Calculus Theory And Applications Volume 1
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Calculus Theory And Applications Volume 1
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Author : Kenneth Kuttler
language : en
Publisher: World Scientific Publishing Company
Release Date : 2010-12-28
Calculus Theory And Applications Volume 1 written by Kenneth Kuttler 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 2010-12-28 with Mathematics categories.
This is a book on single variable calculus including most of the important applications of calculus. It also includes proofs of all theorems presented, either in the text itself, or in an appendix. It also contains an introduction to vectors and vector products which is developed further in Volume 2.While the book does include all the proofs of the theorems, many of the applications are presented more simply and less formally than is often the case in similar titles.
Calculus
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Author : Kenneth Kuttler
language : en
Publisher: World Scientific
Release Date : 2011
Calculus written by Kenneth Kuttler and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
Summary: This is a book on single variable calculus including most of the important applications of calculus. It also includes proofs of all theorems presented, either in the text itself, or in an appendix. It also contains an introduction to vectors and vector products which is developed further in Volume 2. While the book does include all the proofs of the theorems, many of the applications are presented more simply and less formally than is often the case in similar titles.
Calculus
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Author : Kenneth Kuttler
language : en
Publisher: World Scientific
Release Date : 2011
Calculus written by Kenneth Kuttler and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
This is a book on single variable calculus including most of the important applications of calculus. It also includes proofs of all theorems presented, either in the text itself, or in an appendix. It also contains an introduction to vectors and vector products which is developed further in Volume 2. While the book does include all the proofs of the theorems, many of the applications are presented more simply and less formally than is often the case in similar titles. Supplementary materials are available upon request for all instructors who adopt this book as a course text. Please send your request to [email protected]. This book is also available as a set with Volume 2: CALCULUS: Theory and Applications.
Basic Theory
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Author : Anatoly Kochubei
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2019-02-19
Basic Theory written by Anatoly Kochubei and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-19 with Mathematics categories.
This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This first volume collects authoritative chapters covering the mathematical theory of fractional calculus, including fractional-order operators, integral transforms and equations, special functions, calculus of variations, and probabilistic and other aspects.
Calculus Theory And Applications
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Author : Kuttler Kenneth
language : en
Publisher: World Scientific Publishing Company
Release Date : 2011-01-10
Calculus Theory And Applications written by Kuttler Kenneth 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 2011-01-10 with Mathematics categories.
This is a book on many variable calculus. It is the second volume of a set of two. It includes proofs of all theorems presented, either in the text itself, or in an appendix. It also includes a sufficient introduction to linear algebra to allow the accurate presentation of many variable calculus.The use of elementary linear algebra in presenting the topics of multi- variable calculus is more extensive than usual in this book. It makes many of these topics easier to understand and remember. The book will prepare readers for more advanced math courses and also for courses in physical science.
Optimization Theory And Applications
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Author : L. Cesari
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Optimization Theory And Applications written by L. Cesari 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 2012-12-06 with Science categories.
This book has grown out of lectures and courses in calculus of variations and optimization taught for many years at the University of Michigan to graduate students at various stages of their careers, and always to a mixed audience of students in mathematics and engineering. It attempts to present a balanced view of the subject, giving some emphasis to its connections with the classical theory and to a number of those problems of economics and engineering which have motivated so many of the present developments, as well as presenting aspects of the current theory, particularly value theory and existence theorems. However, the presentation ofthe theory is connected to and accompanied by many concrete problems of optimization, classical and modern, some more technical and some less so, some discussed in detail and some only sketched or proposed as exercises. No single part of the subject (such as the existence theorems, or the more traditional approach based on necessary conditions and on sufficient conditions, or the more recent one based on value function theory) can give a sufficient representation of the whole subject. This holds particularly for the existence theorems, some of which have been conceived to apply to certain large classes of problems of optimization. For all these reasons it is essential to present many examples (Chapters 3 and 6) before the existence theorems (Chapters 9 and 11-16), and to investigate these examples by means of the usual necessary conditions, sufficient conditions, and value function theory.
Theory And Applications Of Fractional Differential Equations
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Author : A. Anatolii Aleksandrovich Kilbas
language : en
Publisher: Elsevier Science Limited
Release Date : 2006
Theory And Applications Of Fractional Differential Equations written by A. Anatolii Aleksandrovich Kilbas and has been published by Elsevier Science Limited this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
This monograph provides the most recent and up-to-date developments on fractional differential and fractional integro-differential equations involving many different potentially useful operators of fractional calculus. The subject of fractional calculus and its applications (that is, calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past three decades or so, due mainly to its demonstrated applications in numerous seemingly diverse and widespread fields of science and engineering. Some of the areas of present-day applications of fractional models include Fluid Flow, Solute Transport or Dynamical Processes in Self-Similar and Porous Structures, Diffusive Transport akin to Diffusion, Material Viscoelastic Theory, Electromagnetic Theory, Dynamics of Earthquakes, Control Theory of Dynamical Systems, Optics and Signal Processing, Bio-Sciences, Economics, Geology, Astrophysics, Probability and Statistics, Chemical Physics, and so on. In the above-mentioned areas, there are phenomena with estrange kinetics which have a microscopic complex behaviour, and their macroscopic dynamics can not be characterized by classical derivative models. The fractional modelling is an emergent tool which use fractional differential equations including derivatives of fractional order, that is, we can speak about a derivative of order 1/3, or square root of 2, and so on. Some of such fractional models can have solutions which are non-differentiable but continuous functions, such as Weierstrass type functions. Such kinds of properties are, obviously, impossible for the ordinary models. What are the useful properties of these fractional operators which help in the modelling of so many anomalous processes? From the point of view of the authors and from known experimental results, most of the processes associated with complex systems have non-local dynamics involving long-memory in time, and the fractional integral and fractional derivative operators do have some of those characteristics. This book is written primarily for the graduate students and researchers in many different disciplines in the mathematical, physical, engineering and so many others sciences, who are interested not only in learning about the various mathematical tools and techniques used in the theory and widespread applications of fractional differential equations, but also in further investigations which emerge naturally from (or which are motivated substantially by) the physical situations modelled mathematically in the book. This monograph consists of a total of eight chapters and a very extensive bibliography. The main objective of it is to complement the contents of the other books dedicated to the study and the applications of fractional differential equations. The aim of the book is to present, in a systematic manner, results including the existence and uniqueness of solutions for the Cauchy type problems involving nonlinear ordinary fractional differential equations, explicit solutions of linear differential equations and of the corresponding initial-value problems through different methods, closed-form solutions of ordinary and partial differential equations, and a theory of the so-called sequential linear fractional differential equations including a generalization of the classical Frobenius method, and also to include an interesting set of applications of the developed theory. Key features: - It is mainly application oriented. - It contains a complete theory of Fractional Differential Equations. - It can be used as a postgraduate-level textbook in many different disciplines within science and engineering. - It contains an up-to-date bibliography. - It provides problems and directions for further investigations. - Fractional Modelling is an emergent tool with demonstrated applications in numerous seemingly diverse and widespread fields of science and engineering. - It contains many examples. - and so on!
The H Function
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Author : A.M. Mathai
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-10-10
The H Function written by A.M. Mathai 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 2009-10-10 with Science categories.
TheH-function or popularly known in the literature as Fox’sH-function has recently found applications in a large variety of problems connected with reaction, diffusion, reaction–diffusion, engineering and communication, fractional differ- tial and integral equations, many areas of theoretical physics, statistical distribution theory, etc. One of the standard books and most cited book on the topic is the 1978 book of Mathai and Saxena. Since then, the subject has grown a lot, mainly in the elds of applications. Due to popular demand, the authors were requested to - grade and bring out a revised edition of the 1978 book. It was decided to bring out a new book, mostly dealing with recent applications in statistical distributions, pa- way models, nonextensive statistical mechanics, astrophysics problems, fractional calculus, etc. and to make use of the expertise of Hans J. Haubold in astrophysics area also. It was decided to con ne the discussion toH-function of one scalar variable only. Matrix variable cases and many variable cases are not discussed in detail, but an insight into these areas is given. When going from one variable to many variables, there is nothing called a unique bivariate or multivariate analogue of a givenfunction. Whatever be the criteria used, there may be manydifferentfunctions quali ed to be bivariate or multivariate analogues of a given univariate function. Some of the bivariate and multivariateH-functions, currently in the literature, are also questioned by many authors.
Noncommutative Functional Calculus
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Author : Prof. Fabrizio Colombo Politecnico di Milano
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-18
Noncommutative Functional Calculus written by Prof. Fabrizio Colombo Politecnico di Milano 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 2011-03-18 with Mathematics categories.
This book presents a functional calculus for n-tuples of not necessarily commuting linear operators. In particular, a functional calculus for quaternionic linear operators is developed. These calculi are based on a new theory of hyperholomorphicity for functions with values in a Clifford algebra: the so-called slice monogenic functions which are carefully described in the book. In the case of functions with values in the algebra of quaternions these functions are named slice regular functions. Except for the appendix and the introduction all results are new and appear for the first time organized in a monograph. The material has been carefully prepared to be as self-contained as possible. The intended audience consists of researchers, graduate and postgraduate students interested in operator theory, spectral theory, hypercomplex analysis, and mathematical physics.
The Fractional Calculus Theory And Applications Of Differentiation And Integration To Arbitrary Order
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Author :
language : en
Publisher: Elsevier
Release Date : 1974-09-05
The Fractional Calculus Theory And Applications Of Differentiation And Integration To Arbitrary Order written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974-09-05 with Mathematics categories.
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering