# A First Course in Analysis

• George Pedrick
Book

Part of the Undergraduate Texts in Mathematics book series (UTM)

1. Front Matter
Pages i-xxi
2. ### Background: Number Systems

1. George Pedrick
Pages 1-33
3. ### Analysis

1. Front Matter
Pages 35-35
2. George Pedrick
Pages 37-63
3. George Pedrick
Pages 64-96
4. George Pedrick
Pages 97-130
4. ### Foundations of Calculus

1. Front Matter
Pages 131-131
2. George Pedrick
Pages 133-168
3. George Pedrick
Pages 169-217
4. George Pedrick
Pages 218-265
5. Back Matter
Pages 266-279

### Introduction

The first course in Analysis, which follows calculus, along with other courses, such as differential equations and elementary linear algebra, in the curricu­ lum, presents special pedagogical challenges. There is a change of stress from computational manipulation to "proof. " Indeed, the course can become more a course in Logic than one in Analysis. Many students, caught short by a weak command of the means of mathematical discourse and unsure of what is expected of them, what "the game" is, suffer bouts of a kind of mental paralysis. This text attempts to address these problems in several ways: First, we have attempted to define "the game" as that of "inquiry," by using a form of exposition that begins with a question and proceeds to analyze, ultimately to answer it, bringing in definitions, arguments, conjectures, exam­ ples, etc. , as they arise naturally in the course of a narrative discussion of the question. (The true, historical narrative is too convoluted to serve for first explanations, so no attempt at historical accuracy has been made; our narra­ tives are completely contrived. ) Second, we have kept the logic informal, especially in the course of preliminary speculative discussions, where common sense and plausibility­ tempered by mild skepticism-serve to energize the inquiry.

### Keywords

Derivative Fourier series Fundamental theorem of calculus calculus compactness continuous function differential equation improper integral logarithm measure

#### Authors and affiliations

• George Pedrick
• 1
1. 1.OaklandUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4419-8554-5
• Copyright Information Springer-Verlag New York, Inc. 1994
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-1-4612-6435-4
• Online ISBN 978-1-4419-8554-5
• Series Print ISSN 0172-6056