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Numerical Methods for Partial Differential Equations 🔍
Gwynne A. Evans MA, Dphil, DSc, Jonathan M. Blackledge BSc, PhD, DIC, Peter D. Yardley BSc, PhD (auth.) Springer-Verlag London, Springer Undergraduate Mathematics Series, Springer Undergraduate Mathematics Series, 1, 2000
英语 [en] · PDF · 13.2MB · 2000 · 📘 非小说类图书 · 🚀/lgli/lgrs/nexusstc/scihub/zlib · Save
描述
The subject of partial differential equations holds an exciting and special position in mathematics. Partial differential equations were not consciously created as a subject but emerged in the 18th century as ordinary differential equations failed to describe the physical principles being studied. The subject was originally developed by the major names of mathematics, in particular, Leonard Euler and Joseph-Louis Lagrange who studied waves on strings; Daniel Bernoulli and Euler who considered potential theory, with later developments by Adrien-Marie Legendre and Pierre-Simon Laplace; and Joseph Fourier's famous work on series expansions for the heat equation. Many of the greatest advances in modern science have been based on discovering the underlying partial differential equation for the process in question. James Clerk Maxwell, for example, put electricity and magnetism into a unified theory by establishing Maxwell's equations for electromagnetic theory, which gave solutions for prob lems in radio wave propagation, the diffraction of light and X-ray developments. Schrodinger's equation for quantum mechanical processes at the atomic level leads to experimentally verifiable results which have changed the face of atomic physics and chemistry in the 20th century. In fluid mechanics, the Navier Stokes' equations form a basis for huge number-crunching activities associated with such widely disparate topics as weather forecasting and the design of supersonic aircraft. Inevitably the study of partial differential equations is a large undertaking, and falls into several areas of mathematics.
Erscheinungsdatum: 27.10.1999
备用文件名
lgrsnf/A:\compressed\10.1007%2F978-1-4471-0377-6.pdf
备用文件名
nexusstc/Numerical Methods for Partial Differential Equations/c64fc82b3bf31781106f6854876d765f.pdf
备用文件名
scihub/10.1007/978-1-4471-0377-6.pdf
备用文件名
zlib/Mathematics/Gwynne A. Evans, Peter D. Yardley/Numerical Methods for Partial Differential Equations_2104869.pdf
备选作者
G. Evans, J Blackledge, P. Yardley, Gwynne Evans, G. Evans, J. Blackledge
备选作者
Gwynne Evans, G. Evans, J. Blackledge, P. Yardley
备选作者
G. Evans, J. Blackledge, and P. Yardley
备选作者
Evans, G., Blackledge, J., Yardley, P.
备用出版商
Springer Spektrum. in Springer-Verlag GmbH
备用出版商
Springer London : Imprint : Springer
备用出版商
Steinkopff. in Springer-Verlag GmbH
备用出版商
Springer London, Limited
备用出版商
Springer Nature
备用出版商
Springer Berlin
备用版本
Springer undergraduate mathematics series, London, New York, England, 2000
备用版本
Springer Nature (Textbooks & Major Reference Works), London, 2000
备用版本
Springer undergraduate mathematics series, London, cop. 2000
备用版本
United Kingdom and Ireland, United Kingdom
备用版本
1 edition, November 23, 1999
备用版本
Germany, Germany
备用版本
2000, PS, 1999
备用版本
1, 20121206
元数据中的注释
sm23181893
元数据中的注释
{"container_title":"Springer Undergraduate Mathematics Series","edition":"1","isbns":["1447103777","354076125X","9781447103776","9783540761259"],"issns":["1615-2085"],"last_page":290,"publisher":"Springer London","series":"Springer Undergraduate Mathematics Series"}
元数据中的注释
Includes bibliographical references (p. 287-288) and index
备用描述
The subject of partial differential equations holds an exciting place in mathematics. Inevitably, the subject falls into several areas of mathematics. At one extreme the interest lies in the existence and uniqueness of solutions, and the functional analysis of the proofs of these properties. At the other extreme lies the applied mathematical and engineering quest to find useful solutions, either analytically or numerically, to these important equations which can be used in design and construction. The book presents a clear introduction of the methods and underlying theory used in the numerical solution of partial differential equations. After revising the mathematical preliminaries, the book covers the finite difference method of parabolic or heat equations, hyperbolic or wave equations and elliptic or Laplace equations. Throughout, the emphasis is on the practical solution rather than the theoretical background, without sacrificing rigour.
备用描述
"The book presents a clear introduction of the methods and underlying theory used in the numerical solution of partial differential equations. Throughout, the emphasis is on the practical solution rather than the theoretical background, without sacrificing rigour. After revising the mathematical preliminaries, the book covers the finite difference method of parabolic or heat equations, hyperbolic or wave equations and elliptic or Laplace equations." "Numerical Methods for Partial Differential Equations provides a complete introduction to the subject, suitable for second or third year undergraduates or for non-specialist graduate courses. Many illustrative exercises are provided, most with full solutions or advice on creating appropriate computer algorithms."--Jacket
备用描述
Front Matter....Pages i-xii
Background Mathematics....Pages 1-28
Finite Differences and Parabolic Equations....Pages 29-65
Hyperbolic Equations and Characteristics....Pages 67-94
Elliptic Equations....Pages 95-122
Finite Element Method for Ordinary Differential Equations....Pages 123-164
Finite Elements for Partial Differential Equations....Pages 165-206
Solutions to Exercises....Pages 207-285
Back Matter....Pages 287-290
备用描述
The companion volume of this book, 'Analytic methods for partial differential equations', is concerned with solution of partial differential equations using classical methods which result in analytic solutions.
开源日期
2013-08-01
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