Title:
Closer and closer : introducing real analysis
Personal Author:
Publication Information:
Sudbury, MA : Jones and Bartlett Publishers, 2008
ISBN:
9780763735937
Available:*
Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | 30000010142037 | QA331 S33 2008 | Open Access Book | Book | Searching... |
On Order
Summary
Summary
Closer and Closer is the ideal first introduction to real analysis for upper-level undergraduate Math majors. The text is divided into two main parts; the core material of the subject is covered in Chapters 1-12, and a series of cases, examples, applications, and projects, collectively called Excursions form the second half of the book. These Excursions are designed to bring the concepts of real analysis to light and to allow students to work through numerous interesting problems with ease.
Table of Contents
| Part 1 Central IdeasBasic Building Blocks |
| Chapter 1 The Real Numbers |
| Chapter 2 Measuring Distances |
| Chapter 3 Sets and Limits |
| Chapter 4 Continuity |
| Chapter 5 Real-Valued Functions |
| Chapter 6 Completeness |
| Chapter 7 Compactness |
| Chapter 8 Connectedness |
| Chapter 9 Differentiation of Functions of One Real Variable |
| Chapter 10 Iteration and the Contraction Mapping Theorem |
| Chapter 11 The Riemann Integral |
| Chapter 12 Sequences of Functions |
| Chapter 13 Differentiating f: Rn - Rm |
| Part 2 Excursions |
| Chapter 14 Truth and Provability |
| Chapter 15 Number Properties |
| Chapter 16 Exponents |
| Chapter 17 Sequences in R and Rn |
| Chapter 18 Limits of Functions from R to R |
| Chapter 19 Doubly Indexed Sequences |
| Chapter 20 Subsequences and Convergence |
| Chapter 21 Series of Real Numbers |
| Chapter 22 Probing the Definition of the Riemann Integral |
| Chapter 23 Power Series |
| Chapter 24 Everywhere Continuous, Nowhere Differentiable |
| Chapter 25 Newton's Method |
| Chapter 26 The Implicit Function Theorem |
| Chapter 27 Spaces of Continuous Functions |
| Chapter 28 Solutions to Differential Equations |
