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Introduction to Abstract Analysis (Paperback, 1990)
Loot Price: R2,094
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Introduction to Abstract Analysis (Paperback, 1990)
Series: Chapman Hall/CRC Mathematics Series
Expected to ship within 12 - 17 working days
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Abstract analysis, and particularly the language of normed linear
spaces, now lies at the heart of a major portion of modern
mathematics. Unfortunately, it is also a subject which students
seem to find quite challenging and difficult. This book presumes
that the student has had a first course in mathematical analysis or
advanced calculus, but it does not presume the student has achieved
mastery of such a course. Accordingly, a gentle introduction to the
basic notions of convergence of sequences, continuity of functions,
open and closed set, compactness, completeness and separability is
given.
The pace in the early chapters does not presume in any way that the
readers have at their fingertips the techniques provided by an
introductory course. Instead, considerable care is taken to
introduce and use the basic methods of proof in a slow and explicit
fashion. As the chapters progress, the pace does quicken and later
chapters on differentiation, linear mappings, integration and the
implicit function theorem delve quite deeply into interesting
mathematical areas.
There are many exercises and many examples of applications of the
theory to diverse areas of mathematics. Some of these applications
take considerable space and time to develop, and make interesting
reading in their own right.
The treatment of the subject is deliberately not a comprehensive
one. The aim is to convince the undergraduate reader that analysis
is a stimulating, useful, powerful and comprehensible tool in
modern mathematics. This book will whet the readers' appetite, not
overwhelm them with material.
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