Theory Of Maxima And Minima By Harris Hancock
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Theory Of Maxima And Minima By Harris Hancock
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Author : Harris Hancock
language : en
Publisher:
Release Date : 2004-01-01
Theory Of Maxima And Minima By Harris Hancock 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 2004-01-01 with 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.
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: 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
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: Legare Street Press
Release Date : 2023-07-18
Lectures On The Theory Of Maxima And Minima Of Functions Of Several Variables Weierstrass Theory written by Harris Hancock and has been published by Legare Street Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-18 with categories.
Written for advanced students of mathematics and physics, this influential text provides a rigorous introduction to the Weierstrass Theory of Maxima and Minima. Hancock's lucid and insightful lectures have inspired generations of mathematicians and remain a valuable resource for anyone seeking to deepen their understanding of the calculus of variations. 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.
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]
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.
The Calculus Of Variations
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Author : Harris Hancock
language : en
Publisher:
Release Date : 1895
The Calculus Of Variations 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 1895 with categories.
Theory Of Maxima And Minima
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Author : Harris Hancock
language : en
Publisher: Trieste Publishing
Release Date : 2017-09-15
Theory Of Maxima And Minima written by Harris Hancock and has been published by Trieste Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-15 with History categories.
Trieste Publishing has a massive catalogue of classic book titles. Our aim is to provide readers with the highest quality reproductions of fiction and non-fiction literature that has stood the test of time. The many thousands of books in our collection have been sourced from libraries and private collections around the world.The titles that Trieste Publishing has chosen to be part of the collection have been scanned to simulate the original. Our readers see the books the same way that their first readers did decades or a hundred or more years ago. Books from that period are often spoiled by imperfections that did not exist in the original. Imperfections could be in the form of blurred text, photographs, or missing pages. It is highly unlikely that this would occur with one of our books. Our extensive quality control ensures that the readers of Trieste Publishing's books will be delighted with their purchase. Our staff has thoroughly reviewed every page of all the books in the collection, repairing, or if necessary, rejecting titles that are not of the highest quality. This process ensures that the reader of one of Trieste Publishing's titles receives a volume that faithfully reproduces the original, and to the maximum degree possible, gives them the experience of owning the original work.We pride ourselves on not only creating a pathway to an extensive reservoir of books of the finest quality, but also providing value to every one of our readers. Generally, Trieste books are purchased singly - on demand, however they may also be purchased in bulk. Readers interested in bulk purchases are invited to contact us directly to enquire about our tailored bulk rates.
The National Union Catalog Pre 1956 Imprints
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Author : Library of Congress
language : en
Publisher:
Release Date : 1972
The National Union Catalog Pre 1956 Imprints written by Library of Congress and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Catalogs, Union categories.
