The Theory Of Maxima And Minima
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The Theory Of Maxima And Minima
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Author : Harris Hancock
language : en
Publisher:
Release Date : 2018-12-03
The 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 2018-12-03 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 (≠ 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]
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]
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.
Lectures On The Theory Of Maxima And Minima Of Functions Of Several Variables Weierstrass Theory
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Author : Harris Hancock
language : en
Publisher: Hardpress Publishing
Release Date : 2012-08-01
Lectures On The Theory Of Maxima And Minima Of Functions Of Several Variables Weierstrass Theory written by Harris Hancock and has been published by Hardpress Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-01 with categories.
Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.
Lectures On The Theory Of Maxima And Minima Of Functions Of Several Variables
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Author : Harris Hancock
language : en
Publisher:
Release Date : 1903
Lectures On The Theory Of Maxima And Minima Of Functions Of Several Variables 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 1903 with Maxima and minima categories.
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.
Theory Of Maxima And Minima
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Author : Harris Hancock
language : en
Publisher: Merchant Books
Release Date : 2008-04
Theory Of Maxima And Minima written by Harris Hancock and has been published by Merchant Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04 with Mathematics categories.
An Unabridged Printing With Text And Figures Digitally Enlarged: Functions Of One Variable (Ordinary Maxima And Minima - Extraordinary Maxima And Minima) - Functions Of Several Variables (Ordinary Maxima And Minima - Relative Maxima And Minima) - Functions Of Two Variables (Ordinary Extremes - Incorrectness Of Deductions Made By Earlier And Many Modern Writers - Different Attempts To Improve The Theory) - The Scheeffer Theory (General Criteria For A Greatest And A Least Value Of A Function Of Two Variables; In Particular The Extraordinary Extremes - Homogeneous Functions - The Method Of Victor Vs. Dantscher - Functions Of Three Variables - Maxima And Minima Of Functions Of Several Variables That Are Subjected To No Subsidiary Conditions (Ordinary Extremes - Theory Of The Homogeneous Quadric Forms - Application Of The Theory Of Quadratic Forms To The Problem Of Maxima And Minima) - Theory Of Maxima And Minima Of Functions Of Several Variables That Are Subjected To Subsidiary Conditions Relative To Maxima And Minima (Theory Of Homogeneous Quadratic Forms - Application Of The Criteria Just Found To The Problem Of This Chapter) - Special Cases (Examples Of Improper Extremes - Gauss's Principle - The Reversion Of Series) - Certain Fundamental Conceptions In The Theory Of Analytic Functions (Analytic Dependence - Algebraic Structures In Two Variables) - Index
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.
The Theory Of Maxima And Minima Of A Function Of Two Variables
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Author : William C. McCauley
language : en
Publisher:
Release Date : 1957
The Theory Of Maxima And Minima Of A Function Of Two Variables written by William C. McCauley and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1957 with categories.
Lectures On The Theory Of Maxima And Minima Of Functions Of Several Variables Vol 2
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Author : Harris Hancock
language : en
Publisher: Forgotten Books
Release Date : 2017-12-04
Lectures On The Theory Of Maxima And Minima Of Functions Of Several Variables Vol 2 written by Harris Hancock and has been published by Forgotten Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-04 with categories.
Excerpt from Lectures on the Theory of Maxima and Minima of Functions of Several Variables, Vol. 2: Weierstrass Theory IN his lectures at Berlin the late Professor Weierstrass often indicated the necessity of establishing fundamental parts of the Calculus upon a more exact foundation. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.