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Introduction to Partial Differential Equations de David Borthwick

Introduction to Partial Differential Equations: Universitext

Autor David Borthwick
en Limba Engleză Hardback – 19 ian 2017
This modern take on partial differential equations does not require knowledge beyond vector calculus and linear algebra. The author focuses on the most important classical partial differential equations, including conservation equations and their characteristics, the wave equation, the heat equation, function spaces, and Fourier series, drawing on tools from analysis only as they arise. 

Within each section the author creates a narrative 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 inspirationfor the development of methods. 

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Specificații

ISBN-13: 9783319489346
ISBN-10: 3319489348
Pagini: 278
Ilustrații: XVI, 283 p. 68 illus., 61 illus. in color.
Dimensiuni: 155 x 235 x 21 mm
Greutate: 5.8 kg
Ediția:1st ed. 2016
Editura: Springer International Publishing
Colecția Springer
Seria Universitext

Locul publicării:Cham, Switzerland

Cuprins

1. Introduction.- 2. Preliminaries.- 3. Conservation Equations and Characteristics.- 4. The Wave Equation.- 5. Separation of Variables.- 6. The Heat Equation.- 7. Function Spaces.- 8. Fourier Series.- 9. Maximum Principles.- 10. Weak Solutions.- 11. Variational Methods.- 12. Distributions.- 13. The Fourier Transform.- A. Appendix: Analysis Foundations.- References.- Notation Guide.- Index.

Recenzii

“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)

Notă biografică

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

Textul de pe ultima copertă

This modern take on partial differential equations does not require knowledge beyond vector calculus and linear algebra. The author focuses on the most important classical partial differential equations, including conservation equations and their characteristics, the wave equation, the heat equation, function spaces, and Fourier series, drawing on tools from analysis only as they arise.Within each section the author creates a narrative 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.

Caracteristici

Perfect book for a ?One-semester PDE course Includes a thorough discussion of modeling process for each equation Covers indepth three types of linear PDES: elliptic, parabolic, and hyperbolic? Includes supplementary material: sn.pub/extras