukić Dušan, Mutavdžić Đukić Rada, Reichel Lothar, Spalević Miodrag (2022). Weighted averaged Gaussian quadrature rules for modified Chebyshev measure, FAATNA 2020>22, Book of abstarcts.
M34.

Đukić Dušan, Mutavdžić Đukić Rada, Reichel Lothar, Spalević Miodrag (2022). Optimal averaged Pade approximants, NMLSP conference, Book of abstracts.
Faculty of Mechanical Engineering, University of Belgrade, M34.

Đukić Dušan, Mutavdžić Đukić Rada, Reichel Lothar, Spalević Miodrag (2022). Weighted averaged Gaussian quadrature rules for modified Chebyshev measure, MNA conference, Book of abstracts.
Faculty of Mechanical Engineering, University of Belgrade, M34.

Đukić Dušan, Reichel Lothar, Spalević Miodrag (2018). Internality of truncated averaged Gaussian quadratures, Proceedings Book of MICOPAM2018 conference.
Department of Mathematics, Faculty of Science, Akdeniz University,Turkey, M34.

Đukić Dušan, Reichel Lothar, Spalević Miodrag (2017). Internality of truncated generalized averaged Gaussian quadrature, ACTA 2017, Book of abstarcts.
Serbian Academy of Sciences and Arts, M34.

Đukić Dušan, Reichel Lothar, Spalević Miodrag (2016). GENERALIZED AVERAGED GAUSSIAN QUADRATURE FORMULAS WITH MODIFIED MATRICES, 6th MATHEMATICAL CONFERENCE OF THE REPUBLIC OF SRPSKA, BOOK OF ABSTRACTS.
UNIVERSITY OF EAST SARAJEVO, MATHEMATICAL SOCIETY OF THE REPUBLIC OF SRPSKA, ISBN: 978-99938-47-79-3, M34.

Đukić Dušan, Pejčev Aleksandar, Spalević Miodrag (2016). The error bounds of Gauss-Kronrod quadrature formulae with Bernstein-Szego weight functions, 6th MATHEMATICAL CONFERENCE OF THE REPUBLIC OF SRPSKA, BOOK OF ABSTRACTS.
UNIVERSITY OF EAST SARAJEVO, MATHEMATICAL SOCIETY OF THE REPUBLIC OF SRPSKA, ISBN: 978-99938-47-79-3, M34.

Books

Aranđelović Ivan, Pejčev Aleksandar, Đukić Dušan, Jandrlić Davorka, Tomanović Jelena, Mutavdžić Đukić Rada, Vučić Miloš (2020). Matematika 1: udžbenik i zbirka zadataka, Univerzitet u Beogradu - Mašinski fakultet.
Univerzitet u Beogradu - Mašinski fakultet.

Aranđelović Ivan, Jandrlić Davorka, Pejčev Aleksandar, Đukić Dušan, Tomanović Jelena, Mutavdžić Đukić Rada (2019). Matematika 2, Univerzitet u Beogradu - Mašinski fakultet.
Univerzitet u Beogradu - Mašinski fakultet.

Spalević Miodrag, Aranđelović Ivan, Pejčev Aleksandar, Doder Dragan, Đukić Dušan, Tomanović Jelena (2017). Diferencijalne jednačine, Univerzitet u Beogradu - Mašinski fakultet.
Univerzitet u Beogradu - Mašinski fakultet.

Spalević Miodrag, Cvetković Aleksandar, Aranđelović Ivan, Pejčev Aleksandar, Đukić Dušan, Tomanović Jelena (2015). Višestruki, krivolinijski i površinski integrali i primene, terorija redova, Univerzitet u Beogradu - Mašinski fakultet.
Univerzitet u Beogradu - Mašinski fakultet.