Get this product faster from our US warehouse
This is a textbook designed to teach students who are new to analysis what it's all about. ... The path Zorn takes is based on several very reasonable principles. These include: building on calculus basics; focusing on mathematical proof, structure and language; staying with the basics; offering many examples and many solved exercises; and gradually increasing technical sophistication. ... There are plenty of exercises. They tend to follow a pattern where an exercise that is not completely straightforward is broken into multiple parts to guide the student to a solution.
-- Bill Satzer, MAA Reviews, June 2010
Preface
1 Preliminaries: Numbers, Sets, Proofs, and Bounds
Numbers 101: The Very Basics
Sets 101: Getting Started
Sets 102: The Idea of a Function
Proofs 101: Proofs and Proof-Writing
Types of Proof
Sets 103: Finite and Infinite Sets; Cardinality
Numbers 102: Absolute Values
Bounds
Numbers 103: Completeness
2 Sequences and Series
SequencesandConvergence
WorkingwithSequences
Subsequences
CauchySequences
Series 101: Basic Ideas
Series 102: Testing for Convergence and Estimating Limits
Limsupandliminf:AGuidedDiscovery
3 Limits and Continuity
LimitsofFunctions
Continuous Functions
WhyContinuityMatters:ValueTheorems
UniformContinuity
4 Derivatives
DefiningtheDerivative
CalculatingDerivatives
TheMeanValueTheorem
SequencesofFunctions
5 Integrals
The Riemann Integral: Definition and Examples
Propertiesof the Integral
Integrability
Some Fundamental Theorems
Solutions