English

Solving Real Analysis

The present volume contains hints or full solutions to many of the exercises in the first seven chapters of the text "Elements of Real Analysis," 2nd Edition by Robert G. Bartle, Professor of Mathematics (retired), University of Illinois Urbana-Champaign. Solving problems being an essential part of the learning process, my goal is to provide those learning and teaching mathematical analysis, real analysis, or the theory of functions with a large number of worked out exercises. The following theorem may give an indication as to the level of treatment given in Bartle's book: Bolzano-Weierstrass theorem, Heine-Borel theorem, Cantor intersection theorem, Lebesgue covering theorem, Baire's theorem, fixed point theorem for contradictions, Stone-Weierstrass theorem, Tietze extension theorem, Arzelà–Ascoli theorem, Rie representation theorem (for bounded positive linear functionals), Cauchy-Hadamard theorem, and Bernstein's theorem. Bartle's textbook could well provides a sound basis for a course taught at the undergraduate level for second or third year math students who have studied calculus. Therefore this solutions manual can be helpful to anyone learning or teaching mathematical analy

Sign in with your free account to read, download EPUBs or listen.