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Introduction to Partial Differential Equations

David Borthwick (Autor)

Buch | Hardcover

XVI, 283 Seiten

2017 | 1st ed. 2016
Springer International Publishing (Verlag)
978-3-319-48934-6 (ISBN)

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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.

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)

Erscheinungsdatum	28.01.2017
Reihe/Serie	Universitext
Zusatzinfo	XVI, 283 p. 68 illus., 61 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Naturwissenschaften ► Physik / Astronomie
Schlagworte	Differential calculus and equations • heat equation • Laplace equation • Linear equations • Mathematical Analysis • Mathematical Applications in the Physical Sciences • Mathematical Modelling • Mathematics • mathematics and statistics • Partial differential equations • wave equation
ISBN-10	3-319-48934-8 / 3319489348
ISBN-13	978-3-319-48934-6 / 9783319489346
Zustand	Neuware