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A COURSE IN MATHEMATICAL ANALYSIS

Volume I: Foundations and Elementary Real Analysis

The three volumes of

A Course in Mathematical Analysis

provide a full and

detailed account of all those elements of real and complex analysis that an

undergraduate mathematics student can expect to encounter in the first two

or three years of study. Containing hundreds of exercises, examples and appli-

cations, these books will become an invaluable resource for both students and

instructors.

Volume I focuses on the analysis of real-valued functions of a real variable.

Besides developing the basic theory it describes many applications, including

a chapter on Fourier series. It also includes a Prologue in which the author

introduces the axioms of set theory and uses them to construct the real

number system. Volume II goes on to consider metric and topological spaces,

and functions of several variables. Volume III covers complex analysis and

the theory of measure and integration.

d. j. h. garling

is Emeritus Reader in Mathematical Analysis at the

University of Cambridge and Fellow of St John’s College, Cambridge. He has

fifty years’ experience of teaching undergraduate students in most areas of

pure mathematics, but particularly in analysis.

A COURSE IN

M AT H E M AT I C A L A N A LY S I S

Volume I

Foundations and

Elementary Real Analysis

D. J. H. G A R L I N G

Emeritus Reader in Mathematical Analysis,

University of Cambridge, and

Fellow of St John’s College, Cambridge