First Course in Real Analysis

Description

Undergraduate Texts in Mathematics; A First Course in Real Analysis; Copyright; Preface to the Second Edition; Preface to the First Edition; Contents; CHAPTER 1 The Real Number System ; CHAPTER 2 Continuity and Limits ; CHAPTER 3 Basic Properties of Functions on R1 ; CHAPTER 4 Elementary Theory of Differentiation ; CHAPTER 5 Elementary Theory of Integration ; CHAPTER 6 Elementary Theory of Metric Spaces ; CHAPTER 7 Differentiation in RN ; CHAPTER 8 Integration in RN; CHAPTER 9 Infinite Sequences and Infinite Series ; CHAPTER 10 Fourier Series ; CHAPTER 11 Functions Defined by Integrals. Undergraduate Texts in Mathematics A First Course in Real Analysis Copyright Preface to the Second Edition Preface to the First Edition Contents CHAPTER 1 The Real Number System CHAPTER 2 Continuity and Limits CHAPTER 3 Basic Properties of Functions on R1 CHAPTER 4 Elementary Theory of Differentiation CHAPTER 5 Elementary Theory of Integration CHAPTER 6 Elementary Theory of Metric Spaces CHAPTER 7 Differentiation in RN CHAPTER 8 Integration in RN CHAPTER 9 Infinite Sequences and Infinite Series CHAPTER 10 Fourier Series CHAPTER 11 Functions Defined by Integrals. Improper Integrals CHAPTER 12 The Riemann-Stieltjes Integral and Functions of Bounded Variation CHAPTER 13 Contraction Mappings, Newton's Method, and Differential Equations CHAPTER 14 Implicit Function Theorems and Lagrange Multipliers CHAPTER 15 Functions on Metric Spaces Approximation CHAPTER 16 Vector Field Theory the Theorems of Green and Stokes Appendixes Answers to Odd-Numbered Problems Index.