An Introduction to Real Analysis

Description

"This book provides a compact, but thorough, introduction to the subject of Real Analysis. It is intended for a senior undergraduate and for a beginning graduate one-semester course."--Provided by publisher. Abstract: "This book provides a compact, but thorough, introduction to the subject of Real Analysis. It is intended for a senior undergraduate and for a beginning graduate one-semester course."--Provided by publisher Content: Cover Half Title Title Page Copyright Page Dedication Table of Contents Preface 1: Logic and Proof Techniques 2: Sets and Functions 3: Real Numbers 4: Open and Closed Sets 5: Cardinality 6: Real-Valued Functions 7: Real Sequences 8: Real Sequences (Contd.) 9: Infinite Series 10: Infinite Series (Contd.) 11: Limits of Functions 12: Continuous Functions 13: Discontinuous Functions 14: Uniform and Absolute Continuities and Functions of Bounded Variation 15: Differentiable Functions 16: Higher Order Differentiable Functions 17: Convex Functions 18: Indeterminate Forms 19: Riemann Integration20: Properties of the Riemann Integral 21: Improper Integrals 22: Riemann-Lebesgue Theorem 23: Riemann-Stieltjes Integral 24: Sequences of Functions 25: Sequences of Functions (Contd.) 26: Series of Functions 27: Power and Taylor Series 28: Power and Taylor Series (Contd.) 29: Metric Spaces 30: Metric Spaces (Contd.) Bibliography Index