Calculus With Infinitesimals
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Calculus Set Free
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Author :
language : en
Publisher: Oxford University Press
Release Date : 2021-11-30
Calculus Set Free written by and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-30 with Calculus categories.
Calculus Set Free: Infinitesimals to the Rescue is a single-variable calculus textbook that incorporates the use of infinitesimal methods. The procedures used throughout make many of the calculations simpler and the concepts clearer for undergraduate students, heightening success and easing a significant burden of entry into STEM disciplines. This text features a student-friendly exposition with ample marginal notes, examples, illustrations, and more. The exercises include a wide range of difficulty levels, stretching from very simple rapid response questions to the occasional exercise meant to test knowledge. While some exercises require the use of technology to work through, none are dependent on any specific software. The answers to odd-numbered exercises in the back of the book include both simplified and non-simplified answers, hints, or alternative answers. Throughout the text, notes in the margins include comments meant to supplement understanding, sometimes including line-by-line commentary for worked examples. Without sacrificing academic rigor, Calculus Set Free offers an engaging style that helps students to solidify their understanding on difficult theoretical calculus.
Calculus With Infinitesimals
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Author : Efraín Soto Apolinar
language : en
Publisher: Efrain Soto Apolinar
Release Date : 2020-06-30
Calculus With Infinitesimals written by Efraín Soto Apolinar and has been published by Efrain Soto Apolinar this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-30 with Mathematics categories.
This book covers the most important ideas of calculus and its applications. An emphasis is placed on the use of infinitely small quantities (i.e., infinitesimals), which were used in the creation of this branch of mathematics. The goal of the author is to provide a smoother transition to the understanding of the ideas of infinitesimal quantity, derivative, differential, antiderivative, and the definite integral. In order to give the reader an easier approach to learning and understanding these ideas, the same justifications given by the creators of the calculus are explained in this book. The justification of the formulas to compute derivatives is deduced according to its historical genesis with the use of the idea of infinitesimal as stated by Leibniz. Also, the justification of the formulas for antiderivatives is explained in detail. Some applications of the calculus are also covered, among them, extreme values of functions, related rates, arc length, area of regions in the plane, volume, surface area, mass, the center of mass, the moment of inertia, hydrostatic pressure, work, and several more. Mathematical rigor is not emphasized in this work, but instead, the meaning of the concepts and the understanding of the mathematical procedures in order to prepare the reader to apply the calculus in different contexts, among them: geometry, physics, and engineering problems. To motivate more teachers and students to use this book, the topics covered have been arranged according to most of the traditional calculus courses. However, because the theory of limits and the definitions of the ideas of calculus based on limits, were created many years later by Cauchy and Weierstrass, the limits and some related ideas (like continuity and differentiability) are not detailed covered.
The Origins Of Infinitesimal Calculus
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Author : Margaret E. Baron
language : en
Publisher: Elsevier
Release Date : 2014-05-09
The Origins Of Infinitesimal Calculus written by Margaret E. Baron and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-09 with Mathematics categories.
The Origins of Infinitesimal Calculus focuses on the evolution, development, and applications of infinitesimal calculus. The publication first ponders on Greek mathematics, transition to Western Europe, and some center of gravity determinations in the later 16th century. Discussions focus on the growth of kinematics in the West, latitude of forms, influence of Aristotle, axiomatization of Greek mathematics, theory of proportion and means, method of exhaustion, discovery method of Archimedes, and curves, normals, tangents, and curvature. The manuscript then examines infinitesimals and indivisibles in the early 17th century and further advances in France and Italy. Topics include the link between differential and integral processes, concept of tangent, first investigations of the cycloid, and arithmetization of integration methods. The book reviews the infinitesimal methods in England and Low Countries and rectification of arcs. The publication is a vital source of information for historians, mathematicians, and researchers interested in infinitesimal calculus.
Elementary Calculus
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Author : H. Jerome Keisler
language : en
Publisher: Prindle Weber & Schmidt
Release Date : 1986
Elementary Calculus written by H. Jerome Keisler and has been published by Prindle Weber & Schmidt this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
Infinitesimal Calculus
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Author : James M. Henle
language : en
Publisher: Courier Corporation
Release Date : 2014-01-15
Infinitesimal Calculus written by James M. Henle and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with Mathematics categories.
Introducing calculus at the basic level, this text covers hyperreal numbers and hyperreal line, continuous functions, integral and differential calculus, fundamental theorem, infinite sequences and series, infinite polynomials, more. 1979 edition.
Stochastic Calculus With Infinitesimals
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Author : Frederik S. Herzberg
language : en
Publisher: Springer
Release Date : 2012-11-06
Stochastic Calculus With Infinitesimals written by Frederik S. Herzberg and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-06 with Mathematics categories.
Stochastic analysis is not only a thriving area of pure mathematics with intriguing connections to partial differential equations and differential geometry. It also has numerous applications in the natural and social sciences (for instance in financial mathematics or theoretical quantum mechanics) and therefore appears in physics and economics curricula as well. However, existing approaches to stochastic analysis either presuppose various concepts from measure theory and functional analysis or lack full mathematical rigour. This short book proposes to solve the dilemma: By adopting E. Nelson's "radically elementary" theory of continuous-time stochastic processes, it is based on a demonstrably consistent use of infinitesimals and thus permits a radically simplified, yet perfectly rigorous approach to stochastic calculus and its fascinating applications, some of which (notably the Black-Scholes theory of option pricing and the Feynman path integral) are also discussed in the book.
A Treatise On The Differential Calculus
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Author : Bartholomew Price
language : en
Publisher:
Release Date : 1852
A Treatise On The Differential Calculus written by Bartholomew Price and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1852 with Differential calculus categories.
Elementary Calculus
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Author : H. Jerome Keisler
language : en
Publisher:
Release Date : 1976
Elementary Calculus written by H. Jerome Keisler and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Mathematics categories.
The Teaching Of Elementary Calculus
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Author : Kathleen Anne Sullivan
language : en
Publisher:
Release Date : 1974
The Teaching Of Elementary Calculus written by Kathleen Anne Sullivan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Calculus categories.
A Primer Of Infinitesimal Analysis
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Author : John Lane Bell
language : en
Publisher: Cambridge University Press
Release Date : 1998-07-28
A Primer Of Infinitesimal Analysis written by John Lane Bell 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 1998-07-28 with Mathematics categories.
This is the first elementary book to employ the concept of infinitesimals.