id: 06243674
dt: b
an: 2014e.00634
au: Pons, Matthew A.
ti: Real analysis for the undergraduate. With an invitation to functional
analysis.
so: New York, NY: Springer (ISBN 978-1-4614-9637-3/hbk;
978-1-4614-9638-0/ebook). xviii, 409~p. (2014).
py: 2014
pu: New York, NY: Springer
la: EN
cc: I15
ut: real number system; numerical sequences and series; limits; continuity;
differentiation; sequences and series of functions; Riemann integral;
Lebesgue measure; Lebesgue integral
ci:
li: doi:10.1007/978-1-4614-9638-0
ab: This textbook is intended to introduce students to the basics of real
analysis. The most of the material comes from the standard
undergraduate course including an axiomatic or constructive exploration
of the real number system, sequences and series of numbers, limits and
continuity, differentiation, sequences and series of functions, and
some introductory form of integration. In addition, the reader can find
there the basic measure theory and the Lebesgue integral, and a brief
invitation to functional analysis. Each chapter covers a topic central
to a beginning course in real analysis, the last section in each
chapter introduces a topic from functional analysis which is derived in
a natural way from the core chapter content. Although the book contains
many advanced topics the author made them approachable for beginners
without sacrificing rigor. The reader is supposed to be experienced in
basic calculus (differentiation, integration, sequences and series), in
basic logic and set theory, proof techniques (induction, proof by
contradiction, and proof by contraposition), and basic function theory.
rv: Petr Gurka (Praha)