Partial Differential Equations

Jeffrey Rauch

ISBN 10: 0387974725 / ISBN 13: 9780387974729

Edité par Springer New York, Springer US, 1991

A propos de cet article

Druck auf Anfrage Neuware - Printed after ordering - This book is based on a course I have given five times at the University of Michigan, beginning in 1973. The aim is to present an introduction to a sampling of ideas, phenomena, and methods from the subject of partial differential equations that can be presented in one semester and requires no previous knowledge of differential equations. The problems, with hints and discussion, form an important and integral part of the course. In our department, students with a variety of specialties-notably differen tial geometry, numerical analysis, mathematical physics, complex analysis, physics, and partial differential equations-have a need for such a course. The goal of a one-term course forces the omission of many topics. Everyone, including me, can find fault with the selections that I have made. One of the things that makes partial differential equations difficult to learn is that it uses a wide variety of tools. In a short course, there is no time for the leisurely development of background material. Consequently, I suppose that the reader is trained in advanced calculus, real analysis, the rudiments of complex analysis, and the language offunctional analysis. Such a background is not unusual for the students mentioned above. Students missing one of the 'essentials' can usually catch up simultaneously. A more difficult problem is what to do about the Theory of Distributions.

N° de réf. du vendeur 9780387974729

Détails bibliographiques

• Titre: Partial Differential Equations
• Éditeur: Springer New York, Springer US
• Date de parution: 1991
• Langue: anglais
• ISBN à 10 chiffres: 0387974725
• ISBN à 13 chiffres: 9780387974729
• Reliure: Buch
• État de l'article: Neu

A propos de ce titre

Synopsis

This book is based on a course I have given five times at the University of Michigan, beginning in 1973. The aim is to present an introduction to a sampling of ideas, phenomena, and methods from the subject of partial differential equations that can be presented in one semester and requires no previous knowledge of differential equations. The problems, with hints and discussion, form an important and integral part of the course. In our department, students with a variety of specialties-notably differen- tial geometry, numerical analysis, mathematical physics, complex analysis, physics, and partial differential equations-have a need for such a course. The goal of a one-term course forces the omission of many topics. Everyone, including me, can find fault with the selections that I have made. One of the things that makes partial differential equations difficult to learn is that it uses a wide variety of tools. In a short course, there is no time for the leisurely development of background material. Consequently, I suppose that the reader is trained in advanced calculus, real analysis, the rudiments of complex analysis, and the language offunctional analysis. Such a background is not unusual for the students mentioned above. Students missing one of the "essentials" can usually catch up simultaneously. A more difficult problem is what to do about the Theory of Distributions.

Présentation de l'éditeur

The book intends as an undergraduate text for Partial Differential Equations (PDEs). The topic covered are the method of characteristics for the solution of linear and quasi-linear first order hyperbolic equations and second order linear hyperbolic PDEs. The method of separation of variables for the solution of linear parabolic, elliptic and hyperbolic PDEs as well as the Laplace and Fourier transforms. The book includes an introduction to the finite difference methods for the solution of PDEs and several methods for the solution of a single nonlinear equation.