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Cover: 9783319489346 | Introduction to Partial Differential Equations | David Borthwick | xvi
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Introduction to Partial Differential Equations
Buch von David Borthwick
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.
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.
Über den Autor
David Borthwick, Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322
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: 2017
Fachbereich: Analysis
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Universitext
Inhalt: xvi
283 S.
7 s/w Illustr.
61 farbige Illustr.
283 p. 68 illus.
61 illus. in color.
ISBN-13: 9783319489346
ISBN-10: 3319489348
Sprache: Englisch
Herstellernummer: 978-3-319-48934-6
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Borthwick, David
Auflage: 1st ed. 2016
Hersteller: Springer International Publishing
Springer International Publishing AG
Universitext
Verantwortliche Person für die EU: Books on Demand GmbH, In de Tarpen 42, D-22848 Norderstedt, info@bod.de
Maße: 241 x 160 x 22 mm
Von/Mit: David Borthwick
Erscheinungsdatum: 19.01.2017
Gewicht: 0,623 kg
Artikel-ID: 108293060
Über den Autor
David Borthwick, Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322
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: 2017
Fachbereich: Analysis
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Universitext
Inhalt: xvi
283 S.
7 s/w Illustr.
61 farbige Illustr.
283 p. 68 illus.
61 illus. in color.
ISBN-13: 9783319489346
ISBN-10: 3319489348
Sprache: Englisch
Herstellernummer: 978-3-319-48934-6
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Borthwick, David
Auflage: 1st ed. 2016
Hersteller: Springer International Publishing
Springer International Publishing AG
Universitext
Verantwortliche Person für die EU: Books on Demand GmbH, In de Tarpen 42, D-22848 Norderstedt, info@bod.de
Maße: 241 x 160 x 22 mm
Von/Mit: David Borthwick
Erscheinungsdatum: 19.01.2017
Gewicht: 0,623 kg
Artikel-ID: 108293060
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