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About Real and Convex Analysis
<p>This book is intended to serve as a first course in analysis for scientists and</p><p>engineers. It can be used either at the advanced undergraduate level or as part of</p><p>the curriculum in a graduate program. We have taught from preliminary drafts of the</p><p>book for several years.</p><p>Thebookis built aroundmetricspaces. Inthe first three chapters,we lay thefoun-</p><p>dational material. We cover the all-important “four Cs”: convergence, completeness,</p><p>compactness, and continuity. We have organized the material to be as simple and as</p><p>logical as possible.</p><p>In subsequent chapters, we use the basic tools of analysis to give a brief intro-</p><p>duction to closely related topics such as differential and integral equations, convex</p><p>analysis, and measure theory. The book is short and yet covers in some depth the most</p><p>importantsubjects. We gavecarefulconsiderationto what to includeand what to leave</p><p>out. In all such considerations, we asked ourselves whether the material would be of</p><p>direct and immediate use to scientists and engineers. Our philosophy is “if in doubt,</p><p>do without.”</p><p>What makes this book different? We pull together some of the foundational ma-</p><p>terial one might find, for example, in the classic book by Rudin [Rud76] with material</p><p>onconvexityandoptimizationat a levelcommensurate,say, with the bookbyBorwein</p><p>and Lewis [BL06] and with a completely modern treatment of the basics of measure</p><p>theory. The importance of measure theory has increased over the years as stochastic</p><p>modeling has become more central to all aspects of analysis. Similarly, optimiza-</p><p>tion plays an ever increasing role as one tries to design and analyze the best possible</p><p>“widget.”</p><p>We hope that the reader will enjoy the book and learn some important mathe-</p><p>matics.</p><p>We would like to thank the many students whom we have had the pleasure of</p><p>teaching over the years. We give a special thanks to John D’Angelo; he carefully read</p><p>a draft of the manuscript and made numerous helpful suggestions.</p>
Detailed Information
| Author: | Erhan Çinlar, Robert J Vanderbei |
|---|---|
| Publication Year: | 2013 |
| ISBN: | 1461452562 |
| Pages: | 159 |
| Language: | other |
| File Size: | 3.4864 |
| Format: | |
| Price: | FREE |
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