Introduction to Partial Differential Equations

 
 
Springer (Verlag)
  • erschienen am 13. Juli 2018
 
  • Buch
  • |
  • Softcover
  • |
  • 304 Seiten
978-3-319-84051-2 (ISBN)
 
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: What is the scientific problem we are trying to understand? How do we model that with PDE? What techniques can we use to analyze the PDE? How do those techniques apply to this equation? 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.
Paperback
Softcover reprint of the original 1st ed. 2016
  • Englisch
  • Cham
  • |
  • Schweiz
Springer International Publishing
  • Für Beruf und Forschung
  • 61 farbige Abbildungen, 7 s/w Abbildungen, 100 farbige Tabellen
  • |
  • 100 Tables, color; 61 Illustrations, color; 7 Illustrations, black and white; XVI, 283 p. 68 illus., 61 illus. in color.
  • Höhe: 235 mm
  • |
  • Breite: 162 mm
  • |
  • Dicke: 20 mm
  • 459 gr
978-3-319-84051-2 (9783319840512)
10.1007/978-3-319-48936-0
weitere Ausgaben werden ermittelt
David Borthwick, Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322
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.
"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)
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.

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