Collocation Methods for Volterra Integral and Related Functional Differential Equations

Author: Hermann Brunner
Publisher: Cambridge University Press
ISBN: 0521806151
Release Date: 2004-11-15
Genre: Mathematics

Collocation based on piecewise polynomial approximation represents a powerful class of methods for the numerical solution of initial-value problems for functional differential and integral equations arising in a wide spectrum of applications, including biological and physical phenomena. The present book introduces the reader to the general principles underlying these methods and then describes in detail their convergence properties when applied to ordinary differential equations, functional equations with (Volterra type) memory terms, delay equations, and differential-algebraic and integral-algebraic equations. Each chapter starts with a self-contained introduction to the relevant theory of the class of equations under consideration. Numerous exercises and examples are supplied, along with extensive historical and bibliographical notes utilising the vast annotated reference list of over 1300 items. In sum, Hermann Brunner has written a treatise that can serve as an introduction for students, a guide for users, and a comprehensive resource for experts.

A Concise History of Mathematics

Author: Dirk Jan Struik
Publisher: Courier Corporation
ISBN: 0486602559
Release Date: 1967
Genre: Mathematics

This compact, well-written history covers major mathematical ideas and techniques from the ancient Near East to 20th-century computer theory, surveying the works of Archimedes, Pascal, Gauss, Hilbert, and many others. "The author's ability as a first-class historian as well as an able mathematician has enabled him to produce a work which is unquestionably one of the best." — Nature.

A Concise History of Mathematics

Author: Dirk J. Struik
Publisher: Courier Corporation
ISBN: 9780486138886
Release Date: 2012-06-28
Genre: Science

Compact, well-written survey ranges from the ancient Near East to 20th-century computer theory, covering Archimedes, Pascal, Gauss, Hilbert, and many others. "A work which is unquestionably one of the best." — Nature.

The VNR Concise Encyclopedia of Mathematics

Author: W. Gellert
Publisher: Springer Science & Business Media
ISBN: 9789401169820
Release Date: 2012-12-06
Genre: Juvenile Nonfiction

It is commonplace that in our time sc:iem:e and technology cannot be mastered without the tools of mathematics; but the same applies to an ever growing extent to many domains of everyday life, not least owing to the spread of cybernetic methods and arguments. As a consequence, there is a wide demand for a survey of the results of mathematics. for an unconventional approach that would also make it possible to fill gaps in one's knowledge. We do not think that a mere juxtaposition of theorems or a collection of formulae would be suitable for this purpose, because this would over· emphasize the symbolic language of signs and letters rather than the mathematical idea, the only thing that really matters. Our task was to describe mathematical interrelations as briefly and precisely as possible. In view of the overwhelming amount of material it goes without saying that we did not just compile details from the numerous text-books for individual branches: what we were aiming at is to smooth out the access to the specialist literature for as many readers as possible. Since well over 700000 copies of the German edition of this book have been sold, we hope to have achieved our difficult goal. Colours are used extensively to help the reader. Important definitions and groups of formulae are on a yellow background, examples on blue, and theorems on red.

Concise Encyclopedia of Special Education

Author: Cecil R. Reynolds
Publisher: John Wiley and Sons
ISBN: 0471652512
Release Date: 2004-03-25
Genre: Business & Economics

The Concise Encyclopedia of Special Education, Second Edition is a comprehensive resource for those working in the fields of special education research and practice. Featuring reviews of assessment instruments and teaching approaches, legal issues, overviews of specific learning disabilities, dozens of biographies, and more, this complete desk reference is an indispensable guide for professionals, academics, and students alike. Named an American Library Association Top 25 Reference of the Year in its First Edition, The Concise Encyclopedia serves as an important reference for the education of handicapped and other exceptional children. Written and edited by highly regarded and respected experts in the fields of special education and psychology, this authoritative resource guide provides a reference base for educators as well as professionals in the areas of psychology, neuropsychology, medicine, health care, social work and law. Additionally, this acclaimed reference work is essential for administrators, psychologists, diagnosticians, and school counselors, as well as parents of the handicapped themselves. What's new in this edition Comprehensive coverage of new legislation such as Individuals with Disabilities Act (IDEA) and the Americans with Disabilities Act Cultural competence in Special Education, including new material on culturally/linguistically diverse students Many new entries including notable biographies, new service delivery systems, special education laws, new assessment instruments, cross-cultural issues, neuropsychology, and use of the Internet in research and service delivery. Some of the topics covered Academic assessment Achievement tests Addictions Bilingual education Child and adolescent behavior management Counseling with individuals and families with disabilities Early childhood education Gifted education Intelligence tests Mathematics disabilities Psychoeducational methods Rehabilitation Socioeconomic status Special education parent and student rights Traumatic brain injury

Mathematical Handbook for Scientists and Engineers

Author: Granino A. Korn
Publisher: Courier Corporation
ISBN: 9780486320236
Release Date: 2013-04-26
Genre: Technology & Engineering

Convenient access to information from every area of mathematics: Fourier transforms, Z transforms, linear and nonlinear programming, calculus of variations, random-process theory, special functions, combinatorial analysis, game theory, much more.

The VNR Concise Encyclopedia of Mathematics

Author: Walter Gellert
Publisher: Springer Science & Business Media
ISBN: STANFORD:36105032648516
Release Date: 1977-01-01
Genre: Mathematics

A comprehensive color-coded compilation of information on elementary and higher mathematics and aspects of contemporary mathematics includes scores of worked-out problems, definitions, and theorems.

Numerical Solution of Ordinary Differential Equations

Author: Kendall Atkinson
Publisher: John Wiley & Sons
ISBN: 9781118164525
Release Date: 2011-10-24
Genre: Mathematics

A concise introduction to numerical methodsand the mathematicalframework neededto understand their performance Numerical Solution of Ordinary Differential Equationspresents a complete and easy-to-follow introduction to classicaltopics in the numerical solution of ordinary differentialequations. The book's approach not only explains the presentedmathematics, but also helps readers understand how these numericalmethods are used to solve real-world problems. Unifying perspectives are provided throughout the text, bringingtogether and categorizing different types of problems in order tohelp readers comprehend the applications of ordinary differentialequations. In addition, the authors' collective academic experienceensures a coherent and accessible discussion of key topics,including: Euler's method Taylor and Runge-Kutta methods General error analysis for multi-step methods Stiff differential equations Differential algebraic equations Two-point boundary value problems Volterra integral equations Each chapter features problem sets that enable readers to testand build their knowledge of the presented methods, and a relatedWeb site features MATLAB® programs that facilitate theexploration of numerical methods in greater depth. Detailedreferences outline additional literature on both analytical andnumerical aspects of ordinary differential equations for furtherexploration of individual topics. Numerical Solution of Ordinary Differential Equations isan excellent textbook for courses on the numerical solution ofdifferential equations at the upper-undergraduate and beginninggraduate levels. It also serves as a valuable reference forresearchers in the fields of mathematics and engineering.

Algorithmen Eine Einf hrung

Author: Thomas H. Cormen
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 9783110522013
Release Date: 2013-01-01
Genre: Computers

Der "Cormen" bietet eine umfassende und vielseitige Einführung in das moderne Studium von Algorithmen. Es stellt viele Algorithmen Schritt für Schritt vor, behandelt sie detailliert und macht deren Entwurf und deren Analyse allen Leserschichten zugänglich. Sorgfältige Erklärungen zur notwendigen Mathematik helfen, die Analyse der Algorithmen zu verstehen. Den Autoren ist es dabei geglückt, Erklärungen elementar zu halten, ohne auf Tiefe oder mathematische Exaktheit zu verzichten. Jedes der weitgehend eigenständig gestalteten Kapitel stellt einen Algorithmus, eine Entwurfstechnik, ein Anwendungsgebiet oder ein verwandtes Thema vor. Algorithmen werden beschrieben und in Pseudocode entworfen, der für jeden lesbar sein sollte, der schon selbst ein wenig programmiert hat. Zahlreiche Abbildungen verdeutlichen, wie die Algorithmen arbeiten. Ebenfalls angesprochen werden Belange der Implementierung und andere technische Fragen, wobei, da Effizienz als Entwurfskriterium betont wird, die Ausführungen eine sorgfältige Analyse der Laufzeiten der Programme mit ein schließen. Über 1000 Übungen und Problemstellungen und ein umfangreiches Quellen- und Literaturverzeichnis komplettieren das Lehrbuch, dass durch das ganze Studium, aber auch noch danach als mathematisches Nachschlagewerk oder als technisches Handbuch nützlich ist. Für die dritte Auflage wurde das gesamte Buch aktualisiert. Die Änderungen sind vielfältig und umfassen insbesondere neue Kapitel, überarbeiteten Pseudocode, didaktische Verbesserungen und einen lebhafteren Schreibstil. So wurden etwa - neue Kapitel zu van-Emde-Boas-Bäume und mehrfädigen (engl.: multithreaded) Algorithmen aufgenommen, - das Kapitel zu Rekursionsgleichungen überarbeitet, sodass es nunmehr die Teile-und-Beherrsche-Methode besser abdeckt, - die Betrachtungen zu dynamischer Programmierung und Greedy-Algorithmen überarbeitet; Memoisation und der Begriff des Teilproblem-Graphen als eine Möglichkeit, die Laufzeit eines auf dynamischer Programmierung beruhender Algorithmus zu verstehen, werden eingeführt. - 100 neue Übungsaufgaben und 28 neue Problemstellungen ergänzt. Umfangreiches Dozentenmaterial (auf englisch) ist über die Website des US-Verlags verfügbar.

Discrete Fourier Analysis

Author: M. W. Wong
Publisher: Springer Science & Business Media
ISBN: 9783034801164
Release Date: 2011-05-30
Genre: Mathematics

This textbook presents basic notions and techniques of Fourier analysis in discrete settings. Written in a concise style, it is interlaced with remarks, discussions and motivations from signal analysis. The first part is dedicated to topics related to the Fourier transform, including discrete time-frequency analysis and discrete wavelet analysis. Basic knowledge of linear algebra and calculus is the only prerequisite. The second part is built on Hilbert spaces and Fourier series and culminates in a section on pseudo-differential operators, providing a lucid introduction to this advanced topic in analysis. Some measure theory language is used, although most of this part is accessible to students familiar with an undergraduate course in real analysis. Discrete Fourier Analysis is aimed at advanced undergraduate and graduate students in mathematics and applied mathematics. Enhanced with exercises, it will be an excellent resource for the classroom as well as for self-study.

Choice

Author:
Publisher:
ISBN: UCSC:32106013736290
Release Date: 1998
Genre: Best books


Reelle und Komplexe Analysis

Author: Walter Rudin
Publisher: Walter de Gruyter
ISBN: 348659186X
Release Date: 2009
Genre: Analysis - Lehrbuch

Besonderen Wert legt Rudin darauf, dem Leser die Zusammenhänge unterschiedlicher Bereiche der Analysis zu vermitteln und so die Grundlage für ein umfassenderes Verständnis zu schaffen. Das Werk zeichnet sich durch seine wissenschaftliche Prägnanz und Genauigkeit aus und hat damit die Entwicklung der modernen Analysis in nachhaltiger Art und Weise beeinflusst. Der "Baby-Rudin" gehört weltweit zu den beliebtesten Lehrbüchern der Analysis und ist in 13 Sprachen übersetzt. 1993 wurde es mit dem renommierten Steele Prize for Mathematical Exposition der American Mathematical Society ausgezeichnet. Übersetzt von Uwe Krieg.