Real Analysis for the Undergraduate With an Invitation to Functional Analysis [Hardcover]

This undergraduate textbook introduces students to the basics of real analysis, provides an introduction to more advanced topics including measure theory and Lebesgue integration, and offers an invitation to functional analysis. While these advanced topics are not typically encountered until graduate study, the text is designed for the beginner. The authors engaging style makes advanced topics approachable without sacrificing rigor. The text also consistently encourages the reader to pick up a pencil and take an active part in the learning process. Key features include: - examples to reinforce theory; - thorough explanations preceding definitions, theorems and formal proofs; - illustrations to support intuition; - over 450 exercises designed to develop connections between the concrete and abstract. This text takes students on a journey through the basics of real analysis and provides those who wish to delve deeper the opportunity to experience mathematical ideas that are beyond the standard undergraduate curriculum.

Written in an engaging style that renders complex concepts accessible to a wide readership, and with more than 450 exercises, this textbook introduces the basics of real analysis as well as more advanced topics such as measure theory and Lebesgue integration.

The Real Numbers.- Sequences in R.- Numerical Series.- Continuity.- The Derivative.- Sequence and Series of Functions.- The Riemann Integral.- Lebesgue Measure on R.- Lebesgue Integration.

From the book reviews:

This book is more than just an excellent introduction to real analysis at the undergraduate level. It also provides the basis for students to gain some experience in measure theory, Lebesgue integration, and functional analysis. & Summing Up: Highly recommended. Upper-division undergraduates and above. (D. P. Turner, Choice, Vol. 52 (2), October, 2014)

This book contains a reasonably complete exposition of real analysis theorlc#