國立虎尾科技大學 |

Change and Variations = A History of Differential Equations to 1900 /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Change and Variations/ by Jeremy Gray.
其他題名:	A History of Differential Equations to 1900 /
作者:	Gray, Jeremy.
面頁冊數:	XXII, 419 p. 44 illus., 13 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Mathematics. -
電子資源:	https://doi.org/10.1007/978-3-030-70575-6
ISBN:	9783030705756

Change and Variations = A History of Differential Equations to 1900 /
Gray, Jeremy.

Change and VariationsA History of Differential Equations to 1900 /[electronic resource] :by Jeremy Gray. - 1st ed. 2021. - XXII, 419 p. 44 illus., 13 illus. in color.online resource. - Springer Undergraduate Mathematics Series,2197-4144. - Springer Undergraduate Mathematics Series,.

1 The First Ordinary Differential Equations -- 2 Variational Problems and the Calculus -- 3 The Partial Differential Calculus -- 4 Rational Mechanics -- 5 Partial Differential Equations -- 6 Lagrange's General Theory -- 7 The Calculus of Variations -- 8 Monge and Solutions to Partial Differential Equations -- 9 Revision -- 10 The Heat Equation -- 11 Gauss and the Hypergeometric Equation -- 12 Existence Theorem -- 13 Riemann and Complex Function Theory -- 14 Riemann and the Hypergeometric Equation -- 15 Schwarz and the Complex Hypergeometric Equation -- 16 Complex Ordinary Differential Equations: Poincaré -- 17 More General Partial Differential Equations -- 18 Green's Functions and Dirichlet's Principle -- 19 Attempts on Laplace's Equation -- 20 Applied Wave Equations -- 21 Revision -- 22 Riemann's Shock Wave Paper -- 23 The Example of Minimal Surfaces -- 24 Partial Differential Equations and Mechanics -- 25 Geometrical Interpretations of Mechanics -- 26 The Calculus of Variations in the 19th Century -- 27 Poincaré and Mathematical Physics -- 28 Elliptic Equations and Regular Variational Problems -- 29 Hyperbolic Equations -- 30 Revision -- 32 Translations -- A Newton's Principia Mathematica -- B Characteristics -- C First-order Non-linear Equations -- D Green's Theorem and Heat Conduction -- E Complex Analysis -- F Möbius Transformations -- G Lipschitz and Picard -- H The Assessment -- Bibliography -- Index.

This book presents a history of differential equations, both ordinary and partial, as well as the calculus of variations, from the origins of the subjects to around 1900. Topics treated include the wave equation in the hands of d’Alembert and Euler; Fourier’s solutions to the heat equation and the contribution of Kovalevskaya; the work of Euler, Gauss, Kummer, Riemann, and Poincaré on the hypergeometric equation; Green’s functions, the Dirichlet principle, and Schwarz’s solution of the Dirichlet problem; minimal surfaces; the telegraphists’ equation and Thomson’s successful design of the trans-Atlantic cable; Riemann’s paper on shock waves; the geometrical interpretation of mechanics; and aspects of the study of the calculus of variations from the problems of the catenary and the brachistochrone to attempts at a rigorous theory by Weierstrass, Kneser, and Hilbert. Three final chapters look at how the theory of partial differential equations stood around 1900, as they were treated by Picard and Hadamard. There are also extensive, new translations of original papers by Cauchy, Riemann, Schwarz, Darboux, and Picard. The first book to cover the history of differential equations and the calculus of variations in such breadth and detail, it will appeal to anyone with an interest in the field. Beyond secondary school mathematics and physics, a course in mathematical analysis is the only prerequisite to fully appreciate its contents. Based on a course for third-year university students, the book contains numerous historical and mathematical exercises, offers extensive advice to the student on how to write essays, and can easily be used in whole or in part as a course in the history of mathematics. Several appendices help make the book self-contained and suitable for self-study.

ISBN: 9783030705756

Standard No.: 10.1007/978-3-030-70575-6doiSubjects--Topical Terms:

527692
Mathematics.

LC Class. No.: QA21-27

Dewey Class. No.: 510.9

Change and Variations = A History of Differential Equations to 1900 /
LDR:04643nam a22003975i 4500 001 1055168
003 DE-He213
005 20211215131851.0
007 cr nn 008mamaa
008 220103s2021 sz | s |||| 0|eng d
020 $a 9783030705756 $9 978-3-030-70575-6
024 7 $a 10.1007/978-3-030-70575-6 $2 doi
035 $a 978-3-030-70575-6
050 4 $a QA21-27
072 7 $a PBX $2 bicssc
072 7 $a MAT015000 $2 bisacsh
072 7 $a PBX $2 thema
082 0 4 $a 510.9 $2 23
100 1 $a Gray, Jeremy. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1069912
245 1 0 $a Change and Variations $h [electronic resource] : $b A History of Differential Equations to 1900 / $c by Jeremy Gray.
250 $a 1st ed. 2021.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a XXII, 419 p. 44 illus., 13 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Springer Undergraduate Mathematics Series, $x 2197-4144
505 0 $a 1 The First Ordinary Differential Equations -- 2 Variational Problems and the Calculus -- 3 The Partial Differential Calculus -- 4 Rational Mechanics -- 5 Partial Differential Equations -- 6 Lagrange's General Theory -- 7 The Calculus of Variations -- 8 Monge and Solutions to Partial Differential Equations -- 9 Revision -- 10 The Heat Equation -- 11 Gauss and the Hypergeometric Equation -- 12 Existence Theorem -- 13 Riemann and Complex Function Theory -- 14 Riemann and the Hypergeometric Equation -- 15 Schwarz and the Complex Hypergeometric Equation -- 16 Complex Ordinary Differential Equations: Poincaré -- 17 More General Partial Differential Equations -- 18 Green's Functions and Dirichlet's Principle -- 19 Attempts on Laplace's Equation -- 20 Applied Wave Equations -- 21 Revision -- 22 Riemann's Shock Wave Paper -- 23 The Example of Minimal Surfaces -- 24 Partial Differential Equations and Mechanics -- 25 Geometrical Interpretations of Mechanics -- 26 The Calculus of Variations in the 19th Century -- 27 Poincaré and Mathematical Physics -- 28 Elliptic Equations and Regular Variational Problems -- 29 Hyperbolic Equations -- 30 Revision -- 32 Translations -- A Newton's Principia Mathematica -- B Characteristics -- C First-order Non-linear Equations -- D Green's Theorem and Heat Conduction -- E Complex Analysis -- F Möbius Transformations -- G Lipschitz and Picard -- H The Assessment -- Bibliography -- Index.
520 $a This book presents a history of differential equations, both ordinary and partial, as well as the calculus of variations, from the origins of the subjects to around 1900. Topics treated include the wave equation in the hands of d’Alembert and Euler; Fourier’s solutions to the heat equation and the contribution of Kovalevskaya; the work of Euler, Gauss, Kummer, Riemann, and Poincaré on the hypergeometric equation; Green’s functions, the Dirichlet principle, and Schwarz’s solution of the Dirichlet problem; minimal surfaces; the telegraphists’ equation and Thomson’s successful design of the trans-Atlantic cable; Riemann’s paper on shock waves; the geometrical interpretation of mechanics; and aspects of the study of the calculus of variations from the problems of the catenary and the brachistochrone to attempts at a rigorous theory by Weierstrass, Kneser, and Hilbert. Three final chapters look at how the theory of partial differential equations stood around 1900, as they were treated by Picard and Hadamard. There are also extensive, new translations of original papers by Cauchy, Riemann, Schwarz, Darboux, and Picard. The first book to cover the history of differential equations and the calculus of variations in such breadth and detail, it will appeal to anyone with an interest in the field. Beyond secondary school mathematics and physics, a course in mathematical analysis is the only prerequisite to fully appreciate its contents. Based on a course for third-year university students, the book contains numerous historical and mathematical exercises, offers extensive advice to the student on how to write essays, and can easily be used in whole or in part as a course in the history of mathematics. Several appendices help make the book self-contained and suitable for self-study.
650 0 $a Mathematics. $3 527692
650 0 $a History. $3 669538
650 0 $a Mathematical analysis. $3 527926
650 0 $a Analysis (Mathematics). $3 1253570
650 1 4 $a History of Mathematical Sciences. $3 785417
650 2 4 $a Analysis. $3 669490
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030705749
776 0 8 $i Printed edition: $z 9783030705763
830 0 $a Springer Undergraduate Mathematics Series, $x 1615-2085 $3 1255356
856 4 0 $u https://doi.org/10.1007/978-3-030-70575-6
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)