Maxima And Minima
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Stories About Maxima And Minima
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Author : Vladimir Mikhaĭlovich Tikhomirov
language : en
Publisher: American Mathematical Soc.
Release Date : 1990
Stories About Maxima And Minima written by Vladimir Mikhaĭlovich Tikhomirov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
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.
Maxima And Minima Without Calculus
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Author : Ivan Niven
language : en
Publisher: American Mathematical Soc.
Release Date : 1981-12-31
Maxima And Minima Without Calculus written by Ivan Niven and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981-12-31 with Mathematics categories.
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.
Geometric Problems On Maxima And Minima
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Author : Titu Andreescu
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-31
Geometric Problems On Maxima And Minima written by Titu Andreescu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-31 with Mathematics categories.
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
A Treatise On Problems Of Maxima And Minima Solved By Algebra
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Author : Ramchundra
language : en
Publisher:
Release Date : 1850
A Treatise On Problems Of Maxima And Minima Solved By Algebra written by Ramchundra and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1850 with Algebra categories.
Maxima And Minima
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Author : Ragnar Frisch
language : en
Publisher:
Release Date : 1966
Maxima And Minima written by Ragnar Frisch and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with categories.
Maxima And Minima
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Author : R. Frisch
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-09
Maxima And Minima written by R. Frisch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-09 with Business & Economics categories.
Maxima And Minima
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Author : Morris E. Levenson
language : en
Publisher: New York : Macmillan
Release Date : 1967
Maxima And Minima written by Morris E. Levenson and has been published by New York : Macmillan this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Mathematics categories.
Theory Of Maxima And Minima
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Author : Harris Hancock
language : en
Publisher:
Release Date : 1960
Theory Of Maxima And Minima written by Harris Hancock and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1960 with Maxima and minima categories.
Maxima And Minima Without Calculus
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Author : Ivan Morton Niven
language : en
Publisher:
Release Date : 1981
Maxima And Minima Without Calculus written by Ivan Morton Niven and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.
Theory Of Maxima And Minima
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Author : Harris Hancock
language : en
Publisher: CreateSpace
Release Date : 2015-08-21
Theory Of Maxima And Minima written by Harris Hancock and has been published by CreateSpace this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-21 with categories.
THE theory of maxima and minima contains pitfalls into which have fallen such well-known mathematicians as Lagrange, Bertrand, Serret, and Todhunter. A peculiar interest, therefore, is attached to the subject, and the reader will find Prof. Hancock's book well worth his study. Except that there is no reference to calculus of variations, the author has succeeded in covering the ground fairly thoroughly, and that without allowing the argument to be anywhere tedious. He gives many references, and a few quite interesting examples. After a short investigation of maxima and minima of functions of a single variable, he gives in some detail the methods of Scheeffer and von Dantscher, which introduced rigour into the discussion of functions of two or three variables. The theory here is intimately connected with the theory of quadratic forms and singularities of higher plane curves. The author seems not to have read such books as Bromwich's "Quadratic Forms," Hilton's "Linear Substitutions," or Muth's "Elementartheilar," which would have enabled him in places to simplify his treatment of quadratic forms. In tracing a plane curve near a singularity, the author should have made use of Newton's diagram. He should also have avoided such a phrase as "cusps of the first and second kind," which implies that the cusps in question are comparable. whereas the latter is a singularity of much higher complexity than the former. The chapter on relative maxima and minima is especially interesting. The discussion usually given in the text-books is very scanty, and the fuller treatment here given is very welcome. A valuable point is made in §§ 98-107. The usual proof that the maximum triangle inscribed in a given circle is equilateral runs as follows: "If not, suppose ABC to be the greatest triangle. If AB+AC, let D bisect the arc BAC. Then the triangle BDC>BAC, etc." Is this argument admissible? The reader may compare the following reasoning, due to an Italian author: "Unity is the greatest integer. For, if not, suppose n (not equal to x) the greatest. Then n2 > n, etc." The proofs run parallel, but the tacit assumption (a greatest triangle or integer exists) is lawful in one case and not in the other. -Nature, Vol. 102 [1919]