Please recommend textbook with exercises and full solutions, for a first course on Real Analysis

Question

My Intro to Real Analysis course covers topics such as:

Real numbers and sequences. Metric spaces, compactness and connectedness. Sequences and series of functions, power series; modes of convergence. Interchange of limiting processes; differentiation of integrals. Function spaces; Weierstrass approximation theorem.

My course's textbook is Real Analysis and Applications: Theory in Practice by Davidson and Donsig. The problem with this book is that it doesn't have any solutions for its exercises. Anyone here know of a similar book that covers the same topics and has similar exercises, but with solutions?

Answer 1

You can found solutions on the web for" Royden, Real analysis" . But it is not an introductory text.

Answer 2

I recommend The How and Why of One Variable Calculus by Amol Sasane because it furnishes many color diagrams, and detailed solutions for every exercise in full view!

I STRONGLY DISAGREE with JYM's answer. DON'T use Royden's Real Analysis as an introduction.

Answer 3

Stephen Abbott's Understanding Analysis is a great introduction with elegant proofs and intuitive explanations.