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Introduction to partial differential...

Borthwick, David.

Introduction to partial differential equations

Record Type:	Electronic resources : Monograph/item
Title/Author:	Introduction to partial differential equationsby David Borthwick.
Author:	Borthwick, David.
Published:	Cham :Springer International Publishing :2016.
Description:	xiv, 285 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Differential equations, Partial.
Online resource:	http://dx.doi.org/10.1007/978-3-319-48936-0
ISBN:	9783319489360$q(electronic bk.)

Introduction to partial differential equations
Borthwick, David.

Introduction to partial differential equations[electronic resource] /by David Borthwick. - Cham :Springer International Publishing :2016. - xiv, 285 p. :ill. (some col.), digital ;24 cm. - Universitext,0172-5939. - Universitext..

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.

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.

ISBN: 9783319489360$q(electronic bk.)

Standard No.: 10.1007/978-3-319-48936-0doiSubjects--Topical Terms:

189753
Differential equations, Partial.

LC Class. No.: QA377

Dewey Class. No.: 515.353

Introduction to partial differential equations
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245 1 0 $a Introduction to partial differential equations $h [electronic resource] / $c by David Borthwick.
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300 $a xiv, 285 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Universitext, $x 0172-5939
505 0 $a 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.
520 $a 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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950 $a Mathematics and Statistics (Springer-11649)