Inequalities: With Applications to Engineering

כריכה קדמית
Springer Science & Business Media, 10 במאי 2006 - 150 עמודים
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].
 

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תוכן

Methods from the Calculus
19
Some Standard Inequalities
37
Inequalities in Abstract Spaces
53
Some Applications
67
Appendix Hints for Selected Exercises 127
126
References
143
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מידע על המחבר (2006)

Michael J. Cloud has been a faculty member in the Department of Electrical and Computer Engineering at Lawrence Technological University since 1987 and currently holds the rank of Associate Professor. He has coauthored seven other books.

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