Description

This award-winning text carefully leads the student through the basic topics of Real Analysis. Topics include metric spaces/ open and closed sets/ convergent sequences/ function limits and continuity/ compact sets/ sequences and series of functions/ power series/ differentiation and integration/ Taylor's theorem/ total variation/ rectifiable arcs/ and sufficient conditions of integrability. Well over 500 exercises (many with extensive hints) assist students through the material. For students who need a review of basic mathematical concepts before beginning "epsilon-delta"-style proofs/ the text begins with material on set theory (sets/ quantifiers/ relations and mappings/ countable sets)/ the real numbers (axioms/ natural numbers/ induction/ consequences of the completeness axiom)/ and Euclidean and vector spaces; this material is condensed from the author's Basic Concepts of Mathematics/ the complete version of which can be used as supplementary background material for the present text.