Evans G.A., Blackledge J.M., Yardley P. — Analytic Methods for Partial Differential Equations :: Электронная библиотека попечительского совета мехмата МГУ

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Evans G.A., Blackledge J.M., Yardley P. — Analytic Methods for Partial Differential Equations

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Название: Analytic Methods for Partial Differential Equations

Авторы: Evans G.A., Blackledge J.M., Yardley P.

Аннотация:

The subject of partial differential equations holds an exciting place in 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 objective of this book is to actually solve equations rather than discuss the theoretical properties of their solutions. The topics are approached practically, without losing track of the underlying mathematical foundations of the subject. The topics covered include the separation of variables, the characteristic method, D'Alembert's method, integral transforms and Green's functions. Numerous exercises are provided as an integral part of the learning process, with solutions provided in a substantial appendix.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Издание: 1st edition

Год издания: 1999

Количество страниц: 316

Добавлена в каталог: 30.06.2008

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Предметный указатель

Algebra of generalised functions      38
Analytic functions      30
Analytic Methods for Partial Differential Equations, Fraunhofer approximation      173
Argand diagram      30
Argument of a complex number      30
Asymptotic Born scattering      186
Asymptotic forms of Green functions      173
Bessel functions      24
Bessel’s equation      88
Born approximation      182
Born series      208
Born series solution      212
Calculus of residues      32
Canonical form      9
Cauchy’s residue theorem      144
Cauchy’s Theorem      31
Characteristic curves      8 96
Characteristics      8 101 108
Charpit’s method      98
Circular membrane      85
classifying      2
Comb function      44
Complete integral      99
Complete orthogonal functions      13
Complete solution      99
Complex conjugate      30
Complex functions      30
complex numbers      29
Convolution of generalised functions      44
Convolution theorem      138 152
Cylindrical polar coordinates      77
Dependent variable      2
Differentiating across discontinuities      41
Diffusion equation      3
Dirac delta function      34 39
Dirichlet and Neumann boundary conditions      178
Dirichlet problem      79
Discrete representation of the delta function      46
Divergence theorem      3
D’Alembert      1
D’Alembert’s method      101
Eigenfunctions      16
Eigenvalues      16 53
Eigenvectors      53
Elliptic equations      9 11
Equivalent regular sequences      36
Euler      1
Even functions      120
Exterior Dirichlet problem      79
Feynman diagram      163
Fick’s law      4
First order equations      95
First shift theorem      151
Fourier coefficient      14
Fourier cosine integral      127
Fourier cosine transform      133
Fourier expansions      50
Fourier integrals      124
Fourier series      14 53 68
Fourier sine integral      127
Fourier sine transform      133
Fourier transform of generalised functions      42 298
Fraunhofer diffraction      206
Fresnel approximation      173
Fresnel diffraction      207
Function norm      14
Functions of slow growth      37
General Fourier transform      136
General solution of wave equation      102
Generalised Fourier series      14
Generalised functions      34
Generating function      19
Generating function, grad      3
Green’s function for the diffusion, equation      217
Green’s function solution to Maxwell’s equations      196
Green’s function to Laplace’s equation      221
Green’s function to Poisson’s equation      221
Green’s functions      163
Green’s functions and optics      202
Green’s functions for Maxwell’s equations      194

Green’s functions for Schrodinger’s equation      180
Green’s functions for the Helmholtz equation      180
Green’s functions for the wave equation      168 195
Green’s functions for time dependent problems      194
Green’s functions in one dimension      168
Green’s functions in three dimensions      172
Green’s functions in two dimensions      170
Green’s functions to the      3
Green’s Theorem      177
Heat equation      3 56 130
Heaviside step function      39 152
Helmholtz equation      164
Homogeneous and non-homogeneous, boundary conditions      66
Homogeneous equation      2
Huygen’s principle      166
Hyperbolic equations      9 10
Infinite string      104
Integral representation      26
Integral transforms      123
Interior Dirichlet problem      79
Interval of dependence      109
Inverting Laplace transforms      144
Kirchhoff diffraction theory      202
Laplace transforms      142 157
Laplace’s equation      6 61 77 79 86
Laurent’s theorem      32
Legendre polynomials      18
Legendre’s equation      87 91
Linear equations      2
Maxwell’s equations      1
Modulus of a complex number      30
Navier — Stoke’s equation      1
nd. order equations      8
Newton’s law of radiation      4
Non-linear equations      2
Non-linear first order equations      98
Norms      13
Norms of functions      14
Odd extensions      118
Order      2
Orthogonal functions      13
Parabolic equations      9 10
Parseval’s theorem      43
Poles      32
Propagation of discontinuities      113
Rayleigh scattering      191
Reciprocity theorem      179
Recurrence relations      20
Reduction to canonical form      10
Regular function      30
Regular sequence      36
Residues      32
Rodrigues’ formula      20
Rutherford scattering      188
Rytov approximation      208
Sampling property      40
Schrodinger’s equation      1
Second order equations      2
Second shift theorem      155
Self-adjoint form      17
Semi-infinite strings      117
Separation of variables      50 57 62 67
Series form of Bessel functions      27
simple harmonic motion      2
Singularities in the complex plane      30
Slow growth functions      37
Sommerfeld radiation condition      206
spherical polar coordinates      77
Standard functions in complex plane      30
Standard Laplace transforms      151
standing waves      103
Steady state solutions      67
Stretched string      51
Sturm-Liouville boundary value, problems      16
Taylor’s Theorem      32
Test function      36
Theory of distributions      35
Three term recurrence relations      20 26
Wave equation      4 50 50
Wave propagation      102
WKB approximation      208

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