Introduction to Partial Differential Equations - Rilegato

Borthwick, David

Rilegato

ISBN 10: 3319489348 ISBN 13: 9783319489346

Casa editrice: Springer Nature, 2017

Riassunto

Designed for students without an analysis background, this textbook provides a balanced presentation of partial differential equations through modern methods that do not require knowledge beyond vector calculus and linear algebra. By introducing definitions from analysis only when they are needed in the text, Borthwick reaches more advanced methods and emphasizes the role that tools from analysis play in PDE applications. The material included in this textbook allows students to study the most important classical PDE within a single semester.Borthwick focuses on a particular equation in each section, including conservative equations and their characteristics, the wave equation, the heat equation, function spaces, and Fourier series. He creates a narrative within each section that answers the five questions: (1) What is the scientific problem we are trying to understand?(2) How do we model that with PDE?(3) What techniques can we use to analyze the PDE?(4) How do those techniques apply to this equation?(5) What information or insight did we obtain by developing and analyzing the PDE?The text stresses the interplay between modeling and mathematical analysis, providing a thorough source of problems and an inspiration for the development of methods. 

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Recensione

“The book under review is intended for an introductory course for students. The author gives a balanced presentation that includes modern methods, without requiring prerequisites beyond vector calculus and linear algebra. Concepts and definitions from analysis are introduced only as they are needed in the text.” (Dian K. Palagachev, zbMATH 1364.35001, 2017)

L'autore

David Borthwick, Department of Mathematics and Computer Science, Emory University,  Atlanta, GA 30322

Dettagli dell?edizione

• Editore: Springer Nature
• Data di pubblicazione: 2017
• ISBN 10: 3319489348
• ISBN 13: 9783319489346
• Rilegatura: Copertina rigida
• Lingua: Inglese
• Numero edizione: 1
• Numero di pagine: 304