e-book

Introduction to real analysis

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This is a text for a two-term course in introductory real analysis for junior or senior mathematics
majors and science students with a serious interest in mathematics. Prospective
educators or mathematically gifted high school students can also benefit from the mathematical
maturity that can be gained from an introductory real analysis course.

The book is designed to fill the gaps left in the development of calculus as it is usually
presented in an elementary course, and to provide the background required for insight into
more advanced courses in pure and applied mathematics. The standard elementary calculus
sequence is the only specific prerequisite for Chapters 1–5, which deal with real-valued
functions. (However, other analysis oriented courses, such as elementary differential equation,
also provide useful preparatory experience.) Chapters 6 and 7 require a working
knowledge of determinants, matrices and linear transformations, typically available from a
first course in linear algebra. Chapter 8 is accessible after completion of Chapters 1–5.
Without taking a position for or against the current reforms in mathematics teaching, I
think it is fair to say that the transition from elementary courses such as calculus, linear
algebra, and differential equations to a rigorous real analysis course is a bigger step today
than it was just a few years ago. To make this step today’s students need more help
than their predecessors did, and must be coached and encouraged more. Therefore, while
striving throughout to maintain a high level of rigor, I have tried to write as clearly and informally
as possible. In this connection I find it useful to address the student in the second
person. I have included 295 completely worked out examples to illustrate and clarify all
major theorems and definitions.

I have emphasized careful statements of definitions and theorems and have tried to be
complete and detailed in proofs, except for omissions left to exercises. I give a thorough
treatment of real-valued functions before considering vector-valued functions. In making
the transition from one to several variables and fromreal-valued to vector-valued functions,
I have left to the student some proofs that are essentially repetitions of earlier theorems. I
believe that working through the details of straightforward generalizations of more elementary
results is good practice for the student.

Great care has gone into the preparation of the 761 numbered exercises, many with
multiple parts. They range from routine to very difficult. Hints are provided for the more
difficult parts of the exercises.

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Ketersediaan

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Informasi Detail

Judul Seri

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No. Panggil

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Penerbit

New York : American Institute of Mathematics., 2004

Deskripsi Fisik

QA300.T667 - 515-dc21

Bahasa

English

ISBN/ISSN

0-13-045786-8

Klasifikasi

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Tipe Isi

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Tipe Media

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Tipe Pembawa

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Edisi

Free Hyperlinked Edition 2

Subjek

ANALISIS MATEMATIKA

Info Detail Spesifik

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Pernyataan Tanggungjawab

agus

Versi lain/terkait

Lampiran Berkas

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