{"id":8353,"date":"2026-05-21T14:48:56","date_gmt":"2026-05-21T14:48:56","guid":{"rendered":"https:\/\/akademperiodyka.org.ua\/uk\/?p=8353"},"modified":"2026-05-26T10:59:29","modified_gmt":"2026-05-26T10:59:29","slug":"%d0%be%d0%bf%d0%b5%d1%80%d0%b0%d1%86%d1%96%d0%b9%d0%bd%d0%b5-%d1%87%d0%b8%d1%81%d0%bb%d0%b5%d0%bd%d0%bd%d1%8f","status":"publish","type":"post","link":"https:\/\/akademperiodyka.org.ua\/en\/books\/educational_publications\/operational-calculus\/","title":{"rendered":"Operational calculus"},"content":{"rendered":"

Authors:<\/strong><\/p>\n

VALERII GRIGOROVICH SAMOILENKO,<\/strong> 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
\nV.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.
\nScopus Author ID: https:\/\/www.scopus.com\/authid\/detail.uri?authorId=16414982900<\/a>
\nORCID ID: https:\/\/orcid.org\/0000-0002-3267-2923<\/a>
\nResearch Gate: https:\/\/www.researchgate.net\/profile\/Valerii-Samoilenko?ev=hdr_xprf<\/a>
\nGoogle Scholar: https:\/\/scholar.google.com\/citations?user=83-wktAAAAAJ&hl=en<\/a><\/p>\n

Yuliia Ivanivna SAMOILENKO<\/strong>, Doctor of Physical and Mathematical Sciences, Senior Research Fellow, recipient of the President of Ukraine Award for Young Scientists.
\nScopus Author ID: https:\/\/www.scopus.com\/authid\/detail.uri?authorId=59150754300<\/a>
\nORCID ID: https:\/\/orcid.org\/0000-0002-9923-0986<\/a>
\nResearch Gate: https:\/\/www.researchgate.net\/profile\/Yuliia-Samoilenko-2<\/a>
\nGoogle Scholar: https:\/\/scholar.google.com\/citations?hl=en&user=mu__FqIAAAAJ&view_op=list_works&so<\/a>rtby=pubdate<\/p>\n

Reviewers:<\/strong>
\nV.M. BOYKO,<\/strong> 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>\n

P.F. SAMUSENKO,<\/strong> Professor at the Department of Mathematical Analysis and Probability Theory, National Technical University of Ukraine \u201cIgor Sikorsky Kyiv Polytechnic Institute,\u201d Doctor of Physical and Mathematical Sciences, Professor<\/p>\n

\n
Year:<\/strong> 2026<\/div>\n<\/div>\n
\n
Pages: <\/strong>157<\/div>\n<\/div>\n
\n
ISBN:<\/strong> 978-966-360-576-0<\/div>\n<\/div>\n
\n
\n
\n
Publication Language:<\/strong> Ukrainian<\/div>\n<\/div>\n
\n
Publisher:<\/strong>\u00a0PH \u201cAkademperiodyka\u201d<\/div>\n<\/div>\n
\n
Place Published:<\/strong>\u00a0Kyiv<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n

DOI: <\/strong>https:\/\/doi.org\/10.15407\/akademperiodyka.576.157<\/a><\/p>\n

\n<\/div>\n
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.<\/div>\n
\n

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.<\/p>\n

\n

References:<\/strong><\/p>\n<\/div>\n

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    \n
  1. Bernatska Yu.M. Elementy teorii funktsii. Kyiv: Vydavnychyi dim \u201cKyievo- Mohylianska akademiia\u201d, 2008. 144 s.<\/li>\n
  2. Boiarchuk A.K. Spravochnoe posobye po vysshei matematyke. T. 4: Funktsyy kompleksnoho peremennoho. Moskva: Edytoryal, 1999. 349 s.<\/li>\n
  3. Holberh A.A., Sheremeta M.M., Zabolotskyi M.V., Skaskiv O.B. Kompleksnyi analiz. Lviv: Afisha, 2008. 203 s.<\/li>\n
  4. Hryshchenko O.Yu., Liashko S.I. Teoriia funktsii kompleksnoi zminnoi. Kyiv: VPTs \u201cKyivskyi universytet\u201d, 2009. 495 s.<\/li>\n
  5. Hryshchenko O.Yu., Nahnybida M.I., Nastasiiev P.P. Teoriia funktsii kompleksnoi zminnoi: Rozviazuvannia zadach.\u00a0 Kyiv: Vyshcha shkola, 1994. 375 s.<\/li>\n
  6. Dorohovtsev A.Ya., Silvestrov D.S., Skorokhod A.V., Yadrenko M.Y. Teoriia ymovirnostei: Zbirnyk zadach. Kyiv: Vyshcha shkola, 1976. 384 s.<\/li>\n
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  8. Martynenko V.S. Operatsyonnoe yschyslenye. Kyev: Vyshcha shkola, 1990. 359 s.<\/li>\n
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  14. Samoilenko V.H., Borodin V.A., Verovkina H.V. Loveikin A.V., Romanenko I.B. Kompleksnyi analiz: Pryklady i zadachi. Kyiv: VPTs \u201cKyivskyi universytet\u201d, 2010. 224 s.<\/li>\n
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  16. Sveshnykov A.H., Tykhonov A.N. Teoryia funktsyi kompleksnoho peremennoho. Moskva: Nauka, 1974. 304 s.<\/li>\n
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  19. Shtokalo Y.Z. Operatsyonnoe yschyslenye (obobshchenyia y prylozhenyia). Kyev: Naukova dumka, 1972. 303 s.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

    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 […]<\/p>\n","protected":false},"author":3,"featured_media":8354,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4,17],"tags":[],"class_list":["post-8353","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-books","category-educational_publications"],"_links":{"self":[{"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/posts\/8353","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/comments?post=8353"}],"version-history":[{"count":18,"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/posts\/8353\/revisions"}],"predecessor-version":[{"id":8462,"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/posts\/8353\/revisions\/8462"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/media\/8354"}],"wp:attachment":[{"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/media?parent=8353"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/categories?post=8353"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/akademperiodyka.org.ua\/en\/wp-json\/wp\/v2\/tags?post=8353"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}