Discrete Calculus By Analogy
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Discrete Calculus By Analogy
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Author : F. A. Izadi
language : en
Publisher: Bentham Science Publishers
Release Date : 2009-12-17
Discrete Calculus By Analogy written by F. A. Izadi and has been published by Bentham Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-17 with Mathematics categories.
"With its origins stretching back several centuries, discrete calculus is now an increasingly central methodology for many problems related to discrete systems and algorithms. The topics covered here usually arise in many branches of science and technology"
Discrete Calculus
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Author : Leo J. Grady
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-07-23
Discrete Calculus written by Leo J. Grady and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-23 with Computers categories.
This unique text brings together into a single framework current research in the three areas of discrete calculus, complex networks, and algorithmic content extraction. Many example applications from several fields of computational science are provided.
Discrete Calculus
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Author : Carlo Mariconda
language : en
Publisher: Springer
Release Date : 2016-12-01
Discrete Calculus written by Carlo Mariconda and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-01 with Mathematics categories.
This book provides an introduction to combinatorics, finite calculus, formal series, recurrences, and approximations of sums. Readers will find not only coverage of the basic elements of the subjects but also deep insights into a range of less common topics rarely considered within a single book, such as counting with occupancy constraints, a clear distinction between algebraic and analytical properties of formal power series, an introduction to discrete dynamical systems with a thorough description of Sarkovskii’s theorem, symbolic calculus, and a complete description of the Euler-Maclaurin formulas and their applications. Although several books touch on one or more of these aspects, precious few cover all of them. The authors, both pure mathematicians, have attempted to develop methods that will allow the student to formulate a given problem in a precise mathematical framework. The aim is to equip readers with a sound strategy for classifying and solving problems by pursuing a mathematically rigorous yet user-friendly approach. This is particularly useful in combinatorics, a field where, all too often, exercises are solved by means of ad hoc tricks. The book contains more than 400 examples and about 300 problems, and the reader will be able to find the proof of every result. To further assist students and teachers, important matters and comments are highlighted, and parts that can be omitted, at least during a first and perhaps second reading, are identified.
Handbook Of Discrete And Combinatorial Mathematics
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Author : Kenneth H. Rosen
language : en
Publisher: CRC Press
Release Date : 2017-10-19
Handbook Of Discrete And Combinatorial Mathematics written by Kenneth H. Rosen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-19 with Mathematics categories.
Handbook of Discrete and Combinatorial Mathematics provides a comprehensive reference volume for mathematicians, computer scientists, engineers, as well as students and reference librarians. The material is presented so that key information can be located and used quickly and easily. Each chapter includes a glossary. Individual topics are covered in sections and subsections within chapters, each of which is organized into clearly identifiable parts: definitions, facts, and examples. Examples are provided to illustrate some of the key definitions, facts, and algorithms. Some curious and entertaining facts and puzzles are also included. Readers will also find an extensive collection of biographies. This second edition is a major revision. It includes extensive additions and updates. Since the first edition appeared in 1999, many new discoveries have been made and new areas have grown in importance, which are covered in this edition.
Machines Computations And Universality
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Author : Jérôme Durand-Lose
language : en
Publisher: Springer Nature
Release Date : 2022-08-06
Machines Computations And Universality written by Jérôme Durand-Lose and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-06 with Computers categories.
This book constitutes the refereed proceedings of the 9th International Conference on Machines, Computations, and Universality, MCU 2022, held in Debrecen, Hungary, in August/September 2022. The 10 revised full papers presented were carefully reviewed and selected from 18 submissions. MCU explores computation in the setting of various discrete models (Turing machines, register machines, cellular automata, tile assembly systems, rewriting systems, molecular computing models, neural models, concurrent systems, etc.) and analog and hybrid models (BSS machines, infinite time cellular automata, real machines, quantum computing).
Linear Difference Equations With Discrete Transform Methods
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Author : A.J. Jerri
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Linear Difference Equations With Discrete Transform Methods written by A.J. Jerri and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
This book covers the basic elements of difference equations and the tools of difference and sum calculus necessary for studying and solv ing, primarily, ordinary linear difference equations. Examples from various fields are presented clearly in the first chapter, then discussed along with their detailed solutions in Chapters 2-7. The book is in tended mainly as a text for the beginning undergraduate course in difference equations, where the "operational sum calculus" of the di rect use of the discrete Fourier transforms for solving boundary value problems associated with difference equations represents an added new feature compared to other existing books on the subject at this introductory level. This means that in addition to the familiar meth ods of solving difference equations that are covered in Chapter 3, this book emphasizes the use of discrete transforms. It is an attempt to introduce the methods and mechanics of discrete transforms for solv ing ordinary difference equations. The treatment closely parallels what many students have already learned about using the opera tional (integral) calculus of Laplace and Fourier transforms to solve differential equations. As in the continuous case, discrete operational methods may not solve problems that are intractable by other meth ods, but they can facilitate the solution of a large class of discrete initial and boundary value problems. Such operational methods, or what we shall term "operational sum calculus," may be extended eas ily to solve partial difference equations associated with initial and/or boundary value problems.
Discrete Fractional Calculus
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Author : Christopher Goodrich
language : en
Publisher:
Release Date : 2015
Discrete Fractional Calculus written by Christopher Goodrich and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
This text provides the first comprehensive treatment of the discrete fractional calculus. Experienced researchers will find the text useful as a reference for discrete fractional calculus and topics of current interest. Students who are interested in learning about discrete fractional calculus will find this text to provide a useful starting point. Several exercises are offered at the end of each chapter and select answers have been provided at the end of the book. The presentation of the content is designed to give ample flexibility for potential use in a myriad of courses and for independent study. The novel approach taken by the authors includes a simultaneous treatment of the fractional- and integer-order difference calculus (on a variety of time scales, including both the usual forward and backwards difference operators). The reader will acquire a solid foundation in the classical topics of the discrete calculus while being introduced to exciting recent developments, bringing them to the frontiers of the subject. Most chapters may be covered or omitted, depending upon the background of the student. For example, the text may be used as a primary reference in an introductory course for difference equations which also includes discrete fractional calculus. Chapters 1--2 provide a basic introduction to the delta calculus including fractional calculus on the set of integers. For courses where students already have background in elementary real analysis, Chapters 1--2 may be covered quickly and readers may then skip to Chapters 6--7 which present some basic results in fractional boundary value problems (FBVPs). Chapters 6--7 in conjunction with some of the current literature listed in the Bibliography can provide a basis for a seminar in the current theory of FBVPs. For a two-semester course, Chapters 1--5 may be covered in depth, providing a very thorough introduction to both the discrete fractional calculus as well as the integer-order calculus.
The Art Of Proving Binomial Identities
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Author : Michael Z. Spivey
language : en
Publisher: CRC Press
Release Date : 2019-05-10
The Art Of Proving Binomial Identities written by Michael Z. Spivey and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-10 with Mathematics categories.
The book has two goals: (1) Provide a unified treatment of the binomial coefficients, and (2) Bring together much of the undergraduate mathematics curriculum via one theme (the binomial coefficients). The binomial coefficients arise in a variety of areas of mathematics: combinatorics, of course, but also basic algebra (binomial theorem), infinite series (Newton’s binomial series), differentiation (Leibniz’s generalized product rule), special functions (the beta and gamma functions), probability, statistics, number theory, finite difference calculus, algorithm analysis, and even statistical mechanics.
Induction And Analogy In Mathematics
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Author : G. Polya
language : en
Publisher:
Release Date : 1973
Induction And Analogy In Mathematics written by G. Polya and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with categories.
Computational Methods In The Fractional Calculus Of Variations
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Author : Ricardo Almeida
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015-03-19
Computational Methods In The Fractional Calculus Of Variations written by Ricardo Almeida and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-19 with Mathematics categories.
This book fills a gap in the literature by introducing numerical techniques to solve problems of fractional calculus of variations (FCV). In most cases, finding the analytic solution to such problems is extremely difficult or even impossible, and numerical methods need to be used.The authors are well-known researchers in the area of FCV and the book contains some of their recent results, serving as a companion volume to Introduction to the Fractional Calculus of Variations by A B Malinowska and D F M Torres, where analytical methods are presented to solve FCV problems. After some preliminaries on the subject, different techniques are presented in detail with numerous examples to help the reader to better understand the methods. The techniques presented may be used not only to deal with FCV problems but also in other contexts of fractional calculus, such as fractional differential equations and fractional optimal control. It is suitable as an advanced book for graduate students in mathematics, physics and engineering, as well as for researchers interested in fractional calculus.