國立高雄大學圖資館 |

Language: English

Back

Partial differential equations in actionfrom modelling to theory /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Partial differential equations in actionby Sandro Salsa, Gianmaria Verzini.
Reminder of title:	from modelling to theory /
Author:	Salsa, S.
other author:	Verzini, Gianmaria.
Published:	Cham :Springer International Publishing :2022.
Description:	xviii, 677 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Differential equations, Partial.
Online resource:	https://doi.org/10.1007/978-3-031-21853-8
ISBN:	9783031218538$q(electronic bk.)

Partial differential equations in actionfrom modelling to theory /
Salsa, S.

Partial differential equations in actionfrom modelling to theory /[electronic resource] :by Sandro Salsa, Gianmaria Verzini. - Fourth edition. - Cham :Springer International Publishing :2022. - xviii, 677 p. :ill., digital ;24 cm. - UNITEXT. La matematica per il 3+2,v. 1472038-5757 ;. - UNITEXT.La matematica per il 3+2 ;v. 136..

1 Introduction -- 2 Diffusion -- 3 The Laplace Equation -- 4 Scalar Conservation Laws and First Order Equations -- 5 Waves and Vibration -- 6 Elements of Functional Analysis -- 7 Distributions and Sobolev Spaces -- 8 Variational Formulation of Elliptic Problems -- 9 Weak Formulation of Evolution Problems -- 10 More Advanced Topics -- 11 Systems of Conservation Laws -- Appendix A: Measures and Integrals -- Appendix B: Identities and Formulas.

This work is an updated version of a book evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background for numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In the second part, chapters 6 to 10 concentrate on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear boundary and initial-boundary value problems, while Chapter 11 deals with vector-valued conservation laws, extending the theory developed in Chapter 4. The main differences with respect to the previous editions are: a new section on reaction diffusion models for population dynamics in a heterogeneous environment; several new exercises in almost all chapters; a general restyling and a reordering of the last chapters. The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering.

ISBN: 9783031218538$q(electronic bk.)

Standard No.: 10.1007/978-3-031-21853-8doiSubjects--Topical Terms:

189753
Differential equations, Partial.

LC Class. No.: QA374

Dewey Class. No.: 515.353

Partial differential equations in actionfrom modelling to theory /
LDR:03023nmm a2200349 a 4500 001 634108
003 DE-He213
005 20221208135809.0
006 m d
007 cr nn 008maaau
008 230511s2022 sz s 0 eng d
020 $a 9783031218538$q(electronic bk.)
020 $a 9783031218521$q(paper)
024 7 $a 10.1007/978-3-031-21853-8 $2 doi
035 $a 978-3-031-21853-8
040 $a GP $c GP
041 0 $a eng
050 4 $a QA374
072 7 $a PBKJ $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKJ $2 thema
082 0 4 $a 515.353 $2 23
090 $a QA374 $b .S175 2022
100 1 $a Salsa, S. $3 345387
245 1 0 $a Partial differential equations in action $h [electronic resource] : $b from modelling to theory / $c by Sandro Salsa, Gianmaria Verzini.
250 $a Fourth edition.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2022.
300 $a xviii, 677 p. : $b ill., digital ; $c 24 cm.
490 1 $a UNITEXT. La matematica per il 3+2, $x 2038-5757 ; $v v. 147
505 0 $a 1 Introduction -- 2 Diffusion -- 3 The Laplace Equation -- 4 Scalar Conservation Laws and First Order Equations -- 5 Waves and Vibration -- 6 Elements of Functional Analysis -- 7 Distributions and Sobolev Spaces -- 8 Variational Formulation of Elliptic Problems -- 9 Weak Formulation of Evolution Problems -- 10 More Advanced Topics -- 11 Systems of Conservation Laws -- Appendix A: Measures and Integrals -- Appendix B: Identities and Formulas.
520 $a This work is an updated version of a book evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background for numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In the second part, chapters 6 to 10 concentrate on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear boundary and initial-boundary value problems, while Chapter 11 deals with vector-valued conservation laws, extending the theory developed in Chapter 4. The main differences with respect to the previous editions are: a new section on reaction diffusion models for population dynamics in a heterogeneous environment; several new exercises in almost all chapters; a general restyling and a reordering of the last chapters. The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering.
650 0 $a Differential equations, Partial. $3 189753
700 1 $a Verzini, Gianmaria. $3 725083
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a UNITEXT. $p La matematica per il 3+2 ; $v v. 136. $3 922584
856 4 0 $u https://doi.org/10.1007/978-3-031-21853-8
950 $a Mathematics and Statistics (SpringerNature-11649)