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Applied partial differential equations / J David Logan
New York : Springer, 2015
294 pages. : illustrations
Ký hiệu phân loại (DDC): 515.353
his text presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs.
Emphasis is placed on motivation, concepts, methods, and interpretation, rather than on formal theory.
The concise treatment of the subject is maintained in this third edition covering all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains.
Methods include eigenfunction expansions, integral transforms, and characteristics.
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Introduction to partial differential equations. / David Borthwick
Switzerland : Springer, 2016
293 pages : illustrations
Ký hiệu phân loại (DDC): 515.353
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."--Publisher description.
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Methods of mathematical modelling : continuous systems and differential equations / Thomas Witelski; Mark Bowen
New York : Springer, 2015
309 pages : illustrations
Ký hiệu phân loại (DDC): 511.8
This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations
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