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Introduction to Partial Differential Equations

Previously published in hardcover
BuchKartoniert, Paperback
283 Seiten
Englisch
Springererschienen am13.07.2018Softcover reprint of the original 1st ed. 2016
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 inspirationfor the development of methods.mehr
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Produkt

KlappentextThis 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 inspirationfor the development of methods.
Details
ISBN/GTIN978-3-319-84051-2
ProduktartBuch
EinbandartKartoniert, Paperback
Verlag
Erscheinungsjahr2018
Erscheinungsdatum13.07.2018
AuflageSoftcover reprint of the original 1st ed. 2016
ReiheUniversitext
Seiten283 Seiten
SpracheEnglisch
Gewicht468 g
IllustrationenXVI, 283 p. 68 illus., 61 illus. in color.
Artikel-Nr.45668195

Inhalt/Kritik

Inhaltsverzeichnis
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.mehr
Kritik
"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)mehr