作者力学功底非常深厚,出版了系列经典书籍。"For he who knows not mathematics cannot know any other sciences; what is more, he cannot discover his own ignorance or find its proper remedies. " [Opus Majus] Roger Bacon (1214-1294) The material presented in these monographs is the outcome of the author's long-standing interest in the analytical modelling of problems in mechanics by appeal to the theory of partial differential equations. The impetus for wri ting these volumes was the opportunity to teach the subject matter to both undergraduate and graduate students in engineering at several universities. The approach is distinctly different to that which would adopted should such a course be given to students in pure mathematics; in this sense, the teaching of partial differential equations within an engineering curriculum should be viewed in the broader perspective of "The Modelling of Problems in Engineering" . An engineering student should be given the opportunity to appreciate how the various combination of balance laws, conservation equa tions, kinematic constraints, constitutive responses, thermodynamic restric tions, etc. , culminates in the development of a partial differential equation, or sets of partial differential equations, with potential for applications to en gineering problems. This ability to distill all the diverse information ab out a physical or mechanical process into partial differential equations is a par ticular attraction of the subject area.
图书标准信息
作者 A.P.S.Selvadurai 著
出版社 世界图书出版公司
出版时间 2004-04
版次 1
ISBN 9787506266079
定价 85.00元
装帧 平装
开本 其他
纸张 胶版纸
页数 595页
【内容简介】
The material presented in these monographs is the outcome of the author's long-standing interest in the analytical modelling of problems in mechanics by appeal to the theory of partial differential equations. The impetus for writing these volumes was the opportunity to teach the subject matter to both undergraduate and graduate students in engineering at several universities. The approach is distinctly different to that which would adopted should such a course be given to students in pure mathematics; in this sense, the teaching of partial differential equations within an engineering curriculum should be viewed in the broader perspective of "The Modelling of Problems in Engineering" . An engineering student should be given the opportunity to appreciate how the various combination of balance laws, conservation equations, kinematic constraints, constitutive responses, thermodynamic restrictions, etc., culminates in the development of a partial differential equation, or sets of partial differential equations, with potential for applications to engineering problems. This ability to distill all the diverse information about a physical or mechanical process into partial differential equations is a particular attraction of the subject area.
【目录】
1. Mathematical preliminaries
1.1 Components of a vector
1.2 Dot or scalar product
1.3 Cross or vector product
1.4 Derivative of a vector
1.5 Results involving derivatives
1.6 Partial derivatives of vectors
1.6.1 The gradient of a scalar field
1.6.2 The divergence of a vector field
1.6.3 The Laplacian of a scalar or vector field
1.6.4 The curl of a vector field
1.6.5 Other formulae involving
1.7 Divergence of a vector field: an application
1.8 Divergence or Green‘s theorem
1.9 Green‘s theorem in two dimensions
1.10 Orthogonal curvilinear coordinates
1.11 Gradient and Laplacian in orthogonal curvilinear coordinates
1.12 Integral transforms
1.12.1 Laplace transform
1.12.2 Fourier transforms
1.12.3ccHankelctransforms
1.13 PROBLEM SET 1
2. General concepts in partial differential equations
2.1 Fundamental concepts
2.1.1 The order of a partial differential equation
2.1.2 The linearity of a partial differential equation
2.1.3 Homogeneity of a partial differential equation
2.2 Well-posed problems
2.2.1 Boundary conditions
2.2.2 Initial conditions
2.2.3 Well-posed problems
2.3 PROBLEM SET 2
3.Partial differential equations of the first-order
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