Introduction to Analysis Pearson New International Edition

✍ Scribed by Wade, William R

• Publisher: Pearson Education Limited
• Year: 2014
• Tongue: English
• Leaves: 649
• Edition: 4ed.
• Category: Library

✦ Synopsis

book

✦ Table of Contents

Content: Preface Part I. ONE-DIMENSIONAL THEORY 1. The Real Number System 1.1 Introduction 1.2 Ordered field axioms 1.3 Completeness Axiom 1.4 Mathematical Induction 1.5 Inverse functions and images 1.6 Countable and uncountable sets 2. Sequences in R 2.1 Limits of sequences 2.2 Limit theorems 2.3 Bolzano-Weierstrass Theorem 2.4 Cauchy sequences 2.5 Limits supremum and infimum 3. Continuity on R 3.1 Two-sided limits 3.2 One-sided limits and limits at infinity 3.3 Continuity 3.4 Uniform continuity 4. Differentiability on R 4.1 The derivative 4.2 Differentiability theorems 4.3 The Mean Value Theorem 4.4 Taylor's Theorem and l'Hô
pital's Rule 4.5 Inverse function theorems 5 Integrability on R 5.1 The Riemann integral 5.2 Riemann sums 5.3 The Fundamental Theorem of Calculus 5. 4 Improper Riemann integration 5.5 Functions of bounded variation *5.6 Convex functions 6. Infinite Series of Real Numbers 6.1 Introduction 6. 2 Seri

✦ Subjects

Funktional analyse;Harmonisk analyse