# Inequalities

## With Applications to Engineering

• Michael J. Cloud
• Byron C. Drachman
Book

1. Front Matter
Pages i-viii
2. Pages 1-17
3. Pages 19-36
4. Pages 37-52
5. Pages 53-66
6. Pages 67-125
7. Back Matter
Pages 127-150

### Introduction

We might wonder why it is necessary to study inequalities. Many applied science and engineering problems, for instance, can be pursued without their explicit mention. Nevertheless, a facility with inequalities seems to be necessary for an understanding of much of mathematics at intermediate and higher levels. Inequalities serve a natural purpose of comparison, and they sometimes a?ord us indirect routes of reasoning or problem solving when more direct routes might be inconvenient or unavailable. Thissmallguidetoinequalitieswasoriginallywrittenwithengineersand otherappliedscientistsinmind.Commentsfromthosemathematicianswho have seen the manuscript lead us to hope that some mathematicians will ?nd some of the applications interesting, and that students of mathematics will also ?nd the book useful. It is intended to help ?ll the gap between college-algebra treatments of inequalities and the formidable treatises on the subject that exist in the mathematics literature. Important techniques are all reinforced through the exercises that appear at the end of each chapter,andhintsareincludedtoexpeditethereader’sprogress.Wereview a few topics from calculus, but make no attempt at a thorough review. In order to simplify the discussion, we use a stronger hypothesis than is necessary in some of the statements or proofs of theorems and in some of the exercises. For a review of calculus, we recommend the ?ne classic by Landau [37]. Among the many good books on analysis, we can recommend Stromberg [57].

### Keywords

Algebra Mathematica approximation calculus differential equation integration mathematics problem solving proof theorem

#### Authors and affiliations

• Michael J. Cloud
• 1
• Byron C. Drachman
• 2
1. 1.Department of Electrical EngineeringLawrence Technological UniversitySouthfiedUSA
2. 2.Department of MathematicsMichigan State UniversityEast LansingUSA

### Bibliographic information

• DOI https://doi.org/10.1007/b97652
• Copyright Information Springer-Verlag New York, Inc. 1998
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-0-387-98404-9
• Online ISBN 978-0-387-22626-2
• Buy this book on publisher's site