Quantum Variational Calculus by Agnieszka B. MalinowskaQuantum Variational Calculus by Agnieszka B. Malinowska

Quantum Variational Calculus

byAgnieszka B. Malinowska, Delfim F.M. Torres

Paperback | December 11, 2013

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This Brief puts together two subjects, quantum and variational calculi by considering variational problems involving Hahn quantum operators. The main advantage of its results is that they are able to deal with nondifferentiable (even discontinuous) functions, which are important in applications.

Possible applications in economics are discussed. Economists model time as continuous or discrete. Although individual economic decisions are generally made at discrete time intervals, they may well be less than perfectly synchronized in ways discrete models postulate. On the other hand, the usual assumption that economic activity takes place continuously, is nothing else than a convenient abstraction that in many applications is far from reality. The Hahn quantum calculus helps to bridge the gap between the two families of models: continuous and discrete.

Quantum Variational Calculusis self-contained and unified in presentation. It provides an opportunity for an introduction to the quantum calculus of variations for experienced researchers but may be used as an advanced textbook by graduate students and even ambitious undergraduates as well. The explanations in the book are detailed to capture the interest of the curious reader, and complete to provide the necessary background material needed to go further into the subject and explore the rich research literature, motivating further research activity in the area.

Delfim F. M. Torres was born August 16, 1971, in Nampula, Mozambique. He is currently an Associate Professor with Habilitation at the Department of Mathematics, University of Aveiro (UA), Portugal; Coordinator of the group on Mathematical Theory of Systems and Control of the Center for Research and Development in Mathematics and Applic...
Title:Quantum Variational CalculusFormat:PaperbackDimensions:84 pagesPublished:December 11, 2013Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3319027468

ISBN - 13:9783319027463


Table of Contents

The Classical Calculus of Variations.- The Hahn Quantum Variational Calculus.- The Power Quantum Calculus.- Conclusion.

Editorial Reviews

From the book reviews:"The aim of this book is cover the elementary calculus of variations problems in the context of the Hahn quantum calculus and the power quantum calculus. . The book may serve as an introduction to the Hahn quantum calculus or the power quantum calculus . or as a reference for the Euler-Lagrange equations for the associated calculus of variations problems with fixed or free endpoints." (Roman Simon Hilscher, Mathematical Reviews, October, 2014)