Introductory Analysis An Inquiry Approach 1st Edition by John D Ross, Kendall C Richards ISBN 103217501X 978-1032175010

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Product details:

ISBN 10: 103217501X 

ISBN 13: 978-1032175010

Author:  John D. Ross, Kendall C. Richards

Introductory Analysis: An Inquiry Approach aims to provide a self-contained, inquiry-oriented approach to undergraduate-level real analysis.

The presentation of the material in the book is intended to be “inquiry-oriented'” in that as each major topic is discussed, details of the proofs are left to the student in a way that encourages an active approach to learning. The book is “self-contained” in two major ways: it includes scaffolding (i.e., brief guiding prompts marked as Key Steps in the Proof) for many of the theorems. Second, it includes preliminary material that introduces students to the fundamental framework of logical reasoning and proof-writing techniques. Students will be able to use the guiding prompts (and refer to the preliminary work) to develop their proof-writing skills.

Table of contents: 

Chapter P1: Exploring Mathematical Statements  
Chapter P2: Proving Mathematical Statements  
Chapter P3: Preliminary Content  
Chapter 1: Properties of ℝ  
Chapter 2: Accumulation Points and Closed Sets  
Chapter 3: Open Sets and Open Covers  
Chapter 4: Sequences and Convergence  
Chapter 5: Subsequence and Cauchy Sequences  
Chapter 6: Functions, Limits, and Continuity  
Chapter 7: Connected Sets and the Intermediate Value Theorem  
Chapter 8: Compact Sets  
Chapter 9: Uniform Continuity  
Chapter 10: Introduction to the Derivative  
Chapter 11: The Extreme and Mean Value Theorems  
Chapter 12: The Definite Integral: Part I  
Chapter 13: Introductory Analysis: An Inquiry Approach  
Chapter 14: Introductory Analysis: An Inquiry Approach  
Chapter 15: Series  
Chapter E1: Function Approximation  
Chapter E2: Power Series  
Chapter E3: Sequences and Series of Functions  
Chapter E4: Metric Spaces  
Chapter E5: Iterated Functions and Fixed Point Theorems

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Tags: John D Ross, Kendall C Richards, Introductory Analysis, Inquiry Approach