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Introduction to partial differential equations

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Introduction to partial differential equations/ by David Borthwick.
作者:	Borthwick, David.
出版者:	Cham :Springer International Publishing : : 2016.,
面頁冊數:	xiv, 285 p. :ill. (some col.), digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Differential equations, Partial. -
電子資源:	http://dx.doi.org/10.1007/978-3-319-48936-0
ISBN:	9783319489360

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

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

527784
Differential equations, Partial.

LC Class. No.: QA377

Dewey Class. No.: 515.353

Introduction to partial differential equations
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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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