AN INTRODUCTION TO MATHEMATICAL ANALYSIS is an elementary text on
the theory of functions of one real variable and is intended for
students with a good understanding of calculus. It is supposed to
replace traditional and outmoded courses in mathematical analysis.
The book begins with material on the real number system as a
Dedekind complete ordered field, continuous functions, sequences
and series of constant terms as well as of functions. Pointwise and
uniform convergence of series of functions, power series, treatment
of trigonometric and exponential functions in terms of series are
discussed. A detailed treatment of differentiation, including
differentiation of uniform limits of sequences is provided. Also
included is an example of a continuous nowhere differentiable
function. There is an exhaustive treatment of both Riemann
integration and Riemann-Stieltjes integration. Some features of
this work, such as why Dedekind completeness is necessary for
ensuring that nonconstant functions cannot have derivative zero
everywhere on an interval, irrationality of evaluation of without
using multiple integration are normally not found in textbooks at
this level. There are several illustrative and worked examples, and
a large number of problems with solutions (available on a compact
disc).
General
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