Introduction to Partial Differential Equat...

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Sprache: Englisch

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Beschreibung

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.

Within each section the author creates a narrative that answers the five questions:

The text stresses the interplay between modeling and mathematical analysis, providing a thorough source of problems and an inspirationfor the development of methods.

Über den Autor

David Borthwick is Professor and Director of Graduate Studies in the Department of Mathematics at Emory University, Georgia, USA. His research interests are in spectral theory, global and geometric analysis, and mathematical physics. His monograph Spectral Theory of Infinite-Area Hyperbolic Surfaces appears in Birkhäuser's Progress in Mathematics, and his Introduction to Partial Differential Equations is published in Universitext.

Zusammenfassung

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: [...]

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.

Details

Erscheinungsjahr:	2018
Fachbereich:	Analysis
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Universitext
Inhalt:	xvi 283 S. 7 s/w Illustr. 61 farbige Illustr. 283 p. 68 illus. 61 illus. in color.
ISBN-13:	9783319840512
ISBN-10:	3319840517
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Borthwick, David
Auflage:	Softcover reprint of the original 1st edition 2016
Hersteller:	Springer Springer International Publishing AG Universitext
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 17 mm
Von/Mit:	David Borthwick
Erscheinungsdatum:	13.07.2018
Gewicht:	0,464 kg