Elements of Real Analysis
Comprehensive in coverage, this book explores the principles of logic, the axioms for the real numbers, limits of sequences, limits of functions, differentiation and integration, infinite series, convergence, and uniform convergence for sequences of real-valued functions. Concepts are presented slowly and include the details of calculations as well as substantial explanations as to how and why one proceeds in the given manner.  Uses the words WHY? and HOW? throughout; inviting readers to become active participants and to supply a missing argument or a simple calculation. Contains more than 1000 individual exercises. Stresses and reviews elementary algebra and symbol manipulation as essential tools for success at the kind of computations required in dealing with limiting processes.