Learn Limits Through Problems! ( Pocket Mathematical Library Workbook 2) – Gelfand et al.

In this post, we will see the book Learn Limits Through Problems! ( Pocket Mathematical Library Workbook 2) by S. I. Gelfand; M. L. Gerver; A. A. Kirillov; N. N. Konstantinov; A.G. Kushnirenko.

About the book

This is the second workbook in the Pocket Mathematical Library. It is essentially a programmed text inviting you to learn about limits (a key concept of modern mathematics) by solving a series of 56 problems and reading a little interspersed text. The problems are for the most part equipped with hints and answers (or both), enough for you to get the hang of them (harder problems are marked with asterisks). Moreover, the problems fall into three groups. The first, called “Preli­minaries,” puts you into the right frame of mind for absorbing the limit concept. The second, called “Concepts,” presents the irreducible amount of theoretical material needed to under­stand limits. The third, called “Calculations,” shows you how to evaluate limits once you know what they are.

The core of the book is really the section called “Solutions,” where all 56 problems are worked out in full detail. This section should be read carefully after you have tried solving the problems on your own. Please do not give up too soon, since this will only defeat the purpose of the book.

When you are satisfied that you have mastered the subject matter of the book, try solving the 11 problems in the section called “Test Problems.” These problems make up a little open- book examination, on which you should easily get a passing grade. Otherwise figure out where things went wrong and fill in the gaps in your knowledge. Don’t despair, because nobody finds the notion of a limit easy the first time around. Bon voyage!

The book was translated from Russian by Richard Silverman and was published in 1969.

Credits to original uploader.

You can get the book here.

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Contents

Preface vii

Problems 1

Group 1 (Preliminaries) 1
Group 2 (Concepts) 6
Group 3 (Calculations) 14

Solutions 22
Test Problems 69

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