The Lambert W Function
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The Lambert W Function
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Author : Istvan Mezo
language : en
Publisher: CRC Press
Release Date : 2022-04-10
The Lambert W Function written by Istvan Mezo and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-10 with Mathematics categories.
This book is the very first one in the English language entirely dedicated to the Lambert W function, its generalizations, and its applications. One goal is to promote future research on the topic. The book contains all the information one needs when trying to find a result. The most important formulas and results are framed. The Lambert W function is a multi-valued inverse function with plenty of applications in areas like molecular physics, relativity theory, fuel consumption models, plasma physics, analysis of epidemics, bacterial growth models, delay differential equations, fluid mechanics, game theory, statistics, study of magnetic materials, and so on. The first part of the book gives a full treatise of the W function from theoretical point of view. The second part presents generalizations of this function which have been introduced by the need of applications where the classical W function is insufficient. The third part presents a large number of applications from physics, biology, game theory, bacterial cell growth models, and so on. The second part presents the generalized Lambert functions based on the tools we had developed in the first part. In the third part familiarity with Newtonian physics will be useful. The text is written to be accessible for everyone with only basic knowledge on calculus and complex numbers. Additional features include the Further Notes sections offering interesting research problems and information for further studies. Mathematica codes are included. The Lambert function is arguably the simplest non-elementary transcendental function out of the standard set of sin, cos, log, etc., therefore students who would like to deepen their understanding of real and complex analysis can see a new “almost elementary” function on which they can practice their knowledge.
Time Delay Systems Analysis And Control Using The Lambert W Function
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Author : Patrick W Nelson
language : en
Publisher: World Scientific
Release Date : 2010-06-25
Time Delay Systems Analysis And Control Using The Lambert W Function written by Patrick W Nelson and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-25 with Technology & Engineering categories.
This book comprehensively presents a recently developed novel methodology for analysis and control of time-delay systems. Time-delays frequently occurs in engineering and science. Such time-delays can cause problems (e.g. instability) and limit the achievable performance of control systems. The concise and self-contained volume uses the Lambert W function to obtain solutions to time-delay systems represented by delay differential equations. Subsequently, the solutions are used to analyze essential system properties and to design controllers precisely and effectively.
Analytic Number Theory Approximation Theory And Special Functions
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Author : Gradimir V. Milovanović
language : en
Publisher: Springer
Release Date : 2014-07-08
Analytic Number Theory Approximation Theory And Special Functions written by Gradimir V. Milovanović and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-08 with Mathematics categories.
This book, in honor of Hari M. Srivastava, discusses essential developments in mathematical research in a variety of problems. It contains thirty-five articles, written by eminent scientists from the international mathematical community, including both research and survey works. Subjects covered include analytic number theory, combinatorics, special sequences of numbers and polynomials, analytic inequalities and applications, approximation of functions and quadratures, orthogonality and special and complex functions. The mathematical results and open problems discussed in this book are presented in a simple and self-contained manner. The book contains an overview of old and new results, methods, and theories toward the solution of longstanding problems in a wide scientific field, as well as new results in rapidly progressing areas of research. The book will be useful for researchers and graduate students in the fields of mathematics, physics and other computational and applied sciences.
Optimal Auxiliary Functions Method For Nonlinear Dynamical Systems
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Author : Vasile Marinca
language : en
Publisher: Springer Nature
Release Date : 2021-07-14
Optimal Auxiliary Functions Method For Nonlinear Dynamical Systems written by Vasile Marinca and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-14 with Technology & Engineering categories.
This book presents the optimal auxiliary functions method and applies it to various engineering problems and in particular in boundary layer problems. The cornerstone of the presented procedure is the concept of “optimal auxiliary functions” which are needed to obtain accurate results in an efficient way. Unlike other known analytic approaches, this procedure provides us with a simple but rigorous way to control and adjust the convergence of the solutions of nonlinear dynamical systems. The optimal auxiliary functions are depending on some convergence-control parameters whose optimal values are rigorously determined from mathematical point of view. The capital strength of our procedure is its fast convergence, since after only one iteration, we obtain very accurate analytical solutions which are very easy to be verified. Moreover, no simplifying hypothesis or assumptions are made. The book contains a large amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines, and many more. The book is a continuation of our previous books “Nonlinear Dynamical Systems in Engineering. Some Approximate Approaches”, Springer-2011 and “The Optimal Homotopy Asymptotic Method. Engineering Applications”, Springer-2015.
Artificial Intelligence Automated Reasoning And Symbolic Computation
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Author : Jacques Calmet
language : en
Publisher: Springer
Release Date : 2003-08-02
Artificial Intelligence Automated Reasoning And Symbolic Computation written by Jacques Calmet and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-08-02 with Computers categories.
AISC 2002, the 6th international conference on Arti?cial Intelligence and S- bolic Computation, and Calculemus 2002, the 10th symposium on the Integ- tion of Symbolic Computation and Mechanized Reasoning, were held jointly in Marseille, France on July 1-5, 2002. This event was organized by the three universities in Marseille together with the LSIS (Laboratoire des Sciences de l'Information et des Syst` emes). AISC 2002 was the latest in a series of specialized conferences founded by John Campbell and Jacques Calmet with the initial title "Arti?cial Intelligence and Symbolic Mathematical Computation" (AISMC) and later denoted "Art- cial Intelligence and Symbolic Computation" (AISC). The scope is well de?ned by its successive titles. AISMC-1 (1992), AISMC-2 (1994), AISMC-3 (1996), AISC'98, and AISC 2000 took place in Karlsruhe, Cambridge, Steyr, Plattsburgh (NY), and Madrid respectively. The proceedings were published by Springer-Verlag as LNCS 737, LNCS 958, LNCS 1138, LNAI 1476, and LNAI 1930 respectively. Calculemus 2002 was the 10th symposium in a series which started with three meetings in 1996, two meetings in 1997, and then turned into a yearly event in 1998. Since then, it has become a tradition to hold the meeting jointly with an event in either symbolic computation or automated deduction. Both events share common interests in looking at Symbolic Computation, each from a di?erent point of view: Arti?cial Intelligence in the more general case of AISC and Automated Deduction in the more speci?c case of Calculemus.
Mathematical Foundations For Linear Circuits And Systems In Engineering
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Author : John J. Shynk
language : en
Publisher: John Wiley & Sons
Release Date : 2016-02-22
Mathematical Foundations For Linear Circuits And Systems In Engineering written by John J. Shynk and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-22 with Mathematics categories.
Extensive coverage of mathematical techniques used in engineering with an emphasis on applications in linear circuits and systems Mathematical Foundations for Linear Circuits and Systems in Engineering provides an integrated approach to learning the necessary mathematics specifically used to describe and analyze linear circuits and systems. The chapters develop and examine several mathematical models consisting of one or more equations used in engineering to represent various physical systems. The techniques are discussed in-depth so that the reader has a better understanding of how and why these methods work. Specific topics covered include complex variables, linear equations and matrices, various types of signals, solutions of differential equations, convolution, filter designs, and the widely used Laplace and Fourier transforms. The book also presents a discussion of some mechanical systems that mathematically exhibit the same dynamic properties as electrical circuits. Extensive summaries of important functions and their transforms, set theory, series expansions, various identities, and the Lambert W-function are provided in the appendices. The book has the following features: Compares linear circuits and mechanical systems that are modeled by similar ordinary differential equations, in order to provide an intuitive understanding of different types of linear time-invariant systems. Introduces the theory of generalized functions, which are defined by their behavior under an integral, and describes several properties including derivatives and their Laplace and Fourier transforms. Contains numerous tables and figures that summarize useful mathematical expressions and example results for specific circuits and systems, which reinforce the material and illustrate subtle points. Provides access to a companion website that includes a solutions manual with MATLAB code for the end-of-chapter problems. Mathematical Foundations for Linear Circuits and Systems in Engineering is written for upper undergraduate and first-year graduate students in the fields of electrical and mechanical engineering. This book is also a reference for electrical, mechanical, and computer engineers as well as applied mathematicians. John J. Shynk, PhD, is Professor of Electrical and Computer Engineering at the University of California, Santa Barbara. He was a Member of Technical Staff at Bell Laboratories, and received degrees in systems engineering, electrical engineering, and statistics from Boston University and Stanford University.
Introduction To Maple
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Author : Andre HECK
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-04-08
Introduction To Maple written by Andre HECK 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 2003-04-08 with Computers categories.
This is a fully revised edition of the best-selling Introduction to Maple. The book presents the modern computer algebra system Maple, teaching the reader not only what can be done by Maple, but also how and why it can be done. The book also provides the necessary background for those who want the most of Maple or want to extend its built-in knowledge. Emphasis is on understanding the Maple system more than on factual knowledge of built-in possibilities. To this end, the book contains both elementary and more sophisticated examples as well as many exercises. The typical reader should have a background in mathematics at the intermediate level. Andre Heck began developing and teaching Maple courses at the University of Nijmegen in 1987. In 1989 he was appointed managing director of the CAN Expertise Center in Amsterdam. CAN, Computer Algebra in the Netherlands, stimulates and coordinates the use of computer algebra in education and research. In 1996 the CAN Expertise Center was integrated into the Faculty of Science at the University of Amsterdam, into what became the AMSTEL Institute. The institute program focuses on the innovation of computer activities in mathematics and science education on all levels of education. The author is actively involved in the research and development aimed at the integrated computer learning environment Coach for mathematics and science education at secondary school level.
Delay Ordinary And Partial Differential Equations
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Author : Andrei D. Polyanin
language : en
Publisher: CRC Press
Release Date : 2023-08-28
Delay Ordinary And Partial Differential Equations written by Andrei D. Polyanin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-28 with Mathematics categories.
Delay Ordinary and Partial Differential Equations is devoted to linear and nonlinear ordinary and partial differential equations with constant and variable delay. It considers qualitative features of delay differential equations and formulates typical problem statements. Exact, approximate analytical and numerical methods for solving such equations are described, including the method of steps, methods of integral transformations, method of regular expansion in a small parameter, method of matched asymptotic expansions, iteration-type methods, Adomian decomposition method, collocation method, Galerkin-type projection methods, Euler and Runge-Kutta methods, shooting method, method of lines, finite-difference methods for PDEs, methods of generalized and functional separation of variables, method of functional constraints, method of generating equations, and more. The presentation of the theoretical material is accompanied by examples of the practical application of methods to obtain the desired solutions. Exact solutions are constructed for many nonlinear delay reaction-diffusion and wave-type PDEs that depend on one or more arbitrary functions. A review is given of the most common mathematical models with delay used in population theory, biology, medicine, economics, and other applications. The book contains much new material previously unpublished in monographs. It is intended for a broad audience of scientists, university professors, and graduate and postgraduate students specializing in applied and computational mathematics, mathematical physics, mechanics, control theory, biology, medicine, chemical technology, ecology, economics, and other disciplines. Individual sections of the book and examples are suitable for lecture courses on applied mathematics, mathematical physics, and differential equations for delivering special courses and for practical training.
Electrimacs 2019
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Author : Walter Zamboni
language : en
Publisher: Springer Nature
Release Date : 2020-04-25
Electrimacs 2019 written by Walter Zamboni and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-25 with Science categories.
This book collects a selection of papers presented at ELECTRIMACS 2019, the 13th international conference of the IMACS TC1 Committee, held in Salerno, Italy, on 21st-23rd May 2019. The conference papers deal with modelling, simulation, analysis, control, power management, design optimization, identification and diagnostics in electrical power engineering. The main application fields include electric machines and electromagnetic devices, power electronics, transportation systems, smart grids, electric and hybrid vehicles, renewable energy systems, energy storage, batteries, supercapacitors and fuel cells, and wireless power transfer. The contributions included in Volume 1 are particularly focused on electrical engineering simulation aspects and innovative applications.
Fluid Mechanics Of Viscoplasticity
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Author : Raja R. Huilgol
language : en
Publisher: Springer Nature
Release Date : 2022-04-14
Fluid Mechanics Of Viscoplasticity written by Raja R. Huilgol and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-14 with Technology & Engineering categories.
This book considers the kinematics and dynamics of the flows of fluids exhibiting a yield stress. Continuum mechanics governing the fluid mechanics is described. Two chapters are dedicated to analytical solutions to several steady and unsteady flows of viscoplastic fluids, including flows with pressure-dependent rheological parameters. Perturbation methods, variational inequalities to solve fluid flow problems, and the use of energy methods are discussed. Numerical modeling using augmented Lagrangian, operator splitting, finite difference, and lattice Boltzmann methods are employed. The second edition provides new sections on flows of yield stress fluids with pressure-dependent rheological parameters, on flows with wall slip, and on deriving the fundamental equations for Boltzmann lattice materials. Furthermore new material on the lubrication approximation and applications of finite differences has been added.