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Book Non standard Analysis

    Book Details:
  • Author : Abraham Robinson
  • Publisher : Princeton University Press
  • Release : 2016-08-11
  • ISBN : 1400884225
  • Pages : 315 pages

Download or read book Non standard Analysis written by Abraham Robinson and published by Princeton University Press. This book was released on 2016-08-11 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback reprint of the 1974 revised edition is indispensable reading for anyone interested in non-standard analysis. It treats in rich detail many areas of application, including topology, functions of a real variable, functions of a complex variable, and normed linear spaces, together with problems of boundary layer flow of viscous fluids and rederivations of Saint-Venant's hypothesis concerning the distribution of stresses in an elastic body.

Book L   H  pital s Analyse des infiniments petits

Download or read book L H pital s Analyse des infiniments petits written by Robert E Bradley and published by Birkhäuser. This book was released on 2015-07-20 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is an annotated translation of what is considered to be the world’s first calculus textbook, originally published in French in 1696. That anonymously published textbook on differential calculus was based on lectures given to the Marquis de l’Hôpital in 1691-2 by the great Swiss mathematician, Johann Bernoulli. In the 1920s, a copy of Bernoulli’s lecture notes was discovered in a library in Basel, which presented the opportunity to compare Bernoulli’s notes, in Latin, to l’Hôpital’s text in French. The similarities are remarkable, but there is also much in l’Hôpital’s book that is original and innovative. This book offers the first English translation of Bernoulli's notes, along with the first faithful English translation of l’Hôpital’s text, complete with annotations and commentary. Additionally, a significant portion of the correspondence between l’Hôpital and Bernoulli has been included, also for the fi rst time in English translation. This translation will provide students and researchers with direct access to Bernoulli’s ideas and l’Hôpital’s innovations. Both enthusiasts and scholars of the history of science and the history of mathematics will fi nd food for thought in the texts and notes of the Marquis de l’Hôpital and his teacher, Johann Bernoulli.

Book Analyse des infiniments petits  pour l intelligence des lignes courbes

Download or read book Analyse des infiniments petits pour l intelligence des lignes courbes written by L'Hôpital and published by . This book was released on 1716 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Geometric Differentiation

Download or read book Geometric Differentiation written by I. R. Porteous and published by Cambridge University Press. This book was released on 2001-12-13 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a revised version of the popular Geometric Differentiation, first edition.

Book Analyse des infiniment petits pour l intelligence des lignes courbes par Mr le Marquis De l Hospital

Download or read book Analyse des infiniment petits pour l intelligence des lignes courbes par Mr le Marquis De l Hospital written by Guillaume Francois Antoine : de L'Hospital and published by . This book was released on 1715 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book The Math Book

    Book Details:
  • Author : Clifford A. Pickover
  • Publisher : Union Square + ORM
  • Release : 2011-09-27
  • ISBN : 1402797494
  • Pages : 937 pages

Download or read book The Math Book written by Clifford A. Pickover and published by Union Square + ORM. This book was released on 2011-09-27 with total page 937 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Neumann Prize–winning, illustrated exploration of mathematics—from its timeless mysteries to its history of mind-boggling discoveries. Beginning millions of years ago with ancient “ant odometers” and moving through time to our modern-day quest for new dimensions, The Math Book covers 250 milestones in mathematical history. Among the numerous delights readers will learn about as they dip into this inviting anthology: cicada-generated prime numbers, magic squares from centuries ago, the discovery of pi and calculus, and the butterfly effect. Each topic is lavishly illustrated with colorful art, along with formulas and concepts, fascinating facts about scientists’ lives, and real-world applications of the theorems.

Book Analyse des infiniment petits

Download or read book Analyse des infiniment petits written by Guillaume François Antoine de L'Hôpital and published by . This book was released on 1715 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Analyse des infiniment petits  pour l intelligence des lignes courbes

Download or read book Analyse des infiniment petits pour l intelligence des lignes courbes written by Guillaume François Antoine Marquis de L'Hospital and published by . This book was released on 1716 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Families of Curves and the Origins of Partial Differentiation

Download or read book Families of Curves and the Origins of Partial Differentiation written by S.B. Engelsman and published by Elsevier. This book was released on 2000-04-01 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a detailed description of the main episodes in the emergence of partial differentiation during the period 1690-1740. It argues that the development of this concept - to a considerable degree of perfection - took place almost exclusively in problems concerning families of curves. Thus, the book shows the origins of the ideas and techniques which paved the way for the sudden introduction of partial differential equations in 1750. The main methodological characteristic of the book is its emphasis on a full understanding of the motives, problems and goals of the mathematicians of that time.

Book Thermal Analysis and Thermodynamic Properties of Solids

Download or read book Thermal Analysis and Thermodynamic Properties of Solids written by Jaroslav Sestak and published by Elsevier. This book was released on 2021-08-09 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thermal Analysis and Thermodynamic Properties of Solids, Second Edition covers foundational principles and recent updates in the field, presenting an authoritative overview of theoretical knowledge and practical applications across several fields. Since the first edition of this book was published, large developments have occurred in the theoretical understanding of—and subsequent ability to assess and apply—principles of thermal analysis. Drawing on the knowledge of its expert author, this second edition provides fascinating insight for both new and experienced students, researchers, and industry professionals whose work is influenced or impacted by thermo analysis principles and tools. Part 1 provides a detailed introduction and guide to theoretical aspects of thermal analysis and the related impact of thermodynamics. Key terminology and concepts, the fundamentals of thermophysical examinations, thermostatics, equilibrium background, thermotics, reaction kinetics and models, thermokinetics and the exploitation of fractals are all discussed. Part 2 then goes on to discuss practical applications of this theoretical information to topics such as crystallization kinetics and glass states, thermodynamics in superconductor models, and climate change. - Includes fully updated as well as new chapters on kinetic phase diagrams, thermokinetics in DTA experiments, and crystallization kinetics - Discusses the influence of key derivatives such as thermostatics, thermodynamics, thermotics, and thermokinetics - Helps readers understand and describe reaction kinetics in solids, both in terms of simplified descriptions of the reaction mechanism models and averaged descriptions using fractals

Book Infinitesimal Analysis

    Book Details:
  • Author : E.I. Gordon
  • Publisher : Springer Science & Business Media
  • Release : 2013-03-14
  • ISBN : 940170063X
  • Pages : 435 pages

Download or read book Infinitesimal Analysis written by E.I. Gordon and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: Infinitesimal analysis, once a synonym for calculus, is now viewed as a technique for studying the properties of an arbitrary mathematical object by discriminating between its standard and nonstandard constituents. Resurrected by A. Robinson in the early 1960's with the epithet 'nonstandard', infinitesimal analysis not only has revived the methods of infinitely small and infinitely large quantities, which go back to the very beginning of calculus, but also has suggested many powerful tools for research in every branch of modern mathematics. The book sets forth the basics of the theory, as well as the most recent applications in, for example, functional analysis, optimization, and harmonic analysis. The concentric style of exposition enables this work to serve as an elementary introduction to one of the most promising mathematical technologies, while revealing up-to-date methods of monadology and hyperapproximation. This is a companion volume to the earlier works on nonstandard methods of analysis by A.G. Kusraev and S.S. Kutateladze (1999), ISBN 0-7923-5921-6 and Nonstandard Analysis and Vector Lattices edited by S.S. Kutateladze (2000), ISBN 0-7923-6619-0

Book Calculus and Analysis

    Book Details:
  • Author : Horst R. Beyer
  • Publisher : John Wiley & Sons
  • Release : 2010-04-26
  • ISBN : 0470617950
  • Pages : 695 pages

Download or read book Calculus and Analysis written by Horst R. Beyer and published by John Wiley & Sons. This book was released on 2010-04-26 with total page 695 pages. Available in PDF, EPUB and Kindle. Book excerpt: A NEW APPROACH TO CALCULUS THAT BETTER ENABLES STUDENTS TO PROGRESS TO MORE ADVANCED COURSES AND APPLICATIONS Calculus and Analysis: A Combined Approach bridges the gap between mathematical thinking skills and advanced calculus topics by providing an introduction to the key theory for understanding and working with applications in engineering and the sciences. Through a modern approach that utilizes fully calculated problems, the book addresses the importance of calculus and analysis in the applied sciences, with a focus on differential equations. Differing from the common classical approach to the topic, this book presents a modern perspective on calculus that follows motivations from Otto Toeplitz's famous genetic model. The result is an introduction that leads to great simplifications and provides a focused treatment commonly found in the applied sciences, particularly differential equations. The author begins with a short introduction to elementary mathematical logic. Next, the book explores the concept of sets and maps, providing readers with a strong foundation for understanding and solving modern mathematical problems. Ensuring a complete presentation, topics are uniformly presented in chapters that consist of three parts: Introductory Motivations presents historical mathematical problems or problems arising from applications that led to the development of mathematical solutions Theory provides rigorous development of the essential parts of the machinery of analysis; proofs are intentionally detailed, but simplified as much as possible to aid reader comprehension Examples and Problems promotes problem-solving skills through application-based exercises that emphasize theoretical mechanics, general relativity, and quantum mechanics Calculus and Analysis: A Combined Approach is an excellent book for courses on calculus and mathematical analysis at the upper-undergraduate and graduate levels. It is also a valuable resource for engineers, physicists, mathematicians, and anyone working in the applied sciences who would like to master their understanding of basic tools in modern calculus and analysis.

Book Fundamentals of Analysis with Applications

Download or read book Fundamentals of Analysis with Applications written by Atul Kumar Razdan and published by Springer Nature. This book was released on 2022-03-15 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves as a textbook in real analysis. It focuses on the fundamentals of the structural properties of metric spaces and analytical properties of functions defined between such spaces. Topics include sets, functions and cardinality, real numbers, analysis on R, topology of the real line, metric spaces, continuity and differentiability, sequences and series, Lebesgue integration, and Fourier series. It is primarily focused on the applications of analytical methods to solving partial differential equations rooted in many important problems in mathematics, physics, engineering, and related fields. Both the presentation and treatment of topics are fashioned to meet the expectations of interested readers working in any branch of science and technology. Senior undergraduates in mathematics and engineering are the targeted student readership, and the topical focus with applications to real-world examples will promote higher-level mathematical understanding for undergraduates in sciences and engineering.

Book An Elegant Solution

    Book Details:
  • Author : Paul Robertson
  • Publisher : Baker Books
  • Release : 2013-11-19
  • ISBN : 144126275X
  • Pages : 428 pages

Download or read book An Elegant Solution written by Paul Robertson and published by Baker Books. This book was released on 2013-11-19 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robertson's Latest Mix of Rich History and Deadly Murder For young Leonhard Euler, the Bernoulli family have been more than just friends. Master Johann has been a demanding mentor, and his sons have been Leonhard's allies and companions. But it is also a family torn by jealousy and distrust. Father and sons are engaged in a ruthless competition for prestige among the mathematical elites of Europe, especially the greatest prize: the Chair of Mathematics at the University of Basel, which Johann holds and his sons want. And now, their aspirations may have turned deadly. Lured into an investigation of the suspicious death of Uncle Jacob twenty years ago, Leonhard soon realizes there's more at stake than even a prominent appointment. Surrounded by the most brilliant--and cunning--minds of his generation, Leonhard is forced to see how dangerous his world is. His studies in mathematics have always been entwined with his thoughts on theology, and now, caught in a deadly battle of wills, he'll need both his genius and his faith to survive.

Book Transcendental Curves in the Leibnizian Calculus

Download or read book Transcendental Curves in the Leibnizian Calculus written by Viktor Blasjo and published by Academic Press. This book was released on 2017-04-22 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Transcendental Curves in the Leibnizian Calculus analyzes a mathematical and philosophical conflict between classical and early modern mathematics. In the late 17th century, mathematics was at the brink of an identity crisis. For millennia, mathematical meaning and ontology had been anchored in geometrical constructions, as epitomized by Euclid's ruler and compass. As late as 1637, Descartes had placed himself squarely in this tradition when he justified his new technique of identifying curves with equations by means of certain curve-tracing instruments, thereby bringing together the ancient constructive tradition and modern algebraic methods in a satisfying marriage. But rapid advances in the new fields of infinitesimal calculus and mathematical mechanics soon ruined his grand synthesis. Descartes's scheme left out transcendental curves, i.e. curves with no polynomial equation, but in the course of these subsequent developments such curves emerged as indispensable. It was becoming harder and harder to juggle cutting-edge mathematics and ancient conceptions of its foundations at the same time, yet leading mathematicians, such as Leibniz felt compelled to do precisely this. The new mathematics fit more naturally an analytical conception of curves than a construction-based one, yet no one wanted to betray the latter, as this was seen as virtually tantamount to stop doing mathematics altogether. The credibility and authority of mathematics depended on it. - Brings to light this underlying and often implicit complex of concerns that permeate early calculus - Evaluates the technical conception and mathematical construction of the geometrical method - Reveals a previously unrecognized Liebnizian programmatic cohesion in early calculus - Provides a beautifully written work of outstanding original scholarship

Book 3000 Years of Analysis

Download or read book 3000 Years of Analysis written 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.

Book Thermal Physics and Thermal Analysis

Download or read book Thermal Physics and Thermal Analysis written by Jaroslav Šesták and published by Springer. This book was released on 2017-03-24 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: Features twenty-five chapter contributions from an international array of distinguished academics based in Asia, Eastern and Western Europe, Russia, and the USA. This multi-author contributed volume provides an up-to-date and authoritative overview of cutting-edge themes involving the thermal analysis, applied solid-state physics, micro- and nano-crystallinity of selected solids and their macro- and microscopic thermal properties. Distinctive chapters featured in the book include, among others, calorimetry time scales from days to microseconds, glass transition phenomena, kinetics of non-isothermal processes, thermal inertia and temperature gradients, thermodynamics of nanomaterials, self-organization, significance of temperature and entropy. Advanced undergraduates, postgraduates and researchers working in the field of thermal analysis, thermophysical measurements and calorimetry will find this contributed volume invaluable. This is the third volume of the triptych volumes on thermal behaviour of materials; the previous two receiving thousand of downloads guaranteeing their worldwide impact.