Download Infinite Series in a History of Analysis PDF

Infinite Series in a History of Analysis

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Publisher : Walter de Gruyter GmbH & Co KG
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ISBN 13 : 3110359839
Pages : 142 pages
Rating : 4.8/5 (359 downloads)

Download Infinite Series in a History of Analysis PDF Format Full Free by Hans-Heinrich Körle and published by Walter de Gruyter GmbH & Co KG. This book was released on 2015-09-25 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.


Download Theory of Infinite Sequences and Series PDF

Theory of Infinite Sequences and Series

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Publisher : Springer Nature
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ISBN 13 : 3030794318
Pages : 388 pages
Rating : 4.3/5 (794 downloads)

Download Theory of Infinite Sequences and Series PDF Format Full Free by Ludmila Bourchtein and published by Springer Nature. This book was released on 2021 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook covers the majority of traditional topics of infinite sequences and series, starting from the very beginning the definition and elementary properties of sequences of numbers, and ending with advanced results of uniform convergence and power series. The text is aimed at university students specializing in mathematics and natural sciences, and at all the readers interested in infinite sequences and series. It is designed for the reader who has a good working knowledge of calculus. No additional prior knowledge is required. The text is divided into five chapters, which can be grouped into two parts: the first two chapters are concerned with the sequences and series of numbers, while the remaining three chapters are devoted to the sequences and series of functions, including the power series. Within each major topic, the exposition is inductive and starts with rather simple definitions and/or examples, becoming more compressed and sophisticated as the course progresses. Each key notion and result is illustrated with examples explained in detail. Some more complicated topics and results are marked as complements and can be omitted on a first reading. The text includes a large number of problems and exercises, making it suitable for both classroom use and self-study. Many standard exercises are included in each section to develop basic techniques and test the understanding of key concepts. Other problems are more theoretically oriented and illustrate more intricate points of the theory, or provide counterexamples to false propositions which seem to be natural at first glance. Solutions to additional problems proposed at the end of each chapter are provided as an electronic supplement to this book.


Download A Brief History of Analysis PDF

A Brief History of Analysis

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Publisher : Springer Nature
Release Date :
ISBN 13 : 303100650X
Pages : 265 pages
Rating : 4.5/5 (6 downloads)

Download A Brief History of Analysis PDF Format Full Free by Detlef D. Spalt and published by Springer Nature. This book was released on 2022-09-03 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


Download Analysis by Its History PDF

Analysis by Its History

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Publisher : Springer Science & Business Media
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ISBN 13 : 0387770313
Pages : 382 pages
Rating : 4.3/5 (77 downloads)

Download Analysis by Its History PDF Format Full Free by Ernst Hairer and published by Springer Science & Business Media. This book was released on 2008-06-02 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


Download A History of Analysis PDF

A History of Analysis

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Publisher : American Mathematical Soc.
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ISBN 13 : 9780821890509
Pages : 422 pages
Rating : 4.8/5 (821 downloads)

Download A History of Analysis PDF Format Full Free by Hans Niels Jahnke and published by American Mathematical Soc.. This book was released on with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt:


Download Karl Marx and Mathematics PDF

Karl Marx and Mathematics

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Publisher : Routledge
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ISBN 13 : 1000263185
Pages : 226 pages
Rating : 4.1/5 (263 downloads)

Download Karl Marx and Mathematics PDF Format Full Free by Pradip Baksi and published by Routledge. This book was released on 2020-11-01 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of various texts on Karl Marx and Mathematics is the revised and extended second edition of the Special Supplement to Karl Marx, Mathematical Manuscripts (1994; Calcutta: Viswakos) titled Marx and Mathematics. The sources of the texts included in the three parts of this collection and, some biographical information about their respective authors have been indicated at the end of each text. The emergence and development of the Ethnomathematics movement continue to change our understanding of the history of evolution of plural mathematics on planet earth since the Neolithic age. Rediscovery and study of some of the neglected source texts have further energized investigations on the subsequent history of mathematical cultures, including those on the histories of algebra and analysis in some of the ancient and medieval languages of Asia, like Sanskrit, Arabic and Malayalam. Consequently, it is now possible to indicate some of the larger gaps in the dominant understanding of history of mathematics not only in Marx’s time, but also at the time of editing Marx’s mathematical manuscripts in the twentieth century, and even today. Finally, the emergence and development of mathematical and statistical software packages are vigorously reshaping our ways of conceptualizing and doing mathematics towards an unknown future. It is time now for taking yet another look at all mathematical text from the past and that includes the mathematical manuscripts of Marx. These texts have been divided into three parts. Part one contains some topical texts related to the history of emergence, development, editing, publication and reception of the mathematical manuscripts of Karl Marx. Part two contains a selection of five articles reflecting some of the investigations inspired by these manuscripts in Russia, India and France. Part three contains five articles on plural mathematics before and after Karl Marx (1818-1883). The texts in this collection are followed by two appendices containing two bibliographies: one on Hegel and mathematics and, the other on mathematics and semiotics. Please note: This title is co-published with Aakar Books, Bew Delhi. Taylor & Francis does not sell or distribute the print edition in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan, Maldives or Bhutan).


Download 3000 Years of Analysis PDF

3000 Years of Analysis

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Publisher : Springer Nature
Release Date :
ISBN 13 : 303058223X
Pages : 706 pages
Rating : 4.2/5 (582 downloads)

Download 3000 Years of Analysis PDF Format Full Free by Thomas Sonar and published by Springer Nature. This book was released on 2020-12-27 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


Download Essential Statistical Concepts for the Quality Professional PDF

Essential Statistical Concepts for the Quality Professional

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Publisher : CRC Press
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ISBN 13 : 1439894590
Pages : 510 pages
Rating : 4.5/5 (894 downloads)

Download Essential Statistical Concepts for the Quality Professional PDF Format Full Free by D. H. Stamatis and published by CRC Press. This book was released on 2012-05-02 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: The essence of any root cause analysis in our modern quality thinking is to go beyond the actual problem. This means not only do we have to fix the problem at hand but we also have to identify why the failure occurred and what was the opportunity to apply the appropriate knowledge to avoid the problem in the future. Essential Statistical Concepts for the Quality Professional offers a new non-technical statistical approach to quality for effective improvement and productivity by focusing on very specific and fundamental methodologies and tools for the future. Written by an expert with more than 30 years of experience in management, quality training, and consulting, the book examines the fundamentals of statistical understanding, and by doing so demonstrates the importance of using statistics in the decision making process. The author points out pitfalls to keep in mind when undertaking an experiment for improvement and explains how to use statistics in improvement endeavors. He discusses data interpretation, common tests and confidence intervals, and how to plan experiments for improvement. The book expands the notion of experimentation by dealing with mathematical models such as regression to optimize the improvement and understand the relationship between several factors. It emphasizes the need for sampling and introduces specific techniques to make sure accuracy and precision of the data is appropriate and applicable for the study at hand. The author’s approach is somewhat new and unique; however, he details tools and methodologies that can be used to evaluate the system for prevention. These tools and methodologies focus on structured, repeatable processes that can be instrumental in finding real, fixable causes of the human errors and equipment failures that lead to quality issues.


Download Real Analysis PDF

Real Analysis

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Publisher : John Wiley & Sons
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ISBN 13 : 9780471318521
Pages : 269 pages
Rating : 4.3/5 (471 downloads)

Download Real Analysis PDF Format Full Free by Saul Stahl and published by John Wiley & Sons. This book was released on 1999-08-05 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: A provocative look at the tools and history of real analysis This new work from award-winning author Saul Stahl offers a real treat for students of analysis. Combining historical coverage with a superb introductory treatment, Real Analysis: A Historical Approach 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, introducing the various aspects of the completeness of the real number system, sequential continuity and differentiability, as well as uniform convergence. Finally, he presents applications and examples to reinforce concepts and demonstrate the validity of many of the historical methods and results. Ample exercises, illustrations, and appended excerpts from the original historical works complete this focused, unconventional, highly interesting book. It is an invaluable resource for mathematicians and educators seeking to gain insight into the true language of mathematics.


Download Applied Mathematics PDF

Applied Mathematics

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Publisher : Springer Science & Business Media
Release Date :
ISBN 13 : 1468433121
Pages : 225 pages
Rating : 4.1/5 (433 downloads)

Download Applied Mathematics PDF Format Full Free by F. J. Murray and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary objective of the course presented here is orientation for those interested in applying mathematics, but the course should also be of value or in using math to those interested in mathematical research and teaching ematics in some other professional context. The course should be suitable for college seniors and graduate students, as well as for college juniors who have had mathematics beyond the basic calculus sequence. Maturity is more significant than any formal prerequisite. The presentation involves a number of topics that are significant for applied mathematics but that normally do not appear in the curriculum or are depicted from an entirely different point of view. These topics include engineering simulations, the experience patterns of the exact sciences, the conceptual nature of pure mathematics and its relation to applied mathe matics, the historical development of mathematics, the associated conceptual aspects of the exact sciences, and the metaphysical implications of mathe matical scientific theories. We will associate topics in mathematics with areas of application. This presentation corresponds to a certain logical structure. But there is an enormous wealth of intellectual development available, and this permits considerable flexibility for the instructor in curricula and emphasis. The prime objective is to encourage the student to contact and utilize this rich heritage. Thus, the student's activity is critical, and it is also critical that this activity be precisely formulated and communicated.


Download The Real and the Complex: A History of Analysis in the 19th Century PDF

The Real and the Complex: A History of Analysis in the 19th Century

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Publisher : Springer
Release Date :
ISBN 13 : 3319237152
Pages : 350 pages
Rating : 4.1/5 (237 downloads)

Download The Real and the Complex: A History of Analysis in the 19th Century PDF Format Full Free by Jeremy Gray and published by Springer. This book was released on 2015-10-14 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


Download The Fundamentals of Mathematical Analysis PDF

The Fundamentals of Mathematical Analysis

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Publisher : Elsevier
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ISBN 13 : 1483154130
Pages : 540 pages
Rating : 4.1/5 (154 downloads)

Download The Fundamentals of Mathematical Analysis PDF Format Full Free by G. M. Fikhtengol'ts and published by Elsevier. This book was released on 2014-08-01 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Fundamentals of Mathematical Analysis, Volume 2 is a continuation of the discussion of the fundamentals of mathematical analysis, specifically on the subject of curvilinear and surface integrals, with emphasis on the difference between the curvilinear and surface ""integrals of first kind"" and ""integrals of second kind."" The discussions in the book start with an introduction to the elementary concepts of series of numbers, infinite sequences and their limits, and the continuity of the sum of a series. The definition of improper integrals of unbounded functions and that of uniform convergence of integrals are explained. Curvilinear integrals of the first and second kinds are analyzed mathematically. The book then notes the application of surface integrals, through a parametric representation of a surface, and the calculation of the mass of a solid. The text also highlights that Green's formula, which connects a double integral over a plane domain with curvilinear integral along the contour of the domain, has an analogue in Ostrogradski's formula. The periodic values and harmonic analysis such as that found in the operation of a steam engine are analyzed. The volume ends with a note of further developments in mathematical analysis, which is a chronological presentation of important milestones in the history of analysis. The book is an ideal reference for mathematicians, students, and professors of calculus and advanced mathematics.


Download Teaching and Learning of Calculus PDF

Teaching and Learning of Calculus

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Publisher : Springer
Release Date :
ISBN 13 : 3319329758
Pages : 37 pages
Rating : 4.7/5 (329 downloads)

Download Teaching and Learning of Calculus PDF Format Full Free by David Bressoud and published by Springer. This book was released on 2016-06-14 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: This survey focuses on the main trends in the field of calculus education. Despite their variety, the findings reveal a cornerstone issue that is strongly linked to the formalism of calculus concepts and to the difficulties it generates in the learning and teaching process. As a complement to the main text, an extended bibliography with some of the most important references on this topic is included. Since the diversity of the research in the field makes it difficult to produce an exhaustive state-of-the-art summary, the authors discuss recent developments that go beyond this survey and put forward new research questions.


Download History of Mathematics PDF

History of Mathematics

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Publisher : EOLSS Publications
Release Date :
ISBN 13 : 1848262213
Pages : 396 pages
Rating : 4.2/5 (262 downloads)

Download History of Mathematics PDF Format Full Free by Vagn Lundsgaard Hansen and published by EOLSS Publications. This book was released on 2010-12-20 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: History of Mathematics is a component of Encyclopedia of Mathematical Sciences in the global Encyclopedia of Life Support Systems (EOLSS), which is an integrated compendium of twenty one Encyclopedias. The Theme on History of Mathematics discusses: Mathematics in Egypt and Mesopotamia; History of Trigonometryto 1550; Mathematics in Japan; The Mathematization of The Physical Sciences-Differential Equations of Nature; A Short History of Dynamical Systems Theory:1885-2007; Measure Theories and Ergodicity Problems; The Number Concept and Number Systems; Operations Research and Mathematical Programming: From War to Academia - A Joint Venture; Elementary Mathematics From An Advanced Standpoint; The History and Concept of Mathematical Proof; Geometry in The 20th Century; Bourbaki: An Epiphenomenon in The History of Mathematics This volume is aimed at the following five major target audiences: University and College Students Educators, Professional Practitioners, Research Personnel and Policy Analysts, Managers, and Decision Makers, NGOs and GOs.


Download Deleuze and the History of Mathematics PDF

Deleuze and the History of Mathematics

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Publisher : A&C Black
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ISBN 13 : 1441113894
Pages : 208 pages
Rating : 4.8/5 (113 downloads)

Download Deleuze and the History of Mathematics PDF Format Full Free by Simon Duffy and published by A&C Black. This book was released on 2013-05-09 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gilles Deleuze's engagements with mathematics, replete in his work, rely upon the construction of alternative lineages in the history of mathematics, which challenge some of the self imposed limits that regulate the canonical concepts of the discipline. For Deleuze, these challenges provide an opportunity to reconfigure particular philosophical problems - for example, the problem of individuation - and to develop new concepts in response to them. The highly original research presented in this book explores the mathematical construction of Deleuze's philosophy, as well as addressing the undervalued and often neglected question of the mathematical thinkers who influenced his work. In the wake of Alain Badiou's recent and seemingly devastating attack on the way the relation between mathematics and philosophy is configured in Deleuze's work, Simon B.Duffy offers a robust defence of the structure of Deleuze's philosophy and, in particular, the adequacy of the mathematical problems used in its construction. By reconciling Badiou and Deleuze's seemingly incompatible engagements with mathematics, Duffy succeeds in presenting a solid foundation for Deleuze's philosophy, rebuffing the recent challenges against it.


Download The Historical Development of the Calculus PDF

The Historical Development of the Calculus

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Publisher : Springer Science & Business Media
Release Date :
ISBN 13 : 1461262305
Pages : 368 pages
Rating : 4.3/5 (262 downloads)

Download The Historical Development of the Calculus PDF Format Full Free by C.H.Jr. Edwards and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: The calculus has served for three centuries as the principal quantitative language of Western science. In the course of its genesis and evolution some of the most fundamental problems of mathematics were first con fronted and, through the persistent labors of successive generations, finally resolved. Therefore, the historical development of the calculus holds a special interest for anyone who appreciates the value of a historical perspective in teaching, learning, and enjoying mathematics and its ap plications. My goal in writing this book was to present an account of this development that is accessible, not solely to students of the history of mathematics, but to the wider mathematical community for which my exposition is more specifically intended, including those who study, teach, and use calculus. The scope of this account can be delineated partly by comparison with previous works in the same general area. M. E. Baron's The Origins of the Infinitesimal Calculus (1969) provides an informative and reliable treat ment of the precalculus period up to, but not including (in any detail), the time of Newton and Leibniz, just when the interest and pace of the story begin to quicken and intensify. C. B. Boyer's well-known book (1949, 1959 reprint) met well the goals its author set for it, but it was more ap propriately titled in its original edition-The Concepts of the Calculus than in its reprinting.


Download Anachronisms in the History of Mathematics PDF

Anachronisms in the History of Mathematics

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Publisher : Cambridge University Press
Release Date :
ISBN 13 : 1108834965
Pages : 392 pages
Rating : 4.9/5 (834 downloads)

Download Anachronisms in the History of Mathematics PDF Format Full Free by Niccol- Guicciardini and published by Cambridge University Press. This book was released on 2021-07-22 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover essays by leading scholars on the history of mathematics from ancient to modern times in European and non-European cultures.