Analysis With Ultrasmall Numbers
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Analysis With Ultrasmall Numbers
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Author : Karel Hrbacek
language : en
Publisher: CRC Press
Release Date : 2014-12-01
Analysis With Ultrasmall Numbers written by Karel Hrbacek and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-01 with Mathematics categories.
Analysis with Ultrasmall Numbers presents an intuitive treatment of mathematics using ultrasmall numbers. With this modern approach to infinitesimals, proofs become simpler and more focused on the combinatorial heart of arguments, unlike traditional treatments that use epsilon-delta methods. Students can fully prove fundamental results, such as the
A Course In Abstract Harmonic Analysis
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Author : Gerald B. Folland
language : en
Publisher: CRC Press
Release Date : 2016-02-03
A Course In Abstract Harmonic Analysis written by Gerald B. Folland and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-03 with Mathematics categories.
A Course in Abstract Harmonic Analysis is an introduction to that part of analysis on locally compact groups that can be done with minimal assumptions on the nature of the group. As a generalization of classical Fourier analysis, this abstract theory creates a foundation for a great deal of modern analysis, and it contains a number of elegant resul
Numerical Analysis For Engineers
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Author : Bilal Ayyub
language : en
Publisher: CRC Press
Release Date : 2015-09-18
Numerical Analysis For Engineers written by Bilal Ayyub and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-18 with Mathematics categories.
Numerical Analysis for Engineers: Methods and Applications demonstrates the power of numerical methods in the context of solving complex engineering and scientific problems. The book helps to prepare future engineers and assists practicing engineers in understanding the fundamentals of numerical methods, especially their applications, limitations, and potentials. Each chapter contains many computational examples, as well as a section on applications that contain additional engineering examples. Each chapter also includes a set of exercise problems. The problems are designed to meet the needs of instructors in assigning homework and to help students with practicing the fundamental concepts. Although the book was developed with emphasis on engineering and technological problems, the numerical methods can also be used to solve problems in other fields of science.
Nonstandard Analysis
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Author : Karl Kuhlemann
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-12-16
Nonstandard Analysis written by Karl Kuhlemann and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-16 with Mathematics categories.
Currently, nonstandard analysis is barely considered in university teaching. The author argues that nonstandard analysis is valuable not only for teaching, but also for understanding standard analysis and mathematics itself. An axiomatic approach wich pays attention to different language levels (for example, in the distinction between sums of ones and the natural numbers of the theory) leads naturally to a nonstandard theory. For motivation historical ideas of Leibniz can be taken up. The book contains an elaborated concept that follows this approach and is suitable, for example, as a basis for a lecture-supplementary course. The monograph part presents all major approaches to nonstandard analysis and discusses logical, model-theoretic, and set-theoretic investigations to reveal possible mathematical reasons that may lead to reservations about nonstandard analysis. Also various foundational positions as well as ontological, epistemological, and application-related issues are addressed. It turns out that the one-sided preference for standard analysis is justified neither from a didactic, mathematical nor philosophical point of view. Thus, the book is especially valuable for students and instructors of analysis who are also interested in the foundations of their subject.
Elementary Number Theory
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Author : James S. Kraft
language : en
Publisher: CRC Press
Release Date : 2014-11-24
Elementary Number Theory written by James S. Kraft and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-24 with Mathematics categories.
Elementary Number Theory takes an accessible approach to teaching students about the role of number theory in pure mathematics and its important applications to cryptography and other areas. The first chapter of the book explains how to do proofs and includes a brief discussion of lemmas, propositions, theorems, and corollaries. The core of the text covers linear Diophantine equations; unique factorization; congruences; Fermat’s, Euler’s, and Wilson’s theorems; order and primitive roots; and quadratic reciprocity. The authors also discuss numerous cryptographic topics, such as RSA and discrete logarithms, along with recent developments. The book offers many pedagogical features. The "check your understanding" problems scattered throughout the chapters assess whether students have learned essential information. At the end of every chapter, exercises reinforce an understanding of the material. Other exercises introduce new and interesting ideas while computer exercises reflect the kinds of explorations that number theorists often carry out in their research.
Introduction To Number Theory
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Author : Anthony Vazzana
language : en
Publisher: CRC Press
Release Date : 2015-11-18
Introduction To Number Theory written by Anthony Vazzana and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-18 with Mathematics categories.
Introduction to Number Theory is a classroom-tested, student-friendly text that covers a diverse array of number theory topics, from the ancient Euclidean algorithm for finding the greatest common divisor of two integers to recent developments such as cryptography, the theory of elliptic curves, and the negative solution of Hilbert's tenth problem.
The Mathematics Of Games
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Author : David G. Taylor
language : en
Publisher: CRC Press
Release Date : 2014-12-01
The Mathematics Of Games written by David G. Taylor and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-01 with Mathematics categories.
The Mathematics of Games: An Introduction to Probability takes an inquiry-based approach to teaching the standard material for an introductory probability course. It also discusses different games and ideas that relate to the law of large numbers, as well as some more mathematical topics not typically found in similar books. Written in an accessibl
Applied Differential Equations
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Author : Vladimir A. Dobrushkin
language : en
Publisher: CRC Press
Release Date : 2018-12-07
Applied Differential Equations written by Vladimir A. Dobrushkin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-07 with Mathematics categories.
A Contemporary Approach to Teaching Differential Equations Applied Differential Equations: An Introduction presents a contemporary treatment of ordinary differential equations (ODEs) and an introduction to partial differential equations (PDEs), including their applications in engineering and the sciences. Designed for a two-semester undergraduate course, the text offers a true alternative to books published for past generations of students. It enables students majoring in a range of fields to obtain a solid foundation in differential equations. The text covers traditional material, along with novel approaches to mathematical modeling that harness the capabilities of numerical algorithms and popular computer software packages. It contains practical techniques for solving the equations as well as corresponding codes for numerical solvers. Many examples and exercises help students master effective solution techniques, including reliable numerical approximations. This book describes differential equations in the context of applications and presents the main techniques needed for modeling and systems analysis. It teaches students how to formulate a mathematical model, solve differential equations analytically and numerically, analyze them qualitatively, and interpret the results.
Measure Theory And Fine Properties Of Functions Revised Edition
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Author : Lawrence C. Evans
language : en
Publisher: CRC Press
Release Date : 2015-04-17
Measure Theory And Fine Properties Of Functions Revised Edition written by Lawrence C. Evans and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-17 with Mathematics categories.
This book emphasizes the roles of Hausdorff measure and the capacity in characterizing the fine properties of sets and functions. The book covers theorems and differentiation in Rn , Hausdorff measures, area and coarea formulas for Lipschitz mappings and related change-of-variable formulas, and Sobolev functions and functions of bounded variation. This second edition includes countless improvements in notation, format, and clarity of exposition. Also new are several sections describing the p- theorem, weak compactness criteria in L1, and Young measure methods for weak convergence. In addition, the bibliography has been updated.
Transformational Plane Geometry
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Author : Ronald N. Umble
language : en
Publisher: CRC Press
Release Date : 2014-12-01
Transformational Plane Geometry written by Ronald N. Umble and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-01 with Mathematics categories.
Designed for a one-semester course at the junior undergraduate level, Transformational Plane Geometry takes a hands-on, interactive approach to teaching plane geometry. The book is self-contained, defining basic concepts from linear and abstract algebra gradually as needed. The text adheres to the National Council of Teachers of Mathematics Principles and Standards for School Mathematics and the Common Core State Standards Initiative Standards for Mathematical Practice. Future teachers will acquire the skills needed to effectively apply these standards in their classrooms. Following Felix Klein’s Erlangen Program, the book provides students in pure mathematics and students in teacher training programs with a concrete visual alternative to Euclid’s purely axiomatic approach to plane geometry. It enables geometrical visualization in three ways: Key concepts are motivated with exploratory activities using software specifically designed for performing geometrical constructions, such as Geometer’s Sketchpad. Each concept is introduced synthetically (without coordinates) and analytically (with coordinates). Exercises include numerous geometric constructions that use a reflecting instrument, such as a MIRA. After reviewing the essential principles of classical Euclidean geometry, the book covers general transformations of the plane with particular attention to translations, rotations, reflections, stretches, and their compositions. The authors apply these transformations to study congruence, similarity, and symmetry of plane figures and to classify the isometries and similarities of the plane.