國立虎尾科技大學 |

Elliptic–Hyperbolic Partial Differential Equations = A Mini-Course in Geometric and Quasilinear Methods /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Elliptic–Hyperbolic Partial Differential Equations/ by Thomas H. Otway.
Reminder of title:	A Mini-Course in Geometric and Quasilinear Methods /
Author:	Otway, Thomas H.
Description:	VII, 128 p. 15 illus., 6 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Partial differential equations. -
Online resource:	https://doi.org/10.1007/978-3-319-19761-6
ISBN:	9783319197616

Elliptic–Hyperbolic Partial Differential Equations = A Mini-Course in Geometric and Quasilinear Methods /
Otway, Thomas H.

Elliptic–Hyperbolic Partial Differential EquationsA Mini-Course in Geometric and Quasilinear Methods /[electronic resource] :by Thomas H. Otway. - 1st ed. 2015. - VII, 128 p. 15 illus., 6 illus. in color.online resource. - SpringerBriefs in Mathematics,2191-8198. - SpringerBriefs in Mathematics,.

Introduction -- Overview of elliptic–hyperbolic PDE -- Hodograph and partial hodograph methods -- Boundary value problems -- B¨acklund transformations and Hodge-theoretic methods -- Natural focusing.

This text is a concise introduction to the partial differential equations which change from elliptic to hyperbolic type across a smooth hypersurface of their domain. These are becoming increasingly important in diverse sub-fields of both applied mathematics and engineering, for example: • The heating of fusion plasmas by electromagnetic waves • The behaviour of light near a caustic • Extremal surfaces in the space of special relativity • The formation of rapids; transonic and multiphase fluid flow • The dynamics of certain models for elastic structures • The shape of industrial surfaces such as windshields and airfoils • Pathologies of traffic flow • Harmonic fields in extended projective space They also arise in models for the early universe, for cosmic acceleration, and for possible violation of causality in the interiors of certain compact stars. Within the past 25 years, they have become central to the isometric embedding of Riemannian manifolds and the prescription of Gauss curvature for surfaces: topics in pure mathematics which themselves have important applications. Elliptic−Hyperbolic Partial Differential Equations is derived from a mini-course given at the ICMS Workshop on Differential Geometry and Continuum Mechanics held in Edinburgh, Scotland in June 2013. The focus on geometry in that meeting is reflected in these notes, along with the focus on quasilinear equations. In the spirit of the ICMS workshop, this course is addressed both to applied mathematicians and to mathematically-oriented engineers. The emphasis is on very recent applications and methods, the majority of which have not previously appeared in book form.

ISBN: 9783319197616

Standard No.: 10.1007/978-3-319-19761-6doiSubjects--Topical Terms:

1102982
Partial differential equations.

LC Class. No.: QA370-380

Dewey Class. No.: 515.353

Elliptic–Hyperbolic Partial Differential Equations = A Mini-Course in Geometric and Quasilinear Methods /
LDR:03316nam a22003975i 4500 001 966962
003 DE-He213
005 20200706152536.0
007 cr nn 008mamaa
008 201211s2015 gw | s |||| 0|eng d
020 $a 9783319197616 $9 978-3-319-19761-6
024 7 $a 10.1007/978-3-319-19761-6 $2 doi
035 $a 978-3-319-19761-6
050 4 $a QA370-380
072 7 $a PBKJ $2 bicssc
072 7 $a MAT007000 $2 bisacsh
072 7 $a PBKJ $2 thema
082 0 4 $a 515.353 $2 23
100 1 $a Otway, Thomas H. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 890188
245 1 0 $a Elliptic–Hyperbolic Partial Differential Equations $h [electronic resource] : $b A Mini-Course in Geometric and Quasilinear Methods / $c by Thomas H. Otway.
250 $a 1st ed. 2015.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a VII, 128 p. 15 illus., 6 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 SpringerBriefs in Mathematics, $x 2191-8198
505 0 $a Introduction -- Overview of elliptic–hyperbolic PDE -- Hodograph and partial hodograph methods -- Boundary value problems -- B¨acklund transformations and Hodge-theoretic methods -- Natural focusing.
520 $a This text is a concise introduction to the partial differential equations which change from elliptic to hyperbolic type across a smooth hypersurface of their domain. These are becoming increasingly important in diverse sub-fields of both applied mathematics and engineering, for example: • The heating of fusion plasmas by electromagnetic waves • The behaviour of light near a caustic • Extremal surfaces in the space of special relativity • The formation of rapids; transonic and multiphase fluid flow • The dynamics of certain models for elastic structures • The shape of industrial surfaces such as windshields and airfoils • Pathologies of traffic flow • Harmonic fields in extended projective space They also arise in models for the early universe, for cosmic acceleration, and for possible violation of causality in the interiors of certain compact stars. Within the past 25 years, they have become central to the isometric embedding of Riemannian manifolds and the prescription of Gauss curvature for surfaces: topics in pure mathematics which themselves have important applications. Elliptic−Hyperbolic Partial Differential Equations is derived from a mini-course given at the ICMS Workshop on Differential Geometry and Continuum Mechanics held in Edinburgh, Scotland in June 2013. The focus on geometry in that meeting is reflected in these notes, along with the focus on quasilinear equations. In the spirit of the ICMS workshop, this course is addressed both to applied mathematicians and to mathematically-oriented engineers. The emphasis is on very recent applications and methods, the majority of which have not previously appeared in book form.
650 0 $a Partial differential equations. $3 1102982
650 0 $a Mathematical physics. $3 527831
650 1 4 $a Partial Differential Equations. $3 671119
650 2 4 $a Mathematical Applications in the Physical Sciences. $3 786649
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319197623
776 0 8 $i Printed edition: $z 9783319197609
830 0 $a SpringerBriefs in Mathematics, $x 2191-8198 $3 1255329
856 4 0 $u https://doi.org/10.1007/978-3-319-19761-6
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)