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    Station Eleven

    Emily St. John Mandel 9780385353304

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25 Remote Warehouse Mathematics- Analysis General

This title in other editions

A Course in Calculus and Real Analysis (Undergraduate Texts in Mathematics)

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A Course in Calculus and Real Analysis (Undergraduate Texts in Mathematics) Cover

 

Synopses & Reviews

Publisher Comments:

This book provides a self-contained and rigorous introduction to calculus of functions of one variable. The presentation and sequencing of topics emphasizes the structural development of calculus. At the same time, due importance is given to computational techniques and applications. The authors have strived to make a distinction between the intrinsic definition of a geometric notion and its analytic characterization. Throughout the book, the authors highlight the fact that calculus provides a firm foundation to several concepts and results that are generally encountered in high school and accepted on faith. For example, one can find here a proof of the classical result that the ratio of the circumference of a circle to its diameter is the same for all circles. Also, this book helps students get a clear understanding of the concept of an angle and the definitions of the logarithmic, exponential and trigonometric functions together with a proof of the fact that these are not algebraic functions. A number of topics that may have been inadequately covered in calculus courses and glossed over in real analysis courses are treated here in considerable detail. As such, this book provides a unified exposition of calculus and real analysis. The only prerequisites for reading this book are topics that are normally covered in high school; however, the reader is expected to possess some mathematical maturity and an ability to understand and appreciate proofs. This book can be used as a textbook for a serious undergraduate course in calculus, while parts of the book can be used for advanced undergraduate and graduate courses in real analysis. Each chapter contains several examples and a large selection of exercises, as well as "Notes and Comments" describing salient features of the exposition, related developments and references to relevant literature.

Synopsis:

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.

Table of Contents

Preface.- Numbers and Functions.- Sequences.- Continuity and Limits.- Differentiation.- Applications of Differentiation.- Integration.- Elementary Transcendental Functions.- Applications and Approximations of Riemann Integrals.- Infinite Series and Improper Integrals.- References.- List of Symbols and Abbreviations.- Index.

Product Details

ISBN:
9781441921451
Author:
Ghorpade, Sudhir R.
Publisher:
Springer
Author:
Limaye, Balmohan V.
Subject:
Mathematical Analysis
Subject:
Analysis
Subject:
Real functions
Subject:
Sequences, Series, Summability
Subject:
Sequences, Series, Summability <P>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. Giving due importance is given to computat
Subject:
Mathematics-Analysis General
Copyright:
Edition Description:
Softcover reprint of hardcover 1st ed. 2006
Series:
Undergraduate Texts in Mathematics
Publication Date:
20101129
Binding:
TRADE PAPER
Language:
English
Pages:
442
Dimensions:
235 x 155 mm 668 gr

Related Subjects


Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » Functional Analysis
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Probability and Statistics » General
Science and Mathematics » Mathematics » Probability and Statistics » Statistics

A Course in Calculus and Real Analysis (Undergraduate Texts in Mathematics) New Trade Paper
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Product details 442 pages Not Avail - English 9781441921451 Reviews:
"Synopsis" by , 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.
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