Introductory Analysis An Inquiry Approach 1st Edition by John D Ross, Kendall C Richards ISBN 1351246747 9781351246743
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Product details:
ISBN 10: 1351246747
ISBN 13: 9781351246743
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.
Features
- Structured in such a way that approximately one week of class can be devoted to each chapter
- Suitable as a primary text for undergraduates, or as a supplementary text for some postgraduate courses
- Strikes a unique balance between enquiry-based learning and more traditional approaches to teaching
Table of contents:
Prerequisites
Chapter P1: Exploring Mathematical Statements
Chapter P2: Proving Mathematical Statements
Chapter P3: Preliminary Content
Main 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: Subsequences 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: The Definite Integral: Part II
Chapter 14: The Fundamental Theorem(s) of Calculus
Chapter 15: Series
Extended Explorations
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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