An Introduction To Analysis
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An Introduction To Analysis
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Author : Robert C. Gunning
language : en
Publisher: Princeton University Press
Release Date : 2018-03-20
An Introduction To Analysis written by Robert C. Gunning 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 2018-03-20 with Mathematics categories.
An essential undergraduate textbook on algebra, topology, and calculus An Introduction to Analysis is an essential primer on basic results in algebra, topology, and calculus for undergraduate students considering advanced degrees in mathematics. Ideal for use in a one-year course, this unique textbook also introduces students to rigorous proofs and formal mathematical writing--skills they need to excel. With a range of problems throughout, An Introduction to Analysis treats n-dimensional calculus from the beginning—differentiation, the Riemann integral, series, and differential forms and Stokes's theorem—enabling students who are serious about mathematics to progress quickly to more challenging topics. The book discusses basic material on point set topology, such as normed and metric spaces, topological spaces, compact sets, and the Baire category theorem. It covers linear algebra as well, including vector spaces, linear mappings, Jordan normal form, bilinear mappings, and normal mappings. Proven in the classroom, An Introduction to Analysis is the first textbook to bring these topics together in one easy-to-use and comprehensive volume. Provides a rigorous introduction to calculus in one and several variables Introduces students to basic topology Covers topics in linear algebra, including matrices, determinants, Jordan normal form, and bilinear and normal mappings Discusses differential forms and Stokes's theorem in n dimensions Also covers the Riemann integral, integrability, improper integrals, and series expansions
Introduction To Analysis
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Author : William R. Wade
language : en
Publisher:
Release Date : 2013-11-01
Introduction To Analysis written by William R. Wade and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-01 with categories.
For one- or two-semester junior or senior level courses in Advanced Calculus, Analysis I, or Real Analysis. This text prepares students for future courses that use analytic ideas, such as real and complex analysis, partial and ordinary differential equations, numerical analysis, fluid mechanics, and differential geometry. This book is designed to challenge advanced students while encouraging and helping weaker students. Offering readability, practicality and flexibility, Wade presents fundamental theorems and ideas from a practical viewpoint, showing students the motivation behind the mathematics and enabling them to construct their own proofs.
A Concise Introduction To Analysis
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Author : Daniel W. Stroock
language : en
Publisher: Springer
Release Date : 2015-10-31
A Concise Introduction To Analysis written by Daniel W. Stroock and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-31 with Mathematics categories.
This book provides an introduction to the basic ideas and tools used in mathematical analysis. It is a hybrid cross between an advanced calculus and a more advanced analysis text and covers topics in both real and complex variables. Considerable space is given to developing Riemann integration theory in higher dimensions, including a rigorous treatment of Fubini's theorem, polar coordinates and the divergence theorem. These are used in the final chapter to derive Cauchy's formula, which is then applied to prove some of the basic properties of analytic functions. Among the unusual features of this book is the treatment of analytic function theory as an application of ideas and results in real analysis. For instance, Cauchy's integral formula for analytic functions is derived as an application of the divergence theorem. The last section of each chapter is devoted to exercises that should be viewed as an integral part of the text. A Concise Introduction to Analysis should appeal to upper level undergraduate mathematics students, graduate students in fields where mathematics is used, as well as to those wishing to supplement their mathematical education on their own. Wherever possible, an attempt has been made to give interesting examples that demonstrate how the ideas are used and why it is important to have a rigorous grasp of them.
Mathematical Analysis
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Author : Andrew Browder
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mathematical Analysis written by Andrew Browder 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 2012-12-06 with Mathematics categories.
This is a textbook suitable for a year-long course in analysis at the ad vanced undergraduate or possibly beginning-graduate level. It is intended for students with a strong background in calculus and linear algebra, and a strong motivation to learn mathematics for its own sake. At this stage of their education, such students are generally given a course in abstract algebra, and a course in analysis, which give the fundamentals of these two areas, as mathematicians today conceive them. Mathematics is now a subject splintered into many specialties and sub specialties, but most of it can be placed roughly into three categories: al gebra, geometry, and analysis. In fact, almost all mathematics done today is a mixture of algebra, geometry and analysis, and some of the most in teresting results are obtained by the application of analysis to algebra, say, or geometry to analysis, in a fresh and surprising way. What then do these categories signify? Algebra is the mathematics that arises from the ancient experiences of addition and multiplication of whole numbers; it deals with the finite and discrete. Geometry is the mathematics that grows out of spatial experience; it is concerned with shape and form, and with measur ing, where algebra deals with counting.
An Introduction To Analysis
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Author : Piotr Mikusinski
language : en
Publisher: World Scientific Publishing Company
Release Date : 2017-02-17
An Introduction To Analysis written by Piotr Mikusinski and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-17 with Mathematics categories.
The book contains a rigorous exposition of calculus of a single real variable. It covers the standard topics of an introductory analysis course, namely, functions, continuity, differentiability, sequences and series of numbers, sequences and series of functions, and integration. A direct treatment of the Lebesgue integral, based solely on the concept of absolutely convergent series, is presented, which is a unique feature of a textbook at this level. The standard material is complemented by topics usually not found in comparable textbooks, for example, elementary functions are rigorously defined and their properties are carefully derived and an introduction to Fourier series is presented as an example of application of the Lebesgue integral.The text is for a post-calculus course for students majoring in mathematics or mathematics education. It will provide students with a solid background for further studies in analysis, deepen their understanding of calculus, and provide sound training in rigorous mathematical proof.
Yet Another Introduction To Analysis
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Author : Victor Bryant
language : en
Publisher: Cambridge University Press
Release Date : 1990-06-28
Yet Another Introduction To Analysis written by Victor Bryant 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 1990-06-28 with Mathematics categories.
In this book the author steers a path through the central ideas of real analysis.
Introduction To Analysis Of The Infinite
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Author : Leonhard Euler
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To Analysis Of The Infinite written by Leonhard Euler 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 2012-12-06 with Mathematics categories.
From the preface of the author: "...I have divided this work into two books; in the first of these I have confined myself to those matters concerning pure analysis. In the second book I have explained those thing which must be known from geometry, since analysis is ordinarily developed in such a way that its application to geometry is shown. In the first book, since all of analysis is concerned with variable quantities and functions of such variables, I have given full treatment to functions. I have also treated the transformation of functions and functions as the sum of infinite series. In addition I have developed functions in infinite series..."
Introduction To Analysis
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Author : Edward Gaughan
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Introduction To Analysis written by Edward Gaughan 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 2009 with Mathematics categories.
"The topics are quite standard: convergence of sequences, limits of functions, continuity, differentiation, the Riemann integral, infinite series, power series, and convergence of sequences of functions. Many examples are given to illustrate the theory, and exercises at the end of each chapter are keyed to each section."--pub. desc.
Introduction To Analysis
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Author : Maxwell Rosenlicht
language : en
Publisher: Courier Corporation
Release Date : 2012-05-04
Introduction To Analysis written by Maxwell Rosenlicht and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-04 with Mathematics categories.
Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more. 1968 edition.
An Introduction To Analysis
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Author : Gerald G. Bilodeau
language : en
Publisher: Jones & Bartlett Publishers
Release Date : 2009-07-28
An Introduction To Analysis written by Gerald G. Bilodeau and has been published by Jones & Bartlett Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-28 with Mathematics categories.
Part of the Jones and Bartlett International Series in Advanced Mathematics Completely revised and update, the second edition of An Introduction to Analysis presents a concise and sharply focused introdution to the basic concepts of analysis from the development of the real numbers through uniform convergences of a sequence of functions, and includes supplementary material on the calculus of functions of several variables and differential equations. This student-friendly text maintains a cautious and deliberate pace, and examples and figures are used extensively to assist the reader in understanding the concepts and then applying them. Students will become actively engaged in learning process with a broad and comprehensive collection of problems found at the end of each section.