Introductory analysis : an inquiry approach / John D. Ross, Kendall C. Richards.

Format:

Book

Author/Creator:

Ross, John D.

Contributor:

Richards, Kendall C.

Language:

English

Subjects (All):

Mathematical analysis.

Inquiry-based learning.

Physical Description:

1 online resource (251 pages)

Edition:

1st ed.

Place of Publication:

Boca Raton, FL : CRC Press, 2020.

Summary:

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

Contents:

Exploring mathematical statements

Proving mathematical statements

Preliminary content

Properties of R

Accumulation points and closed sets

Open sets and open covers

Sequences and convergence

Subsequences and Cauchy sequences

Functions, limits, and continuity

Connected sets and the intermediate value theorem

Compact sets

Uniform continuity

Introduction to the derivative

The extreme and mean value theorems

The definite integral : part I

The definite integral : part II

The fundamental theorem(s) of calculus

Series

Function approximation

Power series

Sequences and series of functions

Metric spaces

Iterated functions and fixed point theorems

Brief summary of ordered field properties.

Notes:

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-351-24672-0

1-351-24674-7

9781351246743

OCLC:

1139396273