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Fractional Calculus For Skeptics
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Book Synopsis Fractional Calculus for Skeptics I by : Bruce J. West
Download or read book Fractional Calculus for Skeptics I written by Bruce J. West and published by CRC Press. This book was released on 2024-05-16 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first of its kind on fractional calculus (FC), dedicated to advocating for FC in STEM education and research. Fractional calculus is increasingly used today, but there remains a core population of skeptics regarding the utility of this "new" calculus. This book is intended for those who are skeptical about the need for fractional calculus to describe dynamic complex networks and must be convinced of its use on a case-by-case basis. It is a one-stop resource to rapidly read and replace the appropriate skepticism with new knowledge. It offers compelling reasons from the perspectives of the physical, social, and life sciences as to why fractional calculus is needed when addressing the complexity of an underlying STEM phenomenon. The six chapters are accompanied by useful and essential appendices and chapter-end references. Each includes new (fractional-order) ways of thinking about statistics, complexity dynamics, and what constitutes a solution to a complexity science problem. The book will appeal to students and researchers in all STEM-related fields, such as engineering, physics, biology and biomedicine, climate change, big data, and machine learning. It is also suitable for general readers interested in these fields.
Book Synopsis Fractional Calculus for Skeptics by : Bruce J. West
Download or read book Fractional Calculus for Skeptics written by Bruce J. West and published by . This book was released on 2024 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is the first of its kind on fractional calculus (FC), dedicated to advocating for FC in STEM education and research. Fractional calculus is increasingly used today, but there remains a core population of skeptics regarding the utility of this "new" calculus. This book is intended for those who are skeptical about the need for fractional calculus to describe dynamic complex networks and must be convinced of its use on a case-by-case basis. It is a one-stop resource to rapidly read and replace the appropriate skepticism with new knowledge. It offers compelling reasons from the perspectives of the physical, social, and life sciences as to why fractional calculus is needed when addressing the complexity of an underlying STEM phenomenon. The six chapters are accompanied by useful and essential appendices and chapter-end references. Each includes new (fractional-order) ways of thinking about statistics, complexity dynamics, and what constitutes a solution to a complexity science problem. The book will appeal to students and researchers in all STEM-related fields, engineering, physics, biology and biomedicine, climate change, big data, machine learning, etc. It is also suitable for general readers interested in these fields"--
Book Synopsis On the Fractal Language of Medicine by : Bruce J. West
Download or read book On the Fractal Language of Medicine written by Bruce J. West and published by CRC Press. This book was released on 2024-07-17 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: On the Fractal Language of Medicine bridges a very clear gap among the knowledge gained over the last 20 years in the physical and life sciences on network theory, organ synchronicity and communication, the understanding of fractal signatures in health and disease and the importance of fractional calculus in integrating these concepts. The authors opine that the field of medicine has not appreciated this hard-won knowledge and has suffered greatly as a result. This book addresses this perceived deficiency by introducing medical researchers, clinicians, residents, first-year medical students and members of allied fields to the work of the so-called hard sciences. It seeks to facilitate effective communication between empiricists and theorists by making interdisciplinary efforts to explain complex mathematical concepts to physicians and, equally important, to elucidate complex medical concepts to physicists or mathematicians. This book will be of great interest to medical students, professionals and academics, as well as students and researchers of applied mathematics, especially those interested in fractional calculus and fractals.
Book Synopsis Advances in Fractional Calculus by : J. Sabatier
Download or read book Advances in Fractional Calculus written by J. Sabatier and published by Springer Science & Business Media. This book was released on 2007-07-28 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last two decades, fractional (or non integer) differentiation has played a very important role in various fields such as mechanics, electricity, chemistry, biology, economics, control theory and signal and image processing. For example, in the last three fields, some important considerations such as modelling, curve fitting, filtering, pattern recognition, edge detection, identification, stability, controllability, observability and robustness are now linked to long-range dependence phenomena. Similar progress has been made in other fields listed here. The scope of the book is thus to present the state of the art in the study of fractional systems and the application of fractional differentiation. As this volume covers recent applications of fractional calculus, it will be of interest to engineers, scientists, and applied mathematicians.
Book Synopsis Fractional Processes and Fractional-Order Signal Processing by : Hu Sheng
Download or read book Fractional Processes and Fractional-Order Signal Processing written by Hu Sheng and published by Springer Science & Business Media. This book was released on 2011-10-20 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional processes are widely found in science, technology and engineering systems. In Fractional Processes and Fractional-order Signal Processing, some complex random signals, characterized by the presence of a heavy-tailed distribution or non-negligible dependence between distant observations (local and long memory), are introduced and examined from the ‘fractional’ perspective using simulation, fractional-order modeling and filtering and realization of fractional-order systems. These fractional-order signal processing (FOSP) techniques are based on fractional calculus, the fractional Fourier transform and fractional lower-order moments. Fractional Processes and Fractional-order Signal Processing: presents fractional processes of fixed, variable and distributed order studied as the output of fractional-order differential systems; introduces FOSP techniques and the fractional signals and fractional systems point of view; details real-world-application examples of FOSP techniques to demonstrate their utility; and provides important background material on Mittag–Leffler functions, the use of numerical inverse Laplace transform algorithms and supporting MATLAB® codes together with a helpful survey of relevant webpages. Readers will be able to use the techniques presented to re-examine their signals and signal-processing methods. This text offers an extended toolbox for complex signals from diverse fields in science and engineering. It will give academic researchers and practitioners a novel insight into the complex random signals characterized by fractional properties, and some powerful tools to analyze those signals.
Book Synopsis Fractional Calculus View of Complexity by : Bruce J. West
Download or read book Fractional Calculus View of Complexity written by Bruce J. West and published by CRC Press. This book was released on 2016-01-05 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is not a text devoted to a pedagogical presentation of a specialized topic nor is it a monograph focused on the author's area of research. It accomplishes both these things while providing a rationale for why the reader ought to be interested in learning about fractional calculus. This book is for researchers who has heard about many
Book Synopsis Computation and Modeling for Fractional Order Systems by : Snehashish Chakraverty
Download or read book Computation and Modeling for Fractional Order Systems written by Snehashish Chakraverty and published by Elsevier. This book was released on 2024-02-20 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computation and Modeling for Fractional Order Systems provides readers with problem-solving techniques for obtaining exact and/or approximate solutions of governing equations arising in fractional dynamical systems presented using various analytical, semi-analytical, and numerical methods. In this regard, this book brings together contemporary and computationally efficient methods for investigating real-world fractional order systems in one volume. Fractional calculus has gained increasing popularity and relevance over the last few decades, due to its well-established applications in various fields of science and engineering. It deals with the differential and integral operators with non-integral powers. Fractional differential equations are the pillar of various systems occurring in a wide range of science and engineering disciplines, namely physics, chemical engineering, mathematical biology, financial mathematics, structural mechanics, control theory, circuit analysis, and biomechanics, among others. The fractional derivative has also been used in various other physical problems, such as frequency-dependent damping behavior of structures, motion of a plate in a Newtonian fluid, PID controller for the control of dynamical systems, and many others. The mathematical models in electromagnetics, rheology, viscoelasticity, electrochemistry, control theory, Brownian motion, signal and image processing, fluid dynamics, financial mathematics, and material science are well defined by fractional-order differential equations. Generally, these physical models are demonstrated either by ordinary or partial differential equations. However, modeling these problems by fractional differential equations, on the other hand, can make the physics of the systems more feasible and practical in some cases. In order to know the behavior of these systems, we need to study the solutions of the governing fractional models. The exact solution of fractional differential equations may not always be possible using known classical methods. Generally, the physical models occurring in nature comprise complex phenomena, and it is sometimes challenging to obtain the solution (both analytical and numerical) of nonlinear differential equations of fractional order. Various aspects of mathematical modeling that may include deterministic or uncertain (viz. fuzzy or interval or stochastic) scenarios along with fractional order (singular/non-singular kernels) are important to understand the dynamical systems. Computation and Modeling for Fractional Order Systems covers various types of fractional order models in deterministic and non-deterministic scenarios. Various analytical/semi-analytical/numerical methods are applied for solving real-life fractional order problems. The comprehensive descriptions of different recently developed fractional singular, non-singular, fractal-fractional, and discrete fractional operators, along with computationally efficient methods, are included for the reader to understand how these may be applied to real-world systems, and a wide variety of dynamical systems such as deterministic, stochastic, continuous, and discrete are addressed by the authors of the book.
Book Synopsis Nature’s Patterns and the Fractional Calculus by : Bruce J. West
Download or read book Nature’s Patterns and the Fractional Calculus written by Bruce J. West and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-09-11 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complexity increases with increasing system size in everything from organisms to organizations. The nonlinear dependence of a system’s functionality on its size, by means of an allometry relation, is argued to be a consequence of their joint dependency on complexity (information). In turn, complexity is proven to be the source of allometry and to provide a new kind of force entailed by a system‘s information gradient. Based on first principles, the scaling behavior of the probability density function is determined by the exact solution to a set of fractional differential equations. The resulting lowest order moments in system size and functionality gives rise to the empirical allometry relations. Taking examples from various topics in nature, the book is of interest to researchers in applied mathematics, as well as, investigators in the natural, social, physical and life sciences. Contents Complexity Empirical allometry Statistics, scaling and simulation Allometry theories Strange kinetics Fractional probability calculus
Book Synopsis Advanced Synchronization Control and Bifurcation of Chaotic Fractional-Order Systems by : Boulkroune, Abdesselem
Download or read book Advanced Synchronization Control and Bifurcation of Chaotic Fractional-Order Systems written by Boulkroune, Abdesselem and published by IGI Global. This book was released on 2018-05-11 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the recent years, fractional-order systems have been studied by many researchers in the engineering field. It was found that many systems can be described more accurately by fractional differential equations than by integer-order models. Advanced Synchronization Control and Bifurcation of Chaotic Fractional-Order Systems is a scholarly publication that explores new developments related to novel chaotic fractional-order systems, control schemes, and their applications. Featuring coverage on a wide range of topics including chaos synchronization, nonlinear control, and cryptography, this publication is geared toward engineers, IT professionals, researchers, and upper-level graduate students seeking current research on chaotic fractional-order systems and their applications in engineering and computer science.
Book Synopsis Intelligent Fractional Order Systems and Control by : Indranil Pan
Download or read book Intelligent Fractional Order Systems and Control written by Indranil Pan and published by Springer. This book was released on 2012-08-23 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional order calculus is finding increasing interest in the control system community. Hardware realizations of fractional order controllers have sparked off a renewed zeal into the investigations of control system design in the light of fractional calculus. As such many notions of integer order LTI systems are being modified and extended to incorporate these new concepts. Computational Intelligence (CI) techniques have been applied to engineering problems to find solutions to many hitherto intractable conundrums and is a useful tool for dealing with problems of higher computational complexity. This book borders on the interface between CI techniques and fractional calculus, and looks at ways in which fractional order control systems may be designed or enhanced using CI based paradigms. To the best of the author’s knowledge this is the first book of its kind exclusively dedicated to the application of computational intelligence techniques in fractional order systems and control. The book tries to assimilate various existing concepts in this nascent field of fractional order intelligent control and is aimed at researchers and post graduate students working in this field.
Book Synopsis A Calculus of Ideas by : Ulf Grenander
Download or read book A Calculus of Ideas written by Ulf Grenander and published by World Scientific. This book was released on 2012 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph reports a thought experiment with a mathematical structure intended to illustrate the workings of a mind. It presents a mathematical theory of human thought based on pattern theory with a graph-based approach to thinking. The method illustrated and produced by extensive computer simulations is related to neural networks. Based mainly on introspection, it is speculative rather than empirical such that it differs radically in attitude from the conventional wisdom of current cognitive science.
Book Synopsis The Calculus of Consent by : James M. Buchanan
Download or read book The Calculus of Consent written by James M. Buchanan and published by University of Michigan Press. This book was released on 1965 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: A scientific study of the political and economic factors influencing democratic decision making
Book Synopsis Applications Of Fractional Calculus In Physics by : Rudolf Hilfer
Download or read book Applications Of Fractional Calculus In Physics written by Rudolf Hilfer and published by World Scientific. This book was released on 2000-03-02 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional calculus is a collection of relatively little-known mathematical results concerning generalizations of differentiation and integration to noninteger orders. While these results have been accumulated over centuries in various branches of mathematics, they have until recently found little appreciation or application in physics and other mathematically oriented sciences. This situation is beginning to change, and there are now a growing number of research areas in physics which employ fractional calculus.This volume provides an introduction to fractional calculus for physicists, and collects easily accessible review articles surveying those areas of physics in which applications of fractional calculus have recently become prominent.
Book Synopsis Concrete Mathematics by : Ronald L. Graham
Download or read book Concrete Mathematics written by Ronald L. Graham and published by Addison-Wesley Professional. This book was released on 1994-02-28 with total page 811 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex problems, to evaluate horrendous sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline. Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems." The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories. Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study. Major topics include: Sums Recurrences Integer functions Elementary number theory Binomial coefficients Generating functions Discrete probability Asymptotic methods This second edition includes important new material about mechanical summation. In response to the widespread use of the first edition as a reference book, the bibliography and index have also been expanded, and additional nontrivial improvements can be found on almost every page. Readers will appreciate the informal style of Concrete Mathematics. Particularly enjoyable are the marginal graffiti contributed by students who have taken courses based on this material. The authors want to convey not only the importance of the techniques presented, but some of the fun in learning and using them.
Book Synopsis The Science of Good and Evil by : Michael Shermer
Download or read book The Science of Good and Evil written by Michael Shermer and published by Macmillan. This book was released on 2005-01-02 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: From bestselling author Michael Shermer, an investigation of the evolution of morality that is "a paragon of popularized science and philosophy" The Sun (Baltimore) A century and a half after Darwin first proposed an "evolutionary ethics," science has begun to tackle the roots of morality. Just as evolutionary biologists study why we are hungry (to motivate us to eat) or why sex is enjoyable (to motivate us to procreate), they are now searching for the very nature of humanity. In The Science of Good and Evil, science historian Michael Shermer explores how humans evolved from social primates to moral primates; how and why morality motivates the human animal; and how the foundation of moral principles can be built upon empirical evidence. Along the way he explains the implications of scientific findings for fate and free will, the existence of pure good and pure evil, and the development of early moral sentiments among the first humans. As he closes the divide between science and morality, Shermer draws on stories from the Yanamamö, infamously known as the "fierce people" of the tropical rain forest, to the Stanford studies on jailers' behavior in prisons. The Science of Good and Evil is ultimately a profound look at the moral animal, belief, and the scientific pursuit of truth.
Book Synopsis An Invitation to Abstract Mathematics by : Béla Bajnok
Download or read book An Invitation to Abstract Mathematics written by Béla Bajnok and published by Springer Nature. This book was released on 2020-10-27 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: This undergraduate textbook promotes an active transition to higher mathematics. Problem solving is the heart and soul of this book: each problem is carefully chosen to demonstrate, elucidate, or extend a concept. More than 300 exercises engage the reader in extensive arguments and creative approaches, while exploring connections between fundamental mathematical topics. Divided into four parts, this book begins with a playful exploration of the building blocks of mathematics, such as definitions, axioms, and proofs. A study of the fundamental concepts of logic, sets, and functions follows, before focus turns to methods of proof. Having covered the core of a transition course, the author goes on to present a selection of advanced topics that offer opportunities for extension or further study. Throughout, appendices touch on historical perspectives, current trends, and open questions, showing mathematics as a vibrant and dynamic human enterprise. This second edition has been reorganized to better reflect the layout and curriculum of standard transition courses. It also features recent developments and improved appendices. An Invitation to Abstract Mathematics is ideal for those seeking a challenging and engaging transition to advanced mathematics, and will appeal to both undergraduates majoring in mathematics, as well as non-math majors interested in exploring higher-level concepts. From reviews of the first edition: Bajnok’s new book truly invites students to enjoy the beauty, power, and challenge of abstract mathematics. ... The book can be used as a text for traditional transition or structure courses ... but since Bajnok invites all students, not just mathematics majors, to enjoy the subject, he assumes very little background knowledge. Jill Dietz, MAA Reviews The style of writing is careful, but joyously enthusiastic.... The author’s clear attitude is that mathematics consists of problem solving, and that writing a proof falls into this category. Students of mathematics are, therefore, engaged in problem solving, and should be given problems to solve, rather than problems to imitate. The author attributes this approach to his Hungarian background ... and encourages students to embrace the challenge in the same way an athlete engages in vigorous practice. John Perry, zbMATH
Book Synopsis Mathematical Omnibus by : D. B. Fuks
Download or read book Mathematical Omnibus written by D. B. Fuks and published by American Mathematical Soc.. This book was released on 2007 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book consists of thirty lectures on diverse topics, covering much of the mathematical landscape rather than focusing on one area. The reader will learn numerous results that often belong to neither the standard undergraduate nor graduate curriculum and will discover connections between classical and contemporary ideas in algebra, combinatorics, geometry, and topology. The reader's effort will be rewarded in seeing the harmony of each subject. The common thread in the selected subjects is their illustration of the unity and beauty of mathematics. Most lectures contain exercises, and solutions or answers are given to selected exercises. A special feature of the book is an abundance of drawings (more than four hundred), artwork by an accomplished artist, and about a hundred portraits of mathematicians. Almost every lecture contains surprises for even the seasoned researcher.
