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Catalogue Information
Field name	Details
Dewey Class	515.353
Title	Introduction to Partial Differential Equations ([EBook]) / by David Borthwick.
Author	Borthwick, David
Other name(s)	SpringerLink (Online service)
Publication	Cham : : Springer International Publishing : : Imprint: Springer, , 2016.
Physical Details	XIV, 285 p. 68 illus., 61 illus. in color. : online resource.
Series	Universitext 0172-5939
ISBN	9783319489360
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-319-48936-0
Links to Related Works	Subject References: Mathematical Applications in the Physical Sciences . Mathematical Physics . Mathematics . Partial differential equations . Authors: Borthwick, David . Corporate Authors: SpringerLink (Online service) . Series: Universitext . Classification: 515.353 .

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Introduction to Partial Differential Equations

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