Author : Titu Andreescu
Publisher : Springer Science & Business Media
Page : 273 pages
File Size : 26,69 MB
Release : 2007-12-31
Category : Mathematics
ISBN : 0817644733
Presents hundreds of extreme value problems, examples, and solutions primarily through Euclidean geometry Unified approach to the subject, with emphasis on geometric, algebraic, analytic, and combinatorial reasoning Applications to physics, engineering, and economics Ideal for use at the junior and senior undergraduate level, with wide appeal to students, teachers, professional mathematicians, and puzzle enthusiasts
Author : Vladimir Mikhaĭlovich Tikhomirov
Publisher : American Mathematical Soc.
Page : 201 pages
File Size : 10,9 MB
Release : 1990
Category : Mathematics
ISBN : 0821801651
Throughout the history of mathematics, maximum and minimum problems have played an important role in the evolution of the field. Many beautiful and important problems have appeared in a variety of branches of mathematics and physics, as well as in other fields of sciences. The greatest scientists of the past - Euclid, Archimedes, Heron, the Bernoullis, Newton and many others - took part in seeking solutions to these concrete problems. The solutions stimulated the development of the theory, and, as a result, techniques were elaborated that made possible the solution of a tremendous variety of problems by a single method. This book, copublished with the Mathematical Association of America (MAA), presents fifteen "stories" designed to acquaint readers with the central concepts of the theory of maxima and minima, as well as with its illustrious history. Unlike most AMS publications, the book is accessible to high school students and would likely be of interest to a wide variety of readers. In Part One, the author familiarizes readers with many concrete problems that lead to discussion of the work of some of the greatest mathematicians of all time. Part Two introduces a method for solving maximum and minimum problems that originated with Lagrange. While the content of this method has varied constantly, its basic conception has endured for over two centuries. The final story is addressed primarily to those who teach mathematics, for it impinges on the question of how and why to teach. Throughout the book, the author strives to show how the analysis of diverse facts gives rise to a general idea, how this idea is transformed, how it is enriched by new content, and how to remains the same in spite of these changes.
Author : Harris Hancock
Publisher : Legare Street Press
Page : 0 pages
File Size : 45,96 MB
Release : 2022-10-27
Category :
ISBN : 9781019101612
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Author : Wilfred Kaplan
Publisher : John Wiley & Sons
Page : 298 pages
File Size : 17,1 MB
Release : 2011-10-14
Category : Mathematics
ISBN : 1118031040
This new work by Wilfred Kaplan, the distinguished author of influential mathematics and engineering texts, is destined to become a classic. Timely, concise, and content-driven, it provides an intermediate-level treatment of maxima, minima, and optimization. Assuming only a background in calculus and some linear algebra, Professor Kaplan presents topics in order of difficulty. In four short chapters, he describes basic concepts and geometric aspects of maxima and minima, progresses to problems with side conditions, introduces optimization and programming, and concludes with an in-depth discussion of research topics involving the duality theorems of Fenchel and Rockafellar. Throughout the text, the subject of convexity is gradually developed-from its theoretical underpinnings to problems, and finally, to its role in applications. Other features include: * A strong emphasis on practical applications of maxima and minima * An impressive array of supporting topics such as numerical analysis * An ample number of examples and problems * More than 60 illustrations highlighting the text * Algorithms to reinforce concepts * An appendix reviewing the prerequisite linear algebra Maxima and Minima with Applications is an ideal text for upper-undergraduate and graduate students taking courses in operations research, management, general engineering, and applied mathematics. It can also be used to supplement courses on linear and nonlinear optimization. This volume's broad scope makes it an excellent reference for professionals wishing to learn more about cutting-edge topics in optimization and mathematical programming.
Author : William Heytesbury
Publisher : Springer Science & Business Media
Page : 203 pages
File Size : 28,11 MB
Release : 2012-12-06
Category : History
ISBN : 940096496X
This book began with my edition of the anonymous treatise. A translation and notes seemed essential if the material of the treatise was to be understood. It then seemed that Chapter 5 of Heytesbury's Rules for Solving Sophismata, on which the treatise was based, should also be included. My translation of the Heytesbury treatise is based on a fifteenth-century edition, supplemented by readings from a few of the better manuscripts. (A critical edition from all the manuscripts, of which Chapter 5 will be mine, is now in progress under the supervision of Paul Spade, but only a few insignificant changes in the translation should be necessitated by the completed edition. ) An examination of related materials seemed reasonable, and these included Heytesbury's commentator Gaetano, as well as a chapter from a treatise by Johannes Venator (in an edition in progress provided by Francesco del Punta). It seemed unnecessary to publish Gaetano's and Venator's related works in this volume, but all their departures from Heytesbury and the anonymous treatise are noted here. I have not examined other works in the tradition in any detail. I owe a great deal to my teacher, Norman Kretzmann, not only as regards the edition and translations, but also as regards the notes, study and introduction. The referees of the typescript (to me unknown) made unusually thorough criticisms and suggestions to which I have paid close attention. The book is far better for my having done so.
Author : Georgiĭ Evgenʹevich Shilov
Publisher :
Page : 72 pages
File Size : 36,85 MB
Release : 1963
Category : Graphic methods
ISBN :
Author : Ivan Niven
Publisher : Cambridge University Press
Page : 328 pages
File Size : 50,72 MB
Release : 1981
Category : Mathematics
ISBN : 9780883853061
Describes techniques for solving problems in maxima and minima other than the methods of calculus.
Author : Ivan Niven
Publisher : American Mathematical Soc.
Page : 303 pages
File Size : 31,53 MB
Release : 1981-12-31
Category : Mathematics
ISBN : 1470448750
The purpose of this book is to put together in one place the basic elementary techniques for solving problems in maxima minima other than the methods of calculus and linear programming. The emphasis is not on individual problems, but on methods that solve large classes of problems. The many chapters of the book can be read independently, without references to what precedes or follows. Besides the many problems solved in the book, others are left to the reader to solve, with sketches of solutions given in the later pages.
Author : Stephen Boyd
Publisher : Cambridge University Press
Page : 477 pages
File Size : 39,33 MB
Release : 2018-06-07
Category : Business & Economics
ISBN : 1316518965
A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.
Author : R. McNeill Alexander
Publisher : Princeton University Press
Page : 184 pages
File Size : 35,27 MB
Release : 2020-11-10
Category : Science
ISBN : 069122160X
Optimization theory is designed to find the best ways of doing things. The structures of animals, their movements, their behavior, and their life histories have all been shaped by the optimizing processes of evolution or of learning by trial and error. In this revised edition of R. McNeill Alexander's widely acclaimed Optima for Animals, we see how extraordinarily diverse branches of biology are illuminated by the powerful methods of optimization theory. What is the best strength for a bone? Too weak a bone will probably break but an excessively stout one will be cumbersome. At what speed should humans change from walking to running? Should a bird take only big juicy worms or should it eat every worm it finds, and do birds make the best choices? Why do the males of some species of fishes and the females of others look after the young, while the young of others are looked after by both parents or neither? Is it possible that all these policies can be optimal, in different circumstances? This book shows how these and many other questions can be answered. The mathematics involved is explained very simply, with biology students in mind, but the book is not just for them. It is also for professionals, ranging from teachers to researchers.
