A Brief History Of Analysis

Author : Hans Niels Jahnke
Publisher : American Mathematical Soc.
Page : 436 pages
File Size : 44,9 Mb
Release : 2024-07-01
Category : Mathematics
ISBN : 0821890506

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A History of Analysis by Hans Niels Jahnke Pdf

Analysis as an independent subject was created as part of the scientific revolution in the seventeenth century. Kepler, Galileo, Descartes, Fermat, Huygens, Newton, and Leibniz, to name but a few, contributed to its genesis. Since the end of the seventeenth century, the historical progress of mathematical analysis has displayed unique vitality and momentum. No other mathematical field has so profoundly influenced the development of modern scientific thinking. Describing this multidimensional historical development requires an in-depth discussion which includes a reconstruction of general trends and an examination of the specific problems. This volume is designed as a collective work of authors who are proven experts in the history of mathematics. It clarifies the conceptual change that analysis underwent during its development while elucidating the influence of specific applications and describing the relevance of biographical and philosophical backgrounds. The first ten chapters of the book outline chronological development and the last three chapters survey the history of differential equations, the calculus of variations, and functional analysis. Special features are a separate chapter on the development of the theory of complex functions in the nineteenth century and two chapters on the influence of physics on analysis. One is about the origins of analytical mechanics, and one treats the development of boundary-value problems of mathematical physics (especially potential theory) in the nineteenth century. The book presents an accurate and very readable account of the history of analysis. Each chapter provides a comprehensive bibliography. Mathematical examples have been carefully chosen so that readers with a modest background in mathematics can follow them. It is suitable for mathematical historians and a general mathematical audience.

Author : Ernst Hairer,Gerhard Wanner
Publisher : Springer Science & Business Media
Page : 390 pages
File Size : 44,7 Mb
Release : 2008-05-30
Category : Mathematics
ISBN : 9780387770369

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Analysis by Its History by Ernst Hairer,Gerhard Wanner Pdf

This book presents first-year calculus roughly in the order in which it was first discovered. The first two chapters show how the ancient calculations of practical problems led to infinite series, differential and integral calculus and to differential equations. The establishment of mathematical rigour for these subjects in the 19th century for one and several variables is treated in chapters III and IV. Many quotations are included to give the flavor of the history. The text is complemented by a large number of examples, calculations and mathematical pictures and will provide stimulating and enjoyable reading for students, teachers, as well as researchers.

Author : Detlef D. Spalt
Publisher : Springer Nature
Page : 265 pages
File Size : 41,6 Mb
Release : 2022-08-02
Category : Mathematics
ISBN : 9783031006500

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A Brief History of Analysis by Detlef D. Spalt Pdf

This book explores the origins of mathematical analysis in an accessible, clear, and precise manner. Concepts such as function, continuity, and convergence are presented with a unique historical point of view. In part, this is accomplished by investigating the impact of and connections between famous figures, like Newton, Leibniz, Johann Bernoulli, Euler, and more. Of particular note is the treatment of Karl Weierstraß, whose concept of real numbers has been frequently overlooked until now. By providing such a broad yet detailed survey, this book examines how analysis was formed, how it has changed over time, and how it continues to evolve today. A Brief History of Analysis will appeal to a wide audience of students, instructors, and researchers who are interested in discovering new historical perspectives on otherwise familiar mathematical ideas.

Author : Thomas Sonar
Publisher : Springer Nature
Page : 706 pages
File Size : 41,6 Mb
Release : 2020-12-27
Category : Mathematics
ISBN : 9783030582234

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3000 Years of Analysis by Thomas Sonar Pdf

What exactly is analysis? What are infinitely small or infinitely large quantities? What are indivisibles and infinitesimals? What are real numbers, continuity, the continuum, differentials, and integrals? You’ll find the answers to these and other questions in this unique book! It explains in detail the origins and evolution of this important branch of mathematics, which Euler dubbed the “analysis of the infinite.” A wealth of diagrams, tables, color images and figures serve to illustrate the fascinating history of analysis from Antiquity to the present. Further, the content is presented in connection with the historical and cultural events of the respective epochs, the lives of the scholars seeking knowledge, and insights into the subfields of analysis they created and shaped, as well as the applications in virtually every aspect of modern life that were made possible by analysis.

Author : Michael J. Crowe
Publisher : Courier Corporation
Page : 306 pages
File Size : 41,6 Mb
Release : 1994-01-01
Category : Mathematics
ISBN : 9780486679105

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A History of Vector Analysis by Michael J. Crowe Pdf

Prize-winning study traces the rise of the vector concept from the discovery of complex numbers through the systems of hypercomplex numbers to the final acceptance around 1910 of the modern system of vector analysis.

Author : Jeremy Gray
Publisher : Springer
Page : 350 pages
File Size : 42,5 Mb
Release : 2015-10-14
Category : Mathematics
ISBN : 9783319237152

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The Real and the Complex: A History of Analysis in the 19th Century by Jeremy Gray Pdf

This book contains a history of real and complex analysis in the nineteenth century, from the work of Lagrange and Fourier to the origins of set theory and the modern foundations of analysis. It studies the works of many contributors including Gauss, Cauchy, Riemann, and Weierstrass. This book is unique owing to the treatment of real and complex analysis as overlapping, inter-related subjects, in keeping with how they were seen at the time. It is suitable as a course in the history of mathematics for students who have studied an introductory course in analysis, and will enrich any course in undergraduate real or complex analysis.

Author : Michael Otte,Marco Panza
Publisher : Springer Science & Business Media
Page : 476 pages
File Size : 50,5 Mb
Release : 1997
Category : History
ISBN : 0792345703

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Analysis and Synthesis in Mathematics by Michael Otte,Marco Panza Pdf

The book discusses the main interpretations of the classical distinction between analysis and synthesis with respect to mathematics. In the first part, this is discussed from a historical point of view, by considering different examples from the history of mathematics. In the second part, the question is considered from a philosophical point of view, and some new interpretations are proposed. Finally, in the third part, one of the editors discusses some common aspects of the different interpretations.

Author : Hans-Heinrich Körle
Publisher : Walter de Gruyter GmbH & Co KG
Page : 142 pages
File Size : 44,6 Mb
Release : 2015-09-25
Category : Mathematics
ISBN : 9783110359831

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Infinite Series in a History of Analysis by Hans-Heinrich Körle Pdf

"Higher mathematics" once pointed towards the involvement of infinity. This we label analysis. The ancient Greeks had helped it to a first high point when they mastered the infinite. The book traces the history of analysis along the risky route of serial procedures through antiquity. It took quite long for this type of mathematics to revive in our region. When and where it did, infinite series proved the driving force. Not until a good two millennia had gone by, would analysis head towards Greek rigor again. To follow all that trial, error and final accomplishment, is more than studying history: It provides touching, worthwhile access to advanced calculus. Moreover, some steps beyond convergence show infinite series to naturally fit a wider frame.

Author : Philippe Flajolet,Robert Sedgewick
Publisher : Cambridge University Press
Page : 825 pages
File Size : 42,5 Mb
Release : 2009-01-15
Category : Mathematics
ISBN : 9781139477161

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Analytic Combinatorics by Philippe Flajolet,Robert Sedgewick Pdf

Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.

Author : Robert S. Strichartz
Publisher : Jones & Bartlett Learning
Page : 764 pages
File Size : 51,8 Mb
Release : 2000
Category : Computers
ISBN : 0763714976

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The Way of Analysis by Robert S. Strichartz Pdf

The Way of Analysis gives a thorough account of real analysis in one or several variables, from the construction of the real number system to an introduction of the Lebesgue integral. The text provides proofs of all main results, as well as motivations, examples, applications, exercises, and formal chapter summaries. Additionally, there are three chapters on application of analysis, ordinary differential equations, Fourier series, and curves and surfaces to show how the techniques of analysis are used in concrete settings.

Author : Richard J Cook,Jerald F. Lawless
Publisher : CRC Press
Page : 524 pages
File Size : 45,9 Mb
Release : 2018-05-15
Category : Mathematics
ISBN : 9781351646055

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Multistate Models for the Analysis of Life History Data by Richard J Cook,Jerald F. Lawless Pdf

Multistate Models for the Analysis of Life History Data provides the first comprehensive treatment of multistate modeling and analysis, including parametric, nonparametric and semiparametric methods applicable to many types of life history data. Special models such as illness-death, competing risks and progressive processes are considered, as well as more complex models. The book provides both theoretical development and illustrations of analysis based on data from randomized trials and observational cohort studies in health research. It features: Discusses a wide range of applications of multistate models, Presents methods for both continuously and intermittently observed life history processes, Gives a thorough discussion of conditionally independent censoring and observation processes, Discusses models with random effects and joint models for two or more multistate processes, Discusses and illustrates software for multistate analysis that is available in R, Target audience includes those engaged in research and applications involving multistate models.

Author : Maria Anna Harley
Publisher : Lulu.com
Page : 483 pages
File Size : 47,8 Mb
Release : 2016-06-08
Category : Electronic
ISBN : 9780996398169

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Space and Spatialization in Contemporary Music: History and Analysis, Ideas and Implementations by Maria Anna Harley Pdf

This dissertation presents the history of space in the musical thought of the 20th­ century (from Kurth to Clifton, from Varese to Xenakis) and outlines the development of spatialization in the theory and practice of contemporary music (after 1950). The text emphasizes perceptual and temporal aspects of musical spatiality, thus reflecting the close connection of space and time in human experience. A new definition of spatialization draws from Ingarden's notion of the musical work; a typology of spatial designs embraces music for different acoustic environments, movements of performers and audiences, various positions of musicians in space, etc. The study of spatialization includes a survey of the composers's writings (lves, Boulez, Stockhausen, Cage, etc.) and an examination of their works. The final part presents three unique approaches to spatialization: Brant's simultaneity of sound layers, Xenakis's movement of sound, and Schafer's music of ritual and soundscape.

Author : Paul David Allison
Publisher : SAGE
Page : 92 pages
File Size : 49,8 Mb
Release : 1984-11
Category : Social Science
ISBN : 0803920555

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Event History Analysis by Paul David Allison Pdf

Drawing on recent "event history" analytical methods from biostatistics, engineering, and sociology, this clear and comprehensive monograph explains how longitudinal data can be used to study the causes of deaths, crimes, wars, and many other human events. Allison shows why ordinary multiple regression is not suited to analyze event history data, and demonstrates how innovative regression - like methods can overcome this problem. He then discusses the particular new methods that social scientists should find useful.

Author : Nathaniel Carter Towle
Publisher : Unknown
Page : 466 pages
File Size : 41,9 Mb
Release : 1860
Category : Constitutional history
ISBN : HARVARD:HX4H4M

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A History and Analysis of the Constitution of the United States by Nathaniel Carter Towle Pdf

Author : Barry Salt
Publisher : Unknown
Page : 453 pages
File Size : 40,6 Mb
Release : 2009
Category : Performing Arts
ISBN : 0950906654

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Film Style and Technology by Barry Salt Pdf

Film Style and Technology is a history of film style and its relationship to film technology. It also includes a theory of film analysis and demonstrates this theory using the films of Max Ophuls.