A Radical Approach To Real Analysis
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A Radical Approach To Real Analysis
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Author : David Bressoud
language : en
Publisher: American Mathematical Society
Release Date : 2022-02-22
A Radical Approach To Real Analysis written by David Bressoud and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-22 with Mathematics categories.
In this second edition of the MAA classic, exploration continues to be an essential component. More than 60 new exercises have been added, and the chapters on Infinite Summations, Differentiability and Continuity, and Convergence of Infinite Series have been reorganized to make it easier to identify the key ideas. A Radical Approach to Real Analysis is an introduction to real analysis, rooted in and informed by the historical issues that shaped its development. It can be used as a textbook, as a resource for the instructor who prefers to teach a traditional course, or as a resource for the student who has been through a traditional course yet still does not understand what real analysis is about and why it was created. The book begins with Fourier's introduction of trigonometric series and the problems they created for the mathematicians of the early 19th century. It follows Cauchy's attempts to establish a firm foundation for calculus and considers his failures as well as his successes. It culminates with Dirichlet's proof of the validity of the Fourier series expansion and explores some of the counterintuitive results Riemann and Weierstrass were led to as a result of Dirichlet's proof.
A Radical Approach To Real Analysis
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Author : David M. Bressoud
language : en
Publisher: MAA
Release Date : 2007-04-12
A Radical Approach To Real Analysis written by David M. Bressoud and has been published by MAA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-12 with Mathematics categories.
Second edition of this introduction to real analysis, rooted in the historical issues that shaped its development.
A Radical Approach To Lebesgue S Theory Of Integration
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Author : David M. Bressoud
language : en
Publisher: Cambridge University Press
Release Date : 2008-01-21
A Radical Approach To Lebesgue S Theory Of Integration written by David M. Bressoud and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-21 with Mathematics categories.
Meant for advanced undergraduate and graduate students in mathematics, this introduction to measure theory and Lebesgue integration is motivated by the historical questions that led to its development. The author tells the story of the mathematicians who wrestled with the difficulties inherent in the Riemann integral, leading to the work of Jordan, Borel, and Lebesgue.
A Problem Book In Real Analysis
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Author : Asuman G. Aksoy
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-03-10
A Problem Book In Real Analysis written by Asuman G. Aksoy 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 2010-03-10 with Mathematics categories.
Education is an admirable thing, but it is well to remember from time to time that nothing worth knowing can be taught. Oscar Wilde, “The Critic as Artist,” 1890. Analysis is a profound subject; it is neither easy to understand nor summarize. However, Real Analysis can be discovered by solving problems. This book aims to give independent students the opportunity to discover Real Analysis by themselves through problem solving. ThedepthandcomplexityofthetheoryofAnalysiscanbeappreciatedbytakingaglimpseatits developmental history. Although Analysis was conceived in the 17th century during the Scienti?c Revolution, it has taken nearly two hundred years to establish its theoretical basis. Kepler, Galileo, Descartes, Fermat, Newton and Leibniz were among those who contributed to its genesis. Deep conceptual changes in Analysis were brought about in the 19th century by Cauchy and Weierstrass. Furthermore, modern concepts such as open and closed sets were introduced in the 1900s. Today nearly every undergraduate mathematics program requires at least one semester of Real Analysis. Often, students consider this course to be the most challenging or even intimidating of all their mathematics major requirements. The primary goal of this book is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses. In doing so, we hope that learning analysis becomes less taxing and thereby more satisfying.
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.
Limits
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Author : Alan F. Beardon
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Limits written by Alan F. Beardon 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 2012-12-06 with Mathematics categories.
Intended as an undergraduate text on real analysis, this book includes all the standard material such as sequences, infinite series, continuity, differentiation, and integration, together with worked examples and exercises. By unifying and simplifying all the various notions of limit, the author has successfully presented a novel approach to the subject matter, which has not previously appeared in book form. The author defines the term limit once only, and all of the subsequent limiting processes are seen to be special cases of this one definition. Accordingly, the subject matter attains a unity and coherence that is not to be found in the traditional approach. Students will be able to fully appreciate and understand the common source of the topics they are studying while also realising that they are "variations on a theme", rather than essentially different topics, and therefore, will gain a better understanding of the subject.
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.
Calculus Reordered
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Author : David M. Bressoud
language : en
Publisher: Princeton University Press
Release Date : 2021-05-04
Calculus Reordered written by David M. Bressoud and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-04 with Mathematics categories.
Calculus Reordered takes readers on a remarkable journey through hundreds of years to tell the story of how calculus grew to what we know today. David Bressoud explains why calculus is credited to Isaac Newton and Gottfried Leibniz in the seventeenth century, and how its current structure is based on developments that arose in the nineteenth century. Bressoud argues that a pedagogy informed by the historical development of calculus presents a sounder way for students to learn this fascinating area of mathematics. Delving into calculus's birth in the Hellenistic Eastern Mediterranean--especially Syracuse in Sicily and Alexandria in Egypt--as well as India and the Islamic Middle East, Bressoud considers how calculus developed in response to essential questions emerging from engineering and astronomy. He looks at how Newton and Leibniz built their work on a flurry of activity that occurred throughout Europe, and how Italian philosophers such as Galileo Galilei played a particularly important role. In describing calculus's evolution, Bressoud reveals problems with the standard ordering of its curriculum: limits, differentiation, integration, and series. He contends instead that the historical order--which follows first integration as accumulation, then differentiation as ratios of change, series as sequences of partial sums, and finally limits as they arise from the algebra of inequalities--makes more sense in the classroom environment. Exploring the motivations behind calculus's discovery, Calculus Reordered highlights how this essential tool of mathematics came to be.
Second Year Calculus
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Author : David M. Bressoud
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Second Year Calculus written by David M. Bressoud 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 2012-12-06 with Mathematics categories.
Second Year Calculus: From Celestial Mechanics to Special Relativity covers multi-variable and vector calculus, emphasizing the historical physical problems which gave rise to the concepts of calculus. The book guides us from the birth of the mechanized view of the world in Isaac Newton's Mathematical Principles of Natural Philosophy in which mathematics becomes the ultimate tool for modelling physical reality, to the dawn of a radically new and often counter-intuitive age in Albert Einstein's Special Theory of Relativity in which it is the mathematical model which suggests new aspects of that reality. The development of this process is discussed from the modern viewpoint of differential forms. Using this concept, the student learns to compute orbits and rocket trajectories, model flows and force fields, and derive the laws of electricity and magnetism. These exercises and observations of mathematical symmetry enable the student to better understand the interaction of physics and mathematics.
A Primer Of Lebesgue Integration
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Author : H. S. Bear
language : en
Publisher: Academic Press
Release Date : 2002
A Primer Of Lebesgue Integration written by H. S. Bear and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
The Lebesgue integral is now standard for both applications and advanced mathematics. This books starts with a review of the familiar calculus integral and then constructs the Lebesgue integral from the ground up using the same ideas. A Primer of Lebesgue Integration has been used successfully both in the classroom and for individual study. Bear presents a clear and simple introduction for those intent on further study in higher mathematics. Additionally, this book serves as a refresher providing new insight for those in the field. The author writes with an engaging, commonsense style that appeals to readers at all levels.