Real Analysis Via Sequences And Series
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Real Analysis Via Sequences And Series
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Author : Charles H.C. Little
language : en
Publisher: Springer
Release Date : 2015-05-28
Real Analysis Via Sequences And Series written by Charles H.C. Little and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-28 with Mathematics categories.
This text gives a rigorous treatment of the foundations of calculus. In contrast to more traditional approaches, infinite sequences and series are placed at the forefront. The approach taken has not only the merit of simplicity, but students are well placed to understand and appreciate more sophisticated concepts in advanced mathematics. The authors mitigate potential difficulties in mastering the material by motivating definitions, results and proofs. Simple examples are provided to illustrate new material and exercises are included at the end of most sections. Noteworthy topics include: an extensive discussion of convergence tests for infinite series, Wallis’s formula and Stirling’s formula, proofs of the irrationality of π and e and a treatment of Newton’s method as a special instance of finding fixed points of iterated functions.
The Real Numbers And Real Analysis
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Author : Ethan D. Bloch
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-27
The Real Numbers And Real Analysis written by Ethan D. Bloch 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 2011-05-27 with Mathematics categories.
This text is a rigorous, detailed introduction to real analysis that presents the fundamentals with clear exposition and carefully written definitions, theorems, and proofs. It is organized in a distinctive, flexible way that would make it equally appropriate to undergraduate mathematics majors who want to continue in mathematics, and to future mathematics teachers who want to understand the theory behind calculus. The Real Numbers and Real Analysis will serve as an excellent one-semester text for undergraduates majoring in mathematics, and for students in mathematics education who want a thorough understanding of the theory behind the real number system and calculus.
Basic Real Analysis
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Author : Houshang H. Sohrab
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-06-03
Basic Real Analysis written by Houshang H. Sohrab 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 2003-06-03 with Mathematics categories.
Basic Real Analysis demonstrates the richness of real analysis, giving students an introduction both to mathematical rigor and to the deep theorems and counter examples that arise from such rigor. In this modern and systematic text, all the touchstone results and fundamentals are carefully presented in a style that requires little prior familiarity with proofs or mathematical language. With its many examples, exercises and broad view of analysis, this work is ideal for senior undergraduates and beginning graduate students, either in the classroom or for self-study.
A First Course In Real Analysis
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Author : Sterling K. Berberian
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-10
A First Course In Real Analysis written by Sterling K. Berberian 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 2012-09-10 with Mathematics categories.
Mathematics is the music of science, and real analysis is the Bach of mathematics. There are many other foolish things I could say about the subject of this book, but the foregoing will give the reader an idea of where my heart lies. The present book was written to support a first course in real analysis, normally taken after a year of elementary calculus. Real analysis is, roughly speaking, the modern setting for Calculus, "real" alluding to the field of real numbers that underlies it all. At center stage are functions, defined and taking values in sets of real numbers or in sets (the plane, 3-space, etc.) readily derived from the real numbers; a first course in real analysis traditionally places the emphasis on real-valued functions defined on sets of real numbers. The agenda for the course: (1) start with the axioms for the field ofreal numbers, (2) build, in one semester and with appropriate rigor, the foun dations of calculus (including the "Fundamental Theorem"), and, along theway, (3) develop those skills and attitudes that enable us to continue learning mathematics on our own. Three decades of experience with the exercise have not diminished my astonishment that it can be done.
Real Analysis
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Author : John M. Howie
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Real Analysis written by John M. Howie 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 point of view of strict logic, a rigorous course on real analysis should precede a course on calculus. Strict logic, is, however, overruled by both history and practicality. Historically, calculus, with its origins in the 17th century, came first, and made rapid progress on the basis of informal intuition. Not until well through the 19th century was it possible to claim that the edifice was constructed on sound logical foundations. As for practicality, every university teacher knows that students are not ready for even a semi-rigorous course on analysis until they have acquired the intuitions and the sheer technical skills that come from a traditional calculus course. 1 Real analysis, I have always thought, is the pons asinorv.m of modern mathematics. This shows, I suppose, how much progress we have made in two thousand years, for it is a great deal more sophisticated than the Theorem of Pythagoras, which once received that title. All who have taught the subject know how patient one has to be, for the ideas take root gradually, even in students of good ability. This is not too surprising, since it took more than two centuries for calculus to evolve into what we now call analysis, and even a gifted student, guided by an expert teacher, cannot be expected to grasp all of the issues immediately.
Problems In Mathematical Analysis Real Numbers Sequences And Series
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Author : Wiesława J. Kaczor
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Problems In Mathematical Analysis Real Numbers Sequences And Series written by Wiesława J. Kaczor 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 2000 with Mathematics categories.
Solutions for all the problems are provided."--BOOK JACKET.
A Course In Real Analysis
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Author : Hugo D. Junghenn
language : en
Publisher: CRC Press
Release Date : 2015-02-13
A Course In Real Analysis written by Hugo D. Junghenn and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-13 with Mathematics categories.
A Course in Real Analysis provides a rigorous treatment of the foundations of differential and integral calculus at the advanced undergraduate level. The book's material has been extensively classroom tested in the author's two-semester undergraduate course on real analysis at The George Washington University.The first part of the text presents the
A Course In Calculus And Real Analysis
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Author : Sudhir R. Ghorpade
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-05
A Course In Calculus And Real Analysis written by Sudhir R. Ghorpade 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 2006-06-05 with Mathematics categories.
This book provides a self-contained and rigorous introduction to calculus of functions of one variable, in a presentation which emphasizes the structural development of calculus. Throughout, the authors highlight the fact that calculus provides a firm foundation to concepts and results that are generally encountered in high school and accepted on faith; for example, the classical result that the ratio of circumference to diameter is the same for all circles. A number of topics are treated here in considerable detail that may be inadequately covered in calculus courses and glossed over in real analysis courses.
Real Analysis
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Author : Halsey Royden
language : en
Publisher:
Release Date : 2018
Real Analysis written by Halsey Royden and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Business & Economics categories.
This text is designed for graduate-level courses in real analysis. Real Analysis, 4th Edition, covers the basic material that every graduate student should know in the classical theory of functions of a real variable, measure and integration theory, and some of the more important and elementary topics in general topology and normed linear space theory. This text assumes a general background in undergraduate mathematics and familiarity with the material covered in an undergraduate course on the fundamental concepts of analysis.
A First Course In Real Analysis
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Author : M.H. Protter
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
A First Course In Real Analysis written by M.H. Protter 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.
The first course in analysis which follows elementary calculus is a critical one for students who are seriously interested in mathematics. Traditional advanced calculus was precisely what its name indicates-a course with topics in calculus emphasizing problem solving rather than theory. As a result students were often given a misleading impression of what mathematics is all about; on the other hand the current approach, with its emphasis on theory, gives the student insight in the fundamentals of analysis. In A First Course in Real Analysis we present a theoretical basis of analysis which is suitable for students who have just completed a course in elementary calculus. Since the sixteen chapters contain more than enough analysis for a one year course, the instructor teaching a one or two quarter or a one semester junior level course should easily find those topics which he or she thinks students should have. The first Chapter, on the real number system, serves two purposes. Because most students entering this course have had no experience in devising proofs of theorems, it provides an opportunity to develop facility in theorem proving. Although the elementary processes of numbers are familiar to most students, greater understanding of these processes is acquired by those who work the problems in Chapter 1. As a second purpose, we provide, for those instructors who wish to give a comprehen sive course in analysis, a fairly complete treatment of the real number system including a section on mathematical induction.