Series and Products in the Development of Mathematics: Volume 2
Series and Products in the Development of Mathematics: Volume 2

Author: Ranjan Roy

Publisher: Cambridge University Press

Published: 2021-03-18

Total Pages: 480

ISBN-13: 1108573150

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This is the second volume of a two-volume work that traces the development of series and products from 1380 to 2000 by presenting and explaining the interconnected concepts and results of hundreds of unsung as well as celebrated mathematicians. Some chapters deal with the work of primarily one mathematician on a pivotal topic, and other chapters chronicle the progress over time of a given topic. This updated second edition of Sources in the Development of Mathematics adds extensive context, detail, and primary source material, with many sections rewritten to more clearly reveal the significance of key developments and arguments. Volume 1, accessible even to advanced undergraduate students, discusses the development of the methods in series and products that do not employ complex analytic methods or sophisticated machinery. Volume 2 examines more recent results, including deBranges' resolution of Bieberbach's conjecture and Nevanlinna's theory of meromorphic functions.

Series and Products in the Development of Mathematics: Volume 1
Series and Products in the Development of Mathematics: Volume 1

Author: Ranjan Roy

Publisher: Cambridge University Press

Published: 2021-03-18

Total Pages:

ISBN-13: 1108573185

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This is the first volume of a two-volume work that traces the development of series and products from 1380 to 2000 by presenting and explaining the interconnected concepts and results of hundreds of unsung as well as celebrated mathematicians. Some chapters deal with the work of primarily one mathematician on a pivotal topic, and other chapters chronicle the progress over time of a given topic. This updated second edition of Sources in the Development of Mathematics adds extensive context, detail, and primary source material, with many sections rewritten to more clearly reveal the significance of key developments and arguments. Volume 1, accessible to even advanced undergraduate students, discusses the development of the methods in series and products that do not employ complex analytic methods or sophisticated machinery. Volume 2 treats more recent work, including deBranges' solution of Bieberbach's conjecture, and requires more advanced mathematical knowledge.

Finite Difference Computing with PDEs
Finite Difference Computing with PDEs

Author: Hans Petter Langtangen

Publisher: Springer

Published: 2017-06-21

Total Pages: 522

ISBN-13: 3319554565

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This book is open access under a CC BY 4.0 license. This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algorithms, verification of implementations, analyses of physical behavior as implied by the numerical solutions, and how to apply the methods and software to solve problems in the fields of physics and biology.

Advanced Calculus (Revised Edition)
Advanced Calculus (Revised Edition)

Author: Lynn Harold Loomis

Publisher: World Scientific Publishing Company

Published: 2014-02-26

Total Pages: 595

ISBN-13: 9814583952

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An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.

Symbols and Things
Symbols and Things

Author: Kevin Lambert

Publisher: University of Pittsburgh Press

Published: 2021-10-12

Total Pages: 301

ISBN-13: 0822988410

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In the steam-powered mechanical age of the eighteenth and nineteenth centuries, the work of late Georgian and early Victorian mathematicians depended on far more than the properties of number. British mathematicians came to rely on industrialized paper and pen manufacture, railways and mail, and the print industries of the book, disciplinary journal, magazine, and newspaper. Though not always physically present with one another, the characters central to this book—from George Green to William Rowan Hamilton—relied heavily on communication technologies as they developed their theories in consort with colleagues. The letters they exchanged, together with the equations, diagrams, tables, or pictures that filled their manuscripts and publications, were all tangible traces of abstract ideas that extended mathematicians into their social and material environment. Each chapter of this book explores a thing, or assembling of things, mathematicians needed to do their work—whether a textbook, museum, journal, library, diagram, notebook, or letter—all characteristic of the mid-nineteenth-century British taskscape, but also representative of great change to a discipline brought about by an industrialized world in motion.