NIST Handbook of Mathematical Functions

Author: Frank W. J. Olver

Publisher: Cambridge University Press

ISBN: 0521192250

Category: Mathematics

Page: 951

View: 6948

The new standard reference on mathematical functions, replacing the classic but outdated handbook from Abramowitz and Stegun. Includes PDF version.

Formeln und Sätze für die Speziellen Funktionen der Mathematischen Physik

Author: Wilhelm Magnus,Fritz Oberhettinger

Publisher: Springer-Verlag

ISBN: 366241791X

Category: Science

Page: 172

View: 8499

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Asymptotic Methods for Integrals

Author: Nico M Temme

Publisher: World Scientific

ISBN: 9814612170

Category: Mathematics

Page: 628

View: 3378

This book gives introductory chapters on the classical basic and standard methods for asymptotic analysis, such as Watson's lemma, Laplace's method, the saddle point and steepest descent methods, stationary phase and Darboux's method. The methods, explained in great detail, will obtain asymptotic approximations of the well-known special functions of mathematical physics and probability theory. After these introductory chapters, the methods of uniform asymptotic analysis are described in which several parameters have influence on typical phenomena: turning points and transition points, coinciding saddle and singularities. In all these examples, the special functions are indicated that describe the peculiar behavior of the integrals. The text extensively covers the classical methods with an emphasis on how to obtain expansions, and how to use the results for numerical methods, in particular for approximating special functions. In this way, we work with a computational mind: how can we use certain expansions in numerical analysis and in computer programs, how can we compute coefficients, and so on. Contents:Basic Methods for IntegralsBasic Methods: Examples for Special FunctionsOther Methods for IntegralsUniform Methods for IntegralsUniform Methods for Laplace-Type IntegralsUniform Examples for Special FunctionsA Class of Cumulative Distribution Functions Readership: Researchers in applied mathematics, engineering, physics, mathematical statistics, probability theory and biology. The introductory parts and examples will be useful for post-graduate students in mathematics. Key Features:The book gives a complete overview of the classical asymptotic methods for integralsThe many examples give insight in the behavior of the well-known special functionsThe detailed explanations on how to obtain the coefficients in the expansions make the results useful for numerical applications, in particular, for computing special functionsThe many results on asymptotic representations of special functions supplement and extend those in the NIST Handbook of Mathematical FunctionsKeywords:Asymptotic Analysis;Approximation of Integrals;Asymptotic Approximations;Asymptotic Expansions;Steepest Descent Methods;Saddle Point Methods;Stationary Phase Method;Special Functions;Numerical Approximation of Special Functions;Cumulative Distribution FunctionsReviews: “The book is a useful contribution to the literature. It contains many asymptotic formulas that can be used by practitioners.” Zentralblatt MATH

Springer-Taschenbuch der Mathematik

Begründet von I.N. Bronstein und K.A. Semendjaew Weitergeführt von G. Grosche, V. Ziegler und D. Ziegler Herausgegeben von E. Zeidler

Author: Eberhard Zeidler

Publisher: Springer-Verlag

ISBN: 3834823597

Category: Mathematics

Page: 1310

View: 1537

Das Vieweg+Teubner Taschenbuch der Mathematik erfüllt aktuell, umfassend und kompakt alle Erwartungen, die an ein mathematisches Nachschlagewerk gestellt werden. Es vermittelt ein lebendiges und modernes Bild der heutigen Mathematik. Als Taschenbuch begleitet es die Bachelor-Studierenden vom ersten Semester bis zur letzten Prüfung und der Praktiker nutzt es als ständiges und unentbehrliches Nachschlagewerk in seinem Berufsalltag. Das Taschenbuch bietet alles, was in Bachelor-Studiengängen im Haupt- und Nebenfach Mathematik benötigt wird. Der Text für diese Ausgabe wurde stark überarbeitet. Zu spezielle Inhalte wurden herausgenommen und dafür Themen der Wirtschaftsmathematik und Algorithmik hinzugenommen. Das Vieweg+Teubner Handbuch der Mathematik (eAusgabe) enthält darüberhinaus ergänzendes und weiterführendes Material für das Masterstudium.

Mathematical Software - ICMS 2010

Third International Congress on Mathematical Software, Kobe, Japan, September 13-17, 2010, Proceedings

Author: Komei Fukuda,Joris van der Hoeven,Michael Joswig,Nobuki Takayama

Publisher: Springer Science & Business Media

ISBN: 3642155812

Category: Computers

Page: 368

View: 4029

The ICMS Developer's Meeting is an international congress for which the main theme is mathematical software. The 2010 meeting was the third of a series of meetings of similar theme, the ?rst being held in Beijing, China in 2002,and the second in Castro-Urdiales, Spain in 2006. The ?eld of mathematics has numerous branches, and in each branch we ?nd that algorithms, and also implementations and applications of software s- tems, are studied. Researchers who endeavor to make such studies also have international meetings within their speci'c branches of mathematics, and these meetings have made signi'cant contributions to the ?elds in which they lie. The ICMS (International Congresseson Mathematical Software), on the other hand, is a general (not branch speci'c) meeting on mathematical software, which is held every four years, and is a rare opportunity for developers of mathematical softwarefrom di'erent branchesof mathematics, as well as mathematicians who are interested in mathematical software, to gather together.

The Mathematical-Function Computation Handbook

Programming Using the MathCW Portable Software Library

Author: Nelson H.F. Beebe

Publisher: Springer

ISBN: 3319641107

Category: Computers

Page: 1115

View: 9641

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.

Intelligent Computer Mathematics

MKM, Calculemus, DML, and Systems and Projects 2013, Held as Part of CICM 2013, Bath, UK, July 8-12, 2013, Proceedings

Author: Jacques Carette,David Aspinall,Christoph Lange,Petr Sojka,Wolfgang Windsteiger

Publisher: Springer

ISBN: 3642393209

Category: Computers

Page: 384

View: 6220

This book constitutes the joint refereed proceedings of the 20th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning, Calculemus 2013, 6th International Workshop on Digital Mathematics Libraries, DML 2013, Systems and Projects, held in Bath, UK as part of CICM 2013, the Conferences on Intelligent Computer Mathematics. The 7 revised full papers out of 18 submissions for MKM 2013, 5 revised full papers out of 12 submissions for Calculemus 2013, 6 revised full papers out of 8 submissions for DML 2013, and 12 revised full papers out of 16 submissions for Systems and Project track presented together with 3 invited talks were carefully reviewed and selected, resulting in 33 papers from a total of 73 submissions.

Mittag-Leffler Functions, Related Topics and Applications

Author: Rudolf Gorenflo,Anatoly A. Kilbas,Francesco Mainardi,Sergei V. Rogosin

Publisher: Springer

ISBN: 3662439301

Category: Mathematics

Page: 443

View: 2694

As a result of researchers’ and scientists’ increasing interest in pure as well as applied mathematics in non-conventional models, particularly those using fractional calculus, Mittag-Leffler functions have recently caught the interest of the scientific community. Focusing on the theory of the Mittag-Leffler functions, the present volume offers a self-contained, comprehensive treatment, ranging from rather elementary matters to the latest research results. In addition to the theory the authors devote some sections of the work to the applications, treating various situations and processes in viscoelasticity, physics, hydrodynamics, diffusion and wave phenomena, as well as stochastics. In particular the Mittag-Leffler functions allow us to describe phenomena in processes that progress or decay too slowly to be represented by classical functions like the exponential function and its successors. The book is intended for a broad audience, comprising graduate students, university instructors and scientists in the field of pure and applied mathematics, as well as researchers in applied sciences like mathematical physics, theoretical chemistry, bio-mathematics, theory of control and several other related areas.

Tutorium Quantenfeldtheorie

Was Sie schon immer über QFT wissen wollten, aber bisher nicht zu fragen wagten

Author: Lisa Edelhäuser,Alexander Knochel

Publisher: Springer-Verlag

ISBN: 3642376762

Category: Science

Page: 539

View: 5262

Dieses Buch richtet sich an alle, die sich schon immer gefragt haben, wie die kanonische Quantisierung, die LSZ-Reduktionsformel, Pfadintegrale, Feynman-Graphen und die Renormierung miteinander zusammenhängen. Als locker geschriebene Begleitlektüre zu Vorlesungen über Quantenfeldtheorie oder zum Selbststudium geeignet, gibt sich das Buch gesprächig und liefert Rechentricks und Erklärungen, die für Einsteiger sehr hilfreich sind. Im ersten Teil werden anhand von Skalarfeldern grundlegende Konzepte von der klassischen Feldtheorie bis zur Renormierung eingeführt. Der zweite Teil verallgemeinert diese für Felder mit Spin und legt mit der Einführung des Eichprinzips die Grundlagen für den dritten Teil. Hier werden „Anwendungen auf die reale Welt“ behandelt: Die Quantenelektrodynamik und ihre Renormierung, sowie das Standardmodell der Teilchenphysik und der Higgs-Mechanismus. Durch ausführlich vorgerechnete und in den Text eingebundene Aufgaben eignet sich das Tutorium sowohl zum schnellen Nachschlagen von „Rezepten“, als auch als Lektüre und Arbeitsbuch für Studierende, die eine tiefer gehende Diskussion der Quantenfeldtheorie suchen. Kurze Kapitel zu Grundlagenthemen wie Lie-Algebren und -Gruppen, Relativitätstheorie, Funktionentheorie und Funktionalableitungen ergänzen das Buch. Aus dem Inhalt: Kanonische Quantisierung Green’sche Funktionen, Pfadintegrale und erzeugende Funktionale Feynman-Graphen und Wick-Theorem Regularisierung und Renormierung Eichsymmetrien, Ward-Identitäten und QED Standardmodell der Teilchenphysik und Higgs-Mechanismus Lisa Edelhäuser hat in Würzburg Physik studiert und dort 2012 in theoretischer Elementarteilchenphysik promoviert. Sie war danach als wissenschaftliche Mitarbeiterin an der RWTH Aachen tätig. bAlexander Knochel /bhat in Würzburg und New York Physik studiert und 2009 in Würzburg in theoretischer Elementarteilchenphysik promoviert. Er war als wissenschaftlicher Mitarbeiter an den Universitäten Freiburg, Heidelberg und der RWTH Aachen tätig und hat dabei langjährige Erfahrung bei der Betreuung von Tutorien zur QFT I und II gesammelt.


Algorithmen, Computer, Arithmetik

Author: Jörg Arndt,Christoph Haenel

Publisher: Springer-Verlag

ISBN: 366209360X

Category: Computers

Page: 264

View: 4143


Die Gammafunktion

Author: Niels Nielsen

Publisher: American Mathematical Soc.

ISBN: 9780821838365

Category: Mathematics

Page: 432

View: 1751

This title consists of both original volumes of this classic, now published as one. The first volume is a handbook of the theory of the gamma function. The first part of this volume gives an elementary presentation of the fundamental properties of the gamma function (and related functions) as applications of the theory of analytic functions. The second part covers properties related to the integral representations for $\Gamma(x)$. The third part explores the properties of functions defined via series of factorials: $\Omega(x)=\sum s! a_s/(x(x+1)\ldots(x+s))$, with applications to the gamma function. The Handbook is an often-cited reference in the literature on the gamma function and other transcendental functions. The second (and shorter) volume covers the theory of the logarithmic integral $\mathrm{li}(x)$ and certain related functions. Specific topics include integral representations, asymptotic series, and continued fractions.


Author: Timothy Gowers

Publisher: N.A

ISBN: 9783150187067


Page: 207

View: 6671


1089 oder das Wunder der Zahlen

eine Reise in die Welt der Mathematik

Author: David J. Acheson

Publisher: N.A

ISBN: 9783866470200


Page: 189

View: 2388

Das Buch beginnt mit einem alten Zaubertrick - Man nehme eine 3-stellige Zahl, etwa 782, kehre sie um, ziehe die kleinere von der größeren ab und addiere dazu die Umkehrung. Also - 782 - 287 = 495, dann 495 + 594. Und schon ist man mitten in der Wunderwelt der Mathematik, denn das Ergebnis ist immer - 1089. Mit solchen und vielen weiteren Beispielen aus Alltag, Geschichte und Wissenschaft gelingt es David Acheson, die faszinierende Welt der Mathematik zu erschließen - ein geistreicher Überblick, eine für jeden verständliche Einführung.

Klassische Elektrodynamik

Author: John David Jackson

Publisher: Walter de Gruyter

ISBN: 311033447X

Category: Science

Page: 957

View: 3897

The German translation of this classic of theoretical physics is now available in a further revised edition. This renders theoretical electrodynamics even more comprehensible than before. Unique to this textbook of electrodynamics are the incomparably large number of calculated examples and special cases and the many exercises at the end of each chapter.