A Source Book In Classical Analysis
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A Source Book In Classical Analysis
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Author : Garrett Birkhoff
language : en
Publisher:
Release Date : 1973
A Source Book In Classical Analysis written by Garrett Birkhoff and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Mathematical analysis categories.
An understanding of the developments in classical analysis during the nineteenth century is vital to a full appreciation of the history of twentieth-century mathematical thought. It was during the nineteenth century that the diverse mathematical formulae of the eighteenth century were systematized and the properties of functions of real and complex variables clearly distinguished; and it was then that the calculus matured into the rigorous discipline of today, becoming in the process a dominant influence on mathematics and mathematical physics. This Source Book, a sequel to D. J. Struik's Source Book in Mathematics, 1200-1800, draws together more than eighty selections from the writings of the most influential mathematicians of the period. Thirteen chapters, each with an introduction by the editor, highlight the major developments in mathematical thinking over the century. All material is in English, and great care has been taken to maintain a high standard of accuracy both in translation and in transcription. Of particular value to historians and philosophers of science, the Source Book should serve as a vital reference to anyone seeking to understand the roots of twentieth-century mathematical thought.
A Source Book In Classical Analysis
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Author : Garrett Birkhoff
language : en
Publisher:
Release Date : 1973
A Source Book In Classical Analysis written by Garrett Birkhoff and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Mathematics categories.
An understanding of the developments in classical analysis during the nineteenth century is vital to a full appreciation of the history of twentieth-century mathematical thought. It was during the nineteenth century that the diverse mathematical formulae of the eighteenth century were systematized and the properties of functions of real and complex variables clearly distinguished; and it was then that the calculus matured into the rigorous discipline of today, becoming in the process a dominant influence on mathematics and mathematical physics. This Source Book, a sequel to D. J. Struik's Source Book in Mathematics, 1200-1800, draws together more than eighty selections from the writings of the most influential mathematicians of the period. Thirteen chapters, each with an introduction by the editor, highlight the major developments in mathematical thinking over the century. All material is in English, and great care has been taken to maintain a high standard of accuracy both in translation and in transcription. Of particular value to historians and philosophers of science, the Source Book should serve as a vital reference to anyone seeking to understand the roots of twentieth-century mathematical thought.
Pi A Source Book
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Author : J.L. Berggren
language : en
Publisher: Springer
Release Date : 2014-01-13
Pi A Source Book written by J.L. Berggren and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-13 with Mathematics categories.
This book documents the history of pi from the dawn of mathematical time to the present. One of the beauties of the literature on pi is that it allows for the inclusion of very modern, yet accessible, mathematics. The articles on pi collected herein fall into various classes. First and foremost there is a selection from the mathematical and computational literature of four millennia. There is also a variety of historical studies on the cultural significance of the number. Additionally, there is a selection of pieces that are anecdotal, fanciful, or simply amusing. For this new edition, the authors have updated the original material while adding new material of historical and cultural interest. There is a substantial exposition of the recent history of the computation of digits of pi, a discussion of the normality of the distribution of the digits, and new translations of works by Viete and Huygen.
Invitation To Classical Analysis
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Author : Peter L. Duren
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Invitation To Classical Analysis written by Peter L. Duren 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 2012 with Mathematics categories.
This book gives a rigorous treatment of selected topics in classical analysis, with many applications and examples. The exposition is at the undergraduate level, building on basic principles of advanced calculus without appeal to more sophisticated techniques of complex analysis and Lebesgue integration. Among the topics covered are Fourier series and integrals, approximation theory, Stirling's formula, the gamma function, Bernoulli numbers and polynomials, the Riemann zeta function, Tauberian theorems, elliptic integrals, ramifications of the Cantor set, and a theoretical discussion of differential equations including power series solutions at regular singular points, Bessel functions, hypergeometric functions, and Sturm comparison theory. Preliminary chapters offer rapid reviews of basic principles and further background material such as infinite products and commonly applied inequalities. This book is designed for individual study but can also serve as a text for second-semester courses in advanced calculus. Each chapter concludes with an abundance of exercises. Historical notes discuss the evolution of mathematical ideas and their relevance to physical applications. Special features are capsule scientific biographies of the major players and a gallery of portraits. Although this book is designed for undergraduate students, others may find it an accessible source of information on classical topics that underlie modern developments in pure and applied mathematics.
Pi A Source Book
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Author : Jonathan M. Borwein
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Pi A Source Book written by Jonathan M. Borwein 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 2013-06-29 with Mathematics categories.
Our intention in this collection is to provide, largely through original writings, an ex tended account of pi from the dawn of mathematical time to the present. The story of pi reflects the most seminal, the most serious, and sometimes the most whimsical aspects of mathematics. A surprising amount of the most important mathematics and a signifi cant number of the most important mathematicians have contributed to its unfolding directly or otherwise. Pi is one of the few mathematical concepts whose mention evokes a response of recog nition and interest in those not concerned professionally with the subject. It has been a part of human culture and the educated imagination for more than twenty-five hundred years. The computation of pi is virtually the only topic from the most ancient stratum of mathematics that is still of serious interest to modern mathematical research. To pursue this topic as it developed throughout the millennia is to follow a thread through the history of mathematics that winds through geometry, analysis and special functions, numerical analysis, algebra, and number theory. It offers a subject that provides mathe maticians with examples of many current mathematical techniques as weIl as a palpable sense of their historical development. Why a Source Book? Few books serve wider potential audiences than does a source book. To our knowledge, there is at present no easy access to the bulk of the material we have collected.
A Source Book In Geography
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Author : George Kish
language : en
Publisher: Harvard University Press
Release Date : 1978
A Source Book In Geography written by George Kish and has been published by Harvard University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with History categories.
Presents geographical writings, chronologically arranged, with a wealth of material from non-Western sources. Each section is introduced by the editor.
A Source Book In Medieval Science
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Author : Edward Grant
language : en
Publisher: Harvard University Press
Release Date : 1974
A Source Book In Medieval Science written by Edward Grant and has been published by Harvard University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with History categories.
This Source Book explores a millennium of European scientific thought accompanied by critical commentary and annotation; nearly half the selections appear for the first time in the vernacular. Representing "science" in the medieval sense, selections include alchemy, astrology, logic, and theology as well as mathematics, physics, and biology.
A Source Book In Mathematics 1200 1800
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Author : Dirk Jan Struik
language : en
Publisher: Princeton University Press
Release Date : 2014-07-14
A Source Book In Mathematics 1200 1800 written by Dirk Jan Struik 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 2014-07-14 with Mathematics categories.
These selected mathematical writings cover the years when the foundations were laid for the theory of numbers, analytic geometry, and the calculus. Originally published in 1986. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Excursions In Classical Analysis
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Author : Hongwei Chen
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-12-31
Excursions In Classical Analysis written by Hongwei Chen 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 2010-12-31 with Mathematics categories.
Excursions in Classical Analysis will introduce students to advanced problem solving and undergraduate research in two ways: it will provide a tour of classical analysis, showcasing a wide variety of problems that are placed in historical context, and it will help students gain mastery of mathematical discovery and proof. The [Author]; presents a variety of solutions for the problems in the book. Some solutions reach back to the work of mathematicians like Leonhard Euler while others connect to other beautiful parts of mathematics. Readers will frequently see problems solved by using an idea that, at first glance, might not even seem to apply to that problem. Other solutions employ a specific technique that can be used to solve many different kinds of problems. Excursions emphasizes the rich and elegant interplay between continuous and discrete mathematics by applying induction, recursion, and combinatorics to traditional problems in classical analysis. The book will be useful in students' preparations for mathematics competitions, in undergraduate reading courses and seminars, and in analysis courses as a supplement. The book is also ideal for self study, since the chapters are independent of one another and may be read in any order.
Introduction To Calculus And Classical Analysis
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Author : Omar Hijab
language : en
Publisher: Springer
Release Date : 2016-02-09
Introduction To Calculus And Classical Analysis written by Omar Hijab and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-09 with Mathematics categories.
This text is intended for an honors calculus course or for an introduction to analysis. Involving rigorous analysis, computational dexterity, and a breadth of applications, it is ideal for undergraduate majors. This third edition includes corrections as well as some additional material. Some features of the text include: The text is completely self-contained and starts with the real number axioms; The integral is defined as the area under the graph, while the area is defined for every subset of the plane; There is a heavy emphasis on computational problems, from the high-school quadratic formula to the formula for the derivative of the zeta function at zero; There are applications from many parts of analysis, e.g., convexity, the Cantor set, continued fractions, the AGM, the theta and zeta functions, transcendental numbers, the Bessel and gamma functions, and many more; Traditionally transcendentally presented material, such as infinite products, the Bernoulli series, and the zeta functional equation, is developed over the reals; and There are 385 problems with all the solutions at the back of the text.