A 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.
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.
Traditions Of Analysis And Synthesis
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Author : William R. Newman
language : en
Publisher: Springer Nature
Release Date : 2024-12-23
Traditions Of Analysis And Synthesis written by William R. Newman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-23 with Science categories.
This open access book provides a fresh perspective on analysis and synthesis across several areas of inquiry. The two operations form a primary basis of modern laboratory science, ranging from the spectrographic analysis used in practically every scientific discipline today, to the naming of entire disciplines, such as synthetic organic chemistry. Despite their acknowledged significance, however, the history of analysis, synthesis, and their relations over the longue durée is poorly understood. Several volumes have been devoted to the history of analysis and synthesis in the sense that premodern mathematicians and philosophers used the terms, but very little work has been done on the tradition of material decomposition and recomposition and its relationship to mathematics and philosophy. The present volume brings together scholars in the history of medicine, mathematics, philosophy, chemistry, and alchemy to explore the ways in which these multiple disciplines understood and used analysis and synthesis as experimental, justificatory, and conceptual tools.
A History And Analysis Of The Constitution Of The United States
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Author : Nathaniel Carter Towle
language : en
Publisher:
Release Date : 1860
A History And Analysis Of The Constitution Of The United States written by Nathaniel Carter Towle and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1860 with Constitutional history categories.
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 History 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.
A History And Analysis Of The Constitution Of The United States With A Full Account Of The Confederations Which Preceded It Of The Debates And Acts Of The Convention Which Formed It Of The Judicial Decisions Which Have Construed It With Papers And Tables Illustrative Of The Action Of The Government And The People Under It
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Author : Nathaniel Carter Towle
language : en
Publisher:
Release Date : 1861
A History And Analysis Of The Constitution Of The United States With A Full Account Of The Confederations Which Preceded It Of The Debates And Acts Of The Convention Which Formed It Of The Judicial Decisions Which Have Construed It With Papers And Tables Illustrative Of The Action Of The Government And The People Under It written by Nathaniel Carter Towle and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1861 with Constitutional history categories.
Infinite Series In A History Of Analysis
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Author : Hans-Heinrich Körle
language : en
Publisher: Walter de Gruyter
Release Date : 2015-09
Infinite Series In A History Of Analysis written by Hans-Heinrich Körle and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09 with Mathematics categories.
Infinite series are the unifying thread that runs through the history of mathematical analysis. Ever since the 17th century, they have also been inseparably linked to infinitesimal calculus, and form its backbone. Because of the clarity of their structure, infinite series are a gratifying subject for didactics. The historical reflections, insights and outlooks in this book serve to deepen the student's understanding of analysis.
Real Analysis
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Author : Saul Stahl
language : en
Publisher: John Wiley & Sons
Release Date : 2012-01-10
Real Analysis written by Saul Stahl 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 2012-01-10 with Mathematics categories.
A provocative look at the tools and history of real analysis This new edition of Real Analysis: A Historical Approach continues to serve as an interesting read for students of analysis. Combining historical coverage with a superb introductory treatment, this book helps readers easily make the transition from concrete to abstract ideas. The book begins with an exciting sampling of classic and famous problems first posed by some of the greatest mathematicians of all time. Archimedes, Fermat, Newton, and Euler are each summoned in turn, illuminating the utility of infinite, power, and trigonometric series in both pure and applied mathematics. Next, Dr. Stahl develops the basic tools of advanced calculus, which introduce the various aspects of the completeness of the real number system as well as sequential continuity and differentiability and lead to the Intermediate and Mean Value Theorems. The Second Edition features: A chapter on the Riemann integral, including the subject of uniform continuity Explicit coverage of the epsilon-delta convergence A discussion of the modern preference for the viewpoint of sequences over that of series Throughout the book, numerous applications and examples reinforce concepts and demonstrate the validity of historical methods and results, while appended excerpts from original historical works shed light on the concerns of influential mathematicians in addition to the difficulties encountered in their work. Each chapter concludes with exercises ranging in level of complexity, and partial solutions are provided at the end of the book. Real Analysis: A Historical Approach, Second Edition is an ideal book for courses on real analysis and mathematical analysis at the undergraduate level. The book is also a valuable resource for secondary mathematics teachers and mathematicians.
The Paralysis Of Analysis In African American Studies
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Author : Stephen Ferguson II
language : en
Publisher: Bloomsbury Publishing
Release Date : 2023-09-21
The Paralysis Of Analysis In African American Studies written by Stephen Ferguson II and has been published by Bloomsbury Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-21 with Philosophy categories.
Stephen C. Ferguson II provides a philosophical examination of Black popular culture for the first time. From extensive discussion of the philosophy and political economy of Hip-Hop music through to a developed exploration of the influence of the postmodernism-poststructuralist ideology on African American studies, he argues how postmodernism ideology plays a seminal role in justifying the relationship between corporate capitalism and Black popular culture. Chapters cover topics such as cultural populism, capitalism and Black liberation, the philosophy of Hip-Hop music, and Harold Cruse's influence on the “cultural turn” in African American studies. Ferguson combines case studies of past and contemporary Black cultural and intellectual productions with a Marxist ideological critique to provide a cutting edge reflection on the economic structure in which Black popular culture emerged. He highlights the contradictions that are central to the juxtaposition of Black cultural artists as political participants in socioeconomic struggle and the political participants who perform the rigorous task of social criticism. Adopting capitalism as an explanatory framework, Ferguson investigates the relationship between postmodernism as social theory, current manifestations of Black popular culture, and the theoretical work of Black thinkers and scholars to demonstrate how African American studies have been shaped.