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| Author | : Thomas Ernst |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 491 |
| Release | : 2012-09-13 |
| Genre | : Mathematics |
| ISBN | : 3034804318 |
Download A Comprehensive Treatment of q-Calculus Book in PDF, ePub and Kindle
To date, the theoretical development of q-calculus has rested on a non-uniform basis. Generally, the bulky Gasper-Rahman notation was used, but the published works on q-calculus looked different depending on where and by whom they were written. This confusion of tongues not only complicated the theoretical development but also contributed to q-calculus remaining a neglected mathematical field. This book overcomes these problems by introducing a new and interesting notation for q-calculus based on logarithms.For instance, q-hypergeometric functions are now visually clear and easy to trace back to their hypergeometric parents. With this new notation it is also easy to see the connection between q-hypergeometric functions and the q-gamma function, something that until now has been overlooked. The book covers many topics on q-calculus, including special functions, combinatorics, and q-difference equations. Apart from a thorough review of the historical development of q-calculus, this book also presents the domains of modern physics for which q-calculus is applicable, such as particle physics and supersymmetry, to name just a few.
| Author | : Thomas Ernst |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 491 |
| Release | : 2012-09-08 |
| Genre | : Mathematics |
| ISBN | : 303480430X |
Download A Comprehensive Treatment of q-Calculus Book in PDF, ePub and Kindle
To date, the theoretical development of q-calculus has rested on a non-uniform basis. Generally, the bulky Gasper-Rahman notation was used, but the published works on q-calculus looked different depending on where and by whom they were written. This confusion of tongues not only complicated the theoretical development but also contributed to q-calculus remaining a neglected mathematical field. This book overcomes these problems by introducing a new and interesting notation for q-calculus based on logarithms.For instance, q-hypergeometric functions are now visually clear and easy to trace back to their hypergeometric parents. With this new notation it is also easy to see the connection between q-hypergeometric functions and the q-gamma function, something that until now has been overlooked. The book covers many topics on q-calculus, including special functions, combinatorics, and q-difference equations. Apart from a thorough review of the historical development of q-calculus, this book also presents the domains of modern physics for which q-calculus is applicable, such as particle physics and supersymmetry, to name just a few.
| Author | : Victor Kac |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 121 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461300711 |
Download Quantum Calculus Book in PDF, ePub and Kindle
Simply put, quantum calculus is ordinary calculus without taking limits. This undergraduate text develops two types of quantum calculi, the q-calculus and the h-calculus. As this book develops quantum calculus along the lines of traditional calculus, the reader discovers, with a remarkable inevitability, many important notions and results of classical mathematics. This book is written at the level of a first course in calculus and linear algebra and is aimed at undergraduate and beginning graduate students in mathematics, computer science, and physics. It is based on lectures and seminars given by MIT Professor Kac over the last few years at MIT.
| Author | : Bashir Ahmad |
| Publisher | : Trends in Abstract and Applied Analysis |
| Total Pages | : 276 |
| Release | : 2016 |
| Genre | : Calculus |
| ISBN | : 9789813141520 |
Download Quantum Calculus Book in PDF, ePub and Kindle
The main objective of this book is to extend the scope of the q-calculus based on the definition of q-derivative [Jackson (1910)] to make it applicable to dense domains. As a matter of fact, Jackson's definition of q-derivative fails to work for impulse points while this situation does not arise for impulsive equations on q-time scales as the domains consist of isolated points covering the case of consecutive points. In precise terms, we study quantum calculus on finite intervals. In the first part, we discuss the concepts of qk-derivative and qk-integral, and establish their basic properties. As applications, we study initial and boundary value problems of impulsive qk-difference equations and inclusions equipped with different kinds of boundary conditions. We also transform some classical integral inequalities and develop some new integral inequalities for convex functions in the context of qk-calculus. In the second part, we develop fractional quantum calculus in relation to a new qk-shifting operator and establish some existence and qk uniqueness results for initial and boundary value problems of impulsive fractional qk-difference equations.
| Author | : H. M. Srivastava |
| Publisher | : MDPI |
| Total Pages | : 510 |
| Release | : 2019-11-20 |
| Genre | : Technology & Engineering |
| ISBN | : 303921618X |
Download Integral Transforms and Operational Calculus Book in PDF, ePub and Kindle
Researches and investigations involving the theory and applications of integral transforms and operational calculus are remarkably wide-spread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences. This Special Issue contains a total of 36 carefully-selected and peer-reviewed articles which are authored by established researchers from many countries. Included in this Special Issue are review, expository and original research articles dealing with the recent advances on the topics of integral transforms and operational calculus as well as their multidisciplinary applications
| Author | : Agnieszka B. Malinowska |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 96 |
| Release | : 2013-11-29 |
| Genre | : Mathematics |
| ISBN | : 3319027476 |
Download Quantum Variational Calculus Book in PDF, ePub and Kindle
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 Calculus is 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.
| Author | : J.E. Trinidad-Segovia |
| Publisher | : MDPI |
| Total Pages | : 418 |
| Release | : 2021-02-12 |
| Genre | : Business & Economics |
| ISBN | : 3036501967 |
Download Quantitative Methods for Economics and Finance Book in PDF, ePub and Kindle
This book is a collection of papers for the Special Issue “Quantitative Methods for Economics and Finance” of the journal Mathematics. This Special Issue reflects on the latest developments in different fields of economics and finance where mathematics plays a significant role. The book gathers 19 papers on topics such as volatility clusters and volatility dynamic, forecasting, stocks, indexes, cryptocurrencies and commodities, trade agreements, the relationship between volume and price, trading strategies, efficiency, regression, utility models, fraud prediction, or intertemporal choice.
| Author | : Rekha Srivastava |
| Publisher | : MDPI |
| Total Pages | : 318 |
| Release | : 2021-04-06 |
| Genre | : Mathematics |
| ISBN | : 3036500324 |
Download Mathematical Analysis and Analytic Number Theory 2019 Book in PDF, ePub and Kindle
This volume is a collection of investigations involving the theory and applications of the various tools and techniques of mathematical analysis and analytic number theory, which are remarkably widespread in many diverse areas of the mathematical, biological, physical, chemical, engineering, and statistical sciences. It contains invited and welcome original as well as review-cum-expository research articles dealing with recent and new developments on the topics of mathematical analysis and analytic number theory as well as their multidisciplinary applications.
| Author | : Hans J. Haubold |
| Publisher | : MDPI |
| Total Pages | : 305 |
| Release | : 2018-03-23 |
| Genre | : Mathematics |
| ISBN | : 3038426652 |
Download Special Functions: Fractional Calculus and the Pathway for Entropy Book in PDF, ePub and Kindle
This book is a printed edition of the Special Issue "Special Functions: Fractional Calculus and the Pathway for Entropy Dedicated to Professor Dr. A.M. Mathai on the occasion of his 80th Birthday" that was published in Axioms
| Author | : Narendra Kumar Govil |
| Publisher | : Springer |
| Total Pages | : 541 |
| Release | : 2017-04-03 |
| Genre | : Mathematics |
| ISBN | : 331949242X |
Download Progress in Approximation Theory and Applicable Complex Analysis Book in PDF, ePub and Kindle
Current and historical research methods in approximation theory are presented in this book beginning with the 1800s and following the evolution of approximation theory via the refinement and extension of classical methods and ending with recent techniques and methodologies. Graduate students, postdocs, and researchers in mathematics, specifically those working in the theory of functions, approximation theory, geometric function theory, and optimization will find new insights as well as a guide to advanced topics. The chapters in this book are grouped into four themes; the first, polynomials (Chapters 1 –8), includes inequalities for polynomials and rational functions, orthogonal polynomials, and location of zeros. The second, inequalities and extremal problems are discussed in Chapters 9 –13. The third, approximation of functions, involves the approximants being polynomials, rational functions, and other types of functions and are covered in Chapters 14 –19. The last theme, quadrature, cubature and applications, comprises the final three chapters and includes an article coauthored by Rahman. This volume serves as a memorial volume to commemorate the distinguished career of Qazi Ibadur Rahman (1934–2013) of the Université de Montréal. Rahman was considered by his peers as one of the prominent experts in analytic theory of polynomials and entire functions. The novelty of his work lies in his profound abilities and skills in applying techniques from other areas of mathematics, such as optimization theory and variational principles, to obtain final answers to countless open problems.
