A Brief History Of Analysis
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A History Of Analysis
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Author : Hans Niels Jahnke
language : en
Publisher: American Mathematical Soc.
Release Date :
A History Of Analysis written by Hans Niels Jahnke and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
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.
Analysis By Its History
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Author : Ernst Hairer
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-30
Analysis By Its History written by Ernst Hairer 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 2008-05-30 with Mathematics categories.
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.
A Brief History Of Analysis
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Author : Detlef D. Spalt
language : en
Publisher: Springer Nature
Release Date : 2022-08-02
A Brief History Of Analysis written by Detlef D. Spalt and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-02 with Mathematics categories.
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.
3000 Years Of Analysis
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Author : Thomas Sonar
language : en
Publisher: Springer Nature
Release Date : 2020-12-27
3000 Years Of Analysis written by Thomas Sonar and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-27 with Mathematics categories.
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.
A History Of Vector Analysis
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Author : Michael J. Crowe
language : en
Publisher: Courier Corporation
Release Date : 1994-01-01
A History Of Vector Analysis written by Michael J. Crowe and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01-01 with Mathematics categories.
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.
The Real And The Complex A History Of Analysis In The 19th Century
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Author : Jeremy Gray
language : en
Publisher: Springer
Release Date : 2015-10-14
The Real And The Complex A History Of Analysis In The 19th Century written by Jeremy Gray and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-14 with Mathematics categories.
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.
How We Got From There To Here
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Author : Robert Rogers
language : en
Publisher:
Release Date : 2014
How We Got From There To Here written by Robert Rogers and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.
Analysis And Synthesis In Mathematics
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Author : Michael Otte
language : en
Publisher: Springer Science & Business Media
Release Date : 1997
Analysis And Synthesis In Mathematics written by Michael Otte 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 1997 with History categories.
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.
Infinite Series In A History Of Analysis
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Author : Hans-Heinrich Körle
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2015-09-25
Infinite Series In A History Of Analysis written by Hans-Heinrich Körle and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-25 with Mathematics categories.
"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.
Space And Spatialization In Contemporary Music History And Analysis Ideas And Implementations
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Author : Maria Anna Harley
language : en
Publisher: Lulu.com
Release Date : 2016-06-08
Space And Spatialization In Contemporary Music History And Analysis Ideas And Implementations written by Maria Anna Harley and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-08 with categories.
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.