Elementary Functions
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Elementary Theory Of Analytic Functions Of One Or Several Complex Variables
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Author : Henri Cartan
language : en
Publisher: Courier Corporation
Release Date : 2013-04-22
Elementary Theory Of Analytic Functions Of One Or Several Complex Variables written by Henri Cartan and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-22 with Mathematics categories.
Basic treatment includes existence theorem for solutions of differential systems where data is analytic, holomorphic functions, Cauchy's integral, Taylor and Laurent expansions, more. Exercises. 1973 edition.
Functions Of A Real Variable
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Author : N. Bourbaki
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Functions Of A Real Variable written by N. Bourbaki 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 2013-12-01 with Mathematics categories.
This book is an English translation of the last French edition of Bourbaki’s Fonctions d'une Variable Réelle. The first chapter is devoted to derivatives, Taylor expansions, the finite increments theorem, convex functions. In the second chapter, primitives and integrals (on arbitrary intervals) are studied, as well as their dependence with respect to parameters. Classical functions (exponential, logarithmic, circular and inverse circular) are investigated in the third chapter. The fourth chapter gives a thorough treatment of differential equations (existence and unicity properties of solutions, approximate solutions, dependence on parameters) and of systems of linear differential equations. The local study of functions (comparison relations, asymptotic expansions) is treated in chapter V, with an appendix on Hardy fields. The theory of generalized Taylor expansions and the Euler-MacLaurin formula are presented in the sixth chapter, and applied in the last one to thestudy of the Gamma function on the real line as well as on the complex plane. Although the topics of the book are mainly of an advanced undergraduate level, they are presented in the generality needed for more advanced purposes: functions allowed to take values in topological vector spaces, asymptotic expansions are treated on a filtered set equipped with a comparison scale, theorems on the dependence on parameters of differential equations are directly applicable to the study of flows of vector fields on differential manifolds, etc.
Elementary Functions
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Author : Jean-Michel Muller
language : en
Publisher: Birkhäuser
Release Date : 2016-11-16
Elementary Functions written by Jean-Michel Muller and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-16 with Computers categories.
This textbook presents the concepts and tools necessary to understand, build, and implement algorithms for computing elementary functions (e.g., logarithms, exponentials, and the trigonometric functions). Both hardware- and software-oriented algorithms are included, along with issues related to accurate floating-point implementation. This third edition has been updated and expanded to incorporate the most recent advances in the field, new elementary function algorithms, and function software. After a preliminary chapter that briefly introduces some fundamental concepts of computer arithmetic, such as floating-point arithmetic and redundant number systems, the text is divided into three main parts. Part I considers the computation of elementary functions using algorithms based on polynomial or rational approximations and using table-based methods; the final chapter in this section deals with basic principles of multiple-precision arithmetic. Part II is devoted to a presentation of “shift-and-add” algorithms (hardware-oriented algorithms that use additions and shifts only). Issues related to accuracy, including range reduction, preservation of monotonicity, and correct rounding, as well as some examples of implementation are explored in Part III. Numerous examples of command lines and full programs are provided throughout for various software packages, including Maple, Sollya, and Gappa. New to this edition are an in-depth overview of the IEEE-754-2008 standard for floating-point arithmetic; a section on using double- and triple-word numbers; a presentation of new tools for designing accurate function software; and a section on the Toom-Cook family of multiplication algorithms. The techniques presented in this book will be of interest to implementers of elementary function libraries or circuits and programmers of numerical applications. Additionally, graduate and advanced undergraduate students, professionals, and researchers in scientific computing, numerical analysis, software engineering, and computer engineering will find this a useful reference and resource. PRAISE FOR PREVIOUS EDITIONS “[T]his book seems like an essential reference for the experts (which I'm not). More importantly, this is an interesting book for the curious (which I am). In this case, you'll probably learn many interesting things from this book. If you teach numerical analysis or approximation theory, then this book will give you some good examples to discuss in class." — MAA Reviews (Review of Second Edition) "The rich content of ideas sketched or presented in some detail in this book is supplemented by a list of over three hundred references, most of them of 1980 or more recent. The book also contains some relevant typical programs." — Zentralblatt MATH (Review of Second Edition) “I think that the book will be very valuable to students both in numerical analysis and in computer science. I found [it to be] well written and containing much interesting material, most of the time disseminated in specialized papers published in specialized journals difficult to find." — Numerical Algorithms (Review of First Edition)
Elementary Functions
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Author : William Wooton
language : en
Publisher:
Release Date : 1975
Elementary Functions written by William Wooton and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Mathematics categories.
Differential And Integral Calculus Volume 1
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Author : Richard Courant
language : en
Publisher: John Wiley & Sons
Release Date : 2011-08-15
Differential And Integral Calculus Volume 1 written by Richard Courant 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 2011-08-15 with Mathematics categories.
The classic introduction to the fundamentals of calculus Richard Courant's classic text Differential and Integral Calculus is an essential text for those preparing for a career in physics or applied math. Volume 1 introduces the foundational concepts of "function" and "limit", and offers detailed explanations that illustrate the "why" as well as the "how". Comprehensive coverage of the basics of integrals and differentials includes their applications as well as clearly-defined techniques and essential theorems. Multiple appendices provide supplementary explanation and author notes, as well as solutions and hints for all in-text problems.
The Mathematical Function Computation Handbook
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Author : Nelson H.F. Beebe
language : en
Publisher: Springer
Release Date : 2017-08-20
The Mathematical Function Computation Handbook written by Nelson H.F. Beebe and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-20 with Computers categories.
This highly comprehensive handbook provides a substantial advance in the computation of elementary and special functions of mathematics, extending the function coverage of major programming languages well beyond their international standards, including full support for decimal floating-point arithmetic. Written with clarity and focusing on the C language, the work pays extensive attention to little-understood aspects of floating-point and integer arithmetic, and to software portability, as well as to important historical architectures. It extends support to a future 256-bit, floating-point format offering 70 decimal digits of precision. Select Topics and Features: references an exceptionally useful, author-maintained MathCW website, containing source code for the book’s software, compiled libraries for numerous systems, pre-built C compilers, and other related materials; offers a unique approach to covering mathematical-function computation using decimal arithmetic; provides extremely versatile appendices for interfaces to numerous other languages: Ada, C#, C++, Fortran, Java, and Pascal; presupposes only basic familiarity with computer programming in a common language, as well as early level algebra; supplies a library that readily adapts for existing scripting languages, with minimal effort; supports both binary and decimal arithmetic, in up to 10 different floating-point formats; covers a significant portion (with highly accurate implementations) of the U.S National Institute of Standards and Technology’s 10-year project to codify mathematical functions. This highly practical text/reference is an invaluable tool for advanced undergraduates, recording many lessons of the intermingled history of computer hardw are and software, numerical algorithms, and mathematics. In addition, professional numerical analysts and others will find the handbook of real interest and utility because it builds on research by the mathematical software community over the last four decades.
An Elementary Treatise On Elliptic Functions
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Author : Arthur Cayley
language : en
Publisher:
Release Date : 1895
An Elementary Treatise On Elliptic Functions written by Arthur Cayley and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1895 with Elliptic functions categories.
Elementary Theory Of L Functions And Eisenstein Series
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Author : Haruzo Hida
language : en
Publisher: Cambridge University Press
Release Date : 1993-02-11
Elementary Theory Of L Functions And Eisenstein Series written by Haruzo Hida and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-02-11 with Mathematics categories.
The theory of p-adic and classic modular forms, and the study of arithmetic and p-adic L-functions has proved to be a fruitful area of mathematics over the last decade. Professor Hida has given courses on these topics in the USA, Japan, and in France, and in this book provides the reader with an elementary but detailed insight into the theory of L-functions. The presentation is self contained and concise, and the subject is approached using only basic tools from complex analysis and cohomology theory. Graduate students wishing to know more about L-functions will find that this book offers a unique introduction to this fascinating branch of mathematics.
Integration In Finite Terms Fundamental Sources
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Author : Clemens G. Raab
language : en
Publisher: Springer Nature
Release Date : 2022-06-06
Integration In Finite Terms Fundamental Sources written by Clemens G. Raab and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-06 with Computers categories.
This volume gives an up-to-date review of the subject Integration in Finite Terms. The book collects four significant texts together with an extensive bibliography and commentaries discussing these works and their impact. These texts, either out of print or never published before, are fundamental to the subject of the book. Applications in combinatorics and physics have aroused a renewed interest in this well-developed area devoted to finding solutions of differential equations and, in particular, antiderivatives, expressible in terms of classes of elementary and special functions.
Complex Variables Theory And Applications
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Author : Mr. Rohit Manglik
language : en
Publisher: EduGorilla Publication
Release Date : 2023-06-23
Complex Variables Theory And Applications written by Mr. Rohit Manglik and has been published by EduGorilla Publication this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-23 with Mathematics categories.
Covers complex number theory and its applications in engineering and physical sciences.