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Author : Harris Hancock
Publisher :
ISBN 13 :
Total Pages : 216 pages
Book Rating : 4.91/5 ( download)
Download or read book Theory of Maxima and Minima written by Harris Hancock and published by . This book was released on 1917 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Harris Hancock
Publisher :
ISBN 13 :
Total Pages : 193 pages
Book Rating : 4.20/5 ( download)
Download or read book Theory of Maxima and Minima written by Harris Hancock and published by . This book was released on 1960 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Harris Hancock
Publisher : CreateSpace
ISBN 13 : 9781516995387
Total Pages : 208 pages
Book Rating : 4.84/5 ( download)
Download or read book Theory of Maxima and Minima written by Harris Hancock and published by CreateSpace. This book was released on 2015-08-21 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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]
Author : Harris Hancock
Publisher :
ISBN 13 : 9781790677375
Total Pages : 207 pages
Book Rating : 4.78/5 ( download)
Download or read book The Theory of Maxima and Minima written by Harris Hancock and published by . This book was released on 2018-12-03 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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]
Author : R. Frisch
Publisher : Springer Science & Business Media
ISBN 13 : 9401764085
Total Pages : 188 pages
Book Rating : 4.87/5 ( download)
Download or read book Maxima and Minima written by R. Frisch and published by Springer Science & Business Media. This book was released on 2013-11-09 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Harris Hancock
Publisher : Hardpress Publishing
ISBN 13 : 9781290938624
Total Pages : 130 pages
Book Rating : 4.28/5 ( download)
Download or read book Lectures on the Theory of Maxima and Minima of Functions of Several Variables. (Weierstrass' Theory.) written by Harris Hancock and published by Hardpress Publishing. This book was released on 2012-08-01 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Harris Hancock
Publisher : Merchant Books
ISBN 13 : 9781603861090
Total Pages : 212 pages
Book Rating : 4.92/5 ( download)
Download or read book Theory Of Maxima And Minima written by Harris Hancock and published by Merchant Books. This book was released on 2008-04 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Author : Vladimir Mikhaĭlovich Tikhomirov
Publisher : American Mathematical Soc.
ISBN 13 : 0821801651
Total Pages : 187 pages
Book Rating : 4.59/5 ( download)
Download or read book Stories about Maxima and Minima written by Vladimir Mikhaĭlovich Tikhomirov and published by American Mathematical Soc.. This book was released on 1990 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book 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. This book is accessible to high school students and would likely be of interest to a wide variety of readers.
Author : Harris Hancock
Publisher :
ISBN 13 :
Total Pages : 130 pages
Book Rating : 4.44/5 ( download)
Download or read book Lectures on the Theory of Maxima and Minima of Functions of Several Variables written by Harris Hancock and published by . This book was released on 1903 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Harris Hancock
Publisher :
ISBN 13 : 9781418164935
Total Pages : pages
Book Rating : 4.33/5 ( download)
Download or read book Theory of Maxima and Minima, by Harris Hancock written by Harris Hancock and published by . This book was released on 2004-01-01 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
