id: 06036202
dt: b
an: 2013e.00575
au: Dineen, Seán
ti: Analysis. A gateway to understanding mathematics.
so: Hackensack, NJ: World Scientific (ISBN 978-981-4401-38-8/hbk). xviii,
301~p. (2012).
py: 2012
pu: Hackensack, NJ: World Scientific
la: EN
cc: I15
ut: real functions of one real variable; numbers; sequences; series; continuous
functions; differentiable functions; Riemann integral
ci:
li:
ab: The book is based on the course on differential and integral calculus of
one real variable teached for students of Economics and Finance at the
University College Dublin. The author wanted to show the readers how to
approach and understand mathematics. The book covers the traditional
topics of calculus such as continuity and differentiability of
functions, sequences, infinite series, the Riemann definite integral
and its applications. Moreover, the book also contains chapters on the
foundations of mathematics. Let us mention, for example, an
introduction of real numbers through completion of rational numbers. In
many places in the book the reader can find historical notes related to
topics dealt with. This book may be used as a text in a standard one
variable calculus or analysis course, however it might be also very
useful for better understanding of the fundamentals of the mathematical
analysis.
rv: Petr Gurka (Praha)