Operational calculus

Authors:

VALERII GRIGOROVICH SAMOILENKO, Doctor of Physical and Mathematical Sciences, Professor, Chief Researcher at the Department of Mathematical Physics, Institute of Mathematics of the NAS of Ukraine, recipient of the State Prize of Ukraine in Science and Technology, and the
V.M. Khrushchev, M.V. Ostrogradsky, and Y.O. Mitropolsky Prizes of the National Academy of Sciences of Ukraine, Chair of the Expert Council on Physical and Mathematical Sciences of the Ministry of Education and Science of Ukraine.
Scopus Author ID: https://www.scopus.com/authid/detail.uri?authorId=16414982900
ORCID ID: https://orcid.org/0000-0002-3267-2923
Research Gate: https://www.researchgate.net/profile/Valerii-Samoilenko?ev=hdr_xprf
Google Scholar: https://scholar.google.com/citations?user=83-wktAAAAAJ&hl=en

Yuliia Ivanivna SAMOILENKO, Doctor of Physical and Mathematical Sciences, Senior Research Fellow, recipient of the President of Ukraine Award for Young Scientists.
Scopus Author ID: https://www.scopus.com/authid/detail.uri?authorId=59150754300
ORCID ID: https://orcid.org/0000-0002-9923-0986
Research Gate: https://www.researchgate.net/profile/Yuliia-Samoilenko-2
Google Scholar: https://scholar.google.com/citations?hl=en&user=mu__FqIAAAAJ&view_op=list_works&sortby=pubdate

Reviewers:
V.M. BOYKO, Head of the Department of Mathematical Physics at the Institute of Mathematics of the NAS of Ukraine, Doctor of Physical and Mathematical Sciences, Senior Research Fellow

P.F. SAMUSENKO, Professor at the Department of Mathematical Analysis and Probability Theory, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute,” Doctor of Physical and Mathematical Sciences, Professor

Year: 2026

Pages: 157

ISBN: 978-966-360-576-0

Publication Language: Ukrainian

Publisher: PH “Akademperiodyka”

Place Published: Kyiv

DOI: https://doi.org/10.15407/akademperiodyka.576.157

This textbook systematically presents the theoretical foundations of operational calculus and its applications. It covers the main properties of the Laplace integral transform and elements of residue theory, calculates the Laplace transforms of a number of special functions, and describes methods for finding the original function from its transform. The application of the Laplace transform to solving linear differential equations, integral equations, fundamental problems in mathematical physics, and the summation of numerical series is reviewed. The application of operational calculus to the analysis of electrical engineering problems is presented. The presentation of theoretical principles and the application of operational calculus are illustrated with examples. Each chapter includes questions and exercises for self-assessment and independent study.

The book is intended for students of mathematics, physics, and engineering programs at institutions of higher education, as well as for independent study of the subject.

References:

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