Kompleksna analiza: Učbenik z izpitnimi nalogami

Authors

Marko Jakovac
University of Maribor, Faculty of Natural Sciences and Mathematics
https://orcid.org/0000-0002-4136-7365
Niko Tratnik
University of Maribor, Faculty of Natural Sciences and Mathematics
https://orcid.org/0000-0002-5564-049X
DOI: https://doi.org/10.18690/um.fnm.2.2026

Keywords:

complex analysis, functions of a complex variable, complex differentiation, complex integration, Cauchy’s theorem, Taylor series, Laurent series, residue theorem

Synopsis

Complex Analysis: a Textbook with Exam Problems. The textbook is intended for undergraduate mathematics majors at the Faculty of Natural Sciences and Mathematics, University of Maribor. It covers fundamental topics in complex analysis, including functions of a complex variable, complex differentiation and integration, Cauchy’s theorem, Taylor and Laurent series, and the residue theorem. Special emphasis is placed on the connection between theory and problem solving. Almost all chapters include illustrative examples, while selected chapters conclude with exam problems drawn from written exams and midterms from 2016 to 2023. The textbook also provides answers to exam problems, supporting independent study and effective exam preparation. The material is designed as a comprehensive study resource for understanding the core concepts of complex analysis and reinforcing knowledge through solving typical exam-type problems.

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Author Biographies

Marko Jakovac, University of Maribor, Faculty of Natural Sciences and Mathematics

Assoc. Prof. Dr. Marko Jakovac is employed at the Faculty of Natural Sciences and Mathematics, University of Maribor, where he previously served as Head of the Department of Mathematics and Computer Science and currently holds the position of Vice-Dean for Academic Affairs at the same faculty. His research focuses on discrete mathematics, particularly graph theory, including graph invariants, graph products, and structural properties of graphs. He participates in several national and international research projects and has led multiple bilateral projects. He teaches courses in mathematical analysis, financial mathematics, and actuarial mathematics.

Maribor, Slovenia. E-mail: marko.jakovac@um.si

Niko Tratnik, University of Maribor, Faculty of Natural Sciences and Mathematics

Assoc. Prof. Dr. Niko Tratnik is employed at the Faculty of Natural Sciences and Mathematics, University of Maribor, where he has been Head of the Department of Mathematics and Computer Science since 2024, and is also affiliated with the Institute of Mathematics, Physics and Mechanics. His research focuses on discrete mathematics, particularly chemical graph theory, and more recently on the analysis of complex networks. He leads the basic ARIS project »Contemporary topological measures for molecular graphs and networks« in collaboration with Switzerland. Dr. Tratnik teaches courses in mathematical analysis and statistics, participates in organizing competitions for students, and serves as coordinator of the Educational Mathematics study field in the Subject Teacher study programme.

Maribor, Slovenia. E-mail: niko.tratnik@um.si

References

[1] L. Ahlfors, Complex Analysis, 3rd edition, McGraw-Hill, New York, 1979.

[2] R. B. Ash, W. P. Novinger, Complex Variables, 2nd edition, Dover Publications, New York, 2007.

[3] D. Benkovič, Analiza II, Zbrano gradivo: naloge na vajah, kolokviji in pisni izpiti, Univerza v Mariboru, Fakulteta za naravoslovje in matematiko, Maribor, 2010.

[4] J. B. Conway, Functions of One Complex Variable I, 2nd edition, Springer-Verlag, New York, 1995.

[5] M. Dobovišek, Rešene naloge iz analize II, DMFA, Ljubljana, 2014.

[6] N. Elezovi´c, D. Petrizio, Funkcije kompleksne varijable: zbirka zadataka, Element, Zagreb, 1994.

[7] B. Hvala, Zbirka izpitnih nalog iz analize, DMFA, Ljubljana, 2007.

[8] S. G. Krantz, Handbook of Complex Variables, Birkhauser, Boston, 1999.

[9] P. Mizori-Oblak, Matematika za študente tehnike in naravoslovja. Del 3, Fakulteta za strojništvo, Ljubljana, 1991.

[10] M. Razpet, Rešene naloge iz kompleksne analize: študijsko gradivo (druga, popra-vljena in razširjena izdaja), Univerza v Ljubljani, Pedagoška fakulteta, Ljubljana, 2008. Dostopno 21. 7. 2025 na povezavi:

https://repozitorij.uni-lj.si/Dokument.php?id=208850&lang=slv

[11] W. Rudin, Real and Complex Analysis, 3rd edition, McGraw-Hill Education, New York, 1986.

[12] M. Slapar, Osnove kompleksne analize, Pedagoška fakulteta Univerze v Ljubljani, Ljubljana, 2012. Dostopno 21. 7. 2025 na povezavi:

https://repozitorij.uni-lj.si/Dokument.php?id=208260&lang=slv

[13] M. R. Spiegel, S. Lipschutz, J. J. Schiller, D. Spellman, Schaum’s outlines complex variables: with an introduction to conformal mapping and its applications, 2nd edi-tion, McGraw-Hill, New York, 2009.

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Published

April 3, 2026

Categories

Copyright (c) 2026 University of Maribor, University of Maribor Press

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Details about this monograph

THEMA Subject Codes (93)

P, PB, PBK, PBKD

ISBN-13 (15)

978-961-299-139-5

COBISS.SI ID (00)

274072579

CIP date (35)

2026-04-03

How to Cite

Jakovac, M., & Tratnik, N. (2026). Kompleksna analiza: Učbenik z izpitnimi nalogami. University of Maribor Press. https://doi.org/10.18690/um.fnm.2.2026