harmonic function theory.zip

  • Jhbb
    了解作者
  • Mathematica
    开发工具
  • 74KB
    文件大小
  • zip
    文件格式
  • 0
    收藏次数
  • 1 积分
    下载积分
  • 0
    下载次数
  • 2020-06-14 22:38
    上传日期
谐波函数理论 mathematica .Axler
harmonic function theory.zip
  • HFT.nb
    161KB
  • HFT.m
    66.1KB
  • ComputingWithHarmonicFunctions.nb
    230KB
内容介绍
(******************************************************************* This file was generated automatically by the Mathematica front end. It contains Initialization cells from a Notebook file, which typically will have the same name as this file except ending in ".nb" instead of ".m". This file is intended to be loaded into the Mathematica kernel using the package loading commands Get or Needs. Doing so is equivalent to using the Evaluate Initialization Cells menu command in the front end. DO NOT EDIT THIS FILE. This entire file is regenerated automatically each time the parent Notebook file is saved in the Mathematica front end. Any changes you make to this file will be overwritten. ***********************************************************************) If[$VersionNumber<4, Print["This package will not work correctly with versions of Mathematica \ earlier than Mathematica 4.0. If you need a version of this package that will \ work correctly with earlier versions of Mathematica, please contact Sheldon \ Axler at axler@sfsu.edu."]] Print["HFT; Version 6.10, 9 August 2003"] Print["This Mathematica package, called HFT.m, is designed for computing with \ harmonic functions. Documentation for the use of this package and information \ about the algorithms used in it is available in the Mathematica notebook \ called HFT.nb."] Print["For addional information about harmonic functions, see the book \ Harmonic Function Theory, by Sheldon Axler, Paul Bourdon, and Wade Ramey, \ published by Springer."] Print["This package is copyrighted by Sheldon Axler but is distributed \ without charge. The most recent version of this HFT.m package along with its \ documentation notebook HFT.nb is available over the world wide web at: \ http://www.axler.net"] Print["Comments, suggestions, and bug reports should be sent by electronic \ mail to: axler@sfsu.edu"] Print["* The computer is now unpacking the HFT.m package."] BeginPackage["HFT`"] Annulus::"usage"="Annulus is an option for Region in Dirichlet." AntiLaplacian::"usage"= "AntiLaplacian[f, x] gives a polynomial "<>"whose Laplacian equals f. "<> "Here f must be a polynomial function of x." Ball::"usage"= "Ball is one of the values that may be assigned to the option "<> "Orthonormal." BasisH::"usage"= "BasisH[m, x] gives a basis for the space of harmonic "<> "polynomials homogeneous of degree m in the variable x." BergmanKernel::"usage"= "BergmanKernel[x, y] gives the Bergman "<> "reproducing kernel for the unit ball." BergmanKernelH::"usage"= "BergmanKernel[z, w] gives the Bergman "<> "reproducing kernel for the upper half-space." BergmanProjection::"usage"= "BergmanProjection[ f, x] gives the "<> "orthogonal projection of a polynomial f, as a function of x, "<> "onto the Bergman space of harmonic functions on the ball." BiDirichlet::"usage"= "BiDirichlet[f , x] solves the "<> "BiDirichlet problem with boundary data f, "<>"as a function of x." Delta::"usage"= "Delta[j] is the vector that equals 1 in the j-th "<> "coordinate and 0 in the other coordinates." Dimension::"usage"="Dimension[x] is the dimension of the vector x." DimensionH::"usage"= "DimensionH[m, n] gives the vector space dimension of the "<> "space of spherical harmonics of degree m in n variables." Dirichlet::"usage"= "Dirichlet[f, x] gives the harmonic function "<> "that equals f on the unit sphere. Here f must be a "<> "polynomial function of x." Divergence::"usage"= "Divergence[f, x] gives the divergence of f "<>"with respect to x." DoubleBracketingBar::"usage"="DoubleBracketingBar is equal to the Norm." ExpandNorm::"usage"= "ExpandNorm[f] gives f with all terms of the form |x + y| "<> "replaced by Sqrt[ |x|^2 + |y|^2 + 2 x.y ]." ExteriorSphere::"usage"= "ExteriorSphere is an option for Dirichlet, "<> "specifying that the region should be the exterior " <> "of the unit sphere." ExteriorNeumann::"usage"= "ExteriorNeumann[f , x] solves the "<> "exterior Neumann problem with boundary data f, "<>"as a function of x." Grad::"usage"="Grad[f, x] gives the gradient of f with "<>"respect to x." HarmonicConjugate::"usage"= "HarmonicConjugate[u, x, y] gives "<> "the harmonic conjugate of u with respect to the variables x, y." HarmonicDecomposition::"usage"= "HarmonicDecomposition[u, x] "<> "gives the harmonic decomposition of u with respect to "<> "the variable x." HilbertSchmidt::"usage"= "HilbertSchmidt[A] gives the "<>"HilbertSchmidt norm of a matrix A." Homogeneous::"usage"= "Homogeneous[f, d, x] gives the homogenous "<> "part of f of degree d, with respect to x." Hyperplane::"usage"="Hyperplane[b, c] denotes the hyperplane "<>"b.x = c." IntegrateBall::"usage"= "IntegrateBall[f, x] gives the integral "<> "of f, as a function of x, over the unit ball." IntegrateSphere::"usage"= "IntegrateSphere[f, x] gives the "<> "integral of f, as a function of x, over the unit sphere "<> "with respect to normalized surface area measure." Reflection::"usage"="Reflection[x] gives the reflection of x "<> "in the unit sphere." J::"usage"="J[f, x] gives the Jacobian of f with "<>"respect to x." Kelvin::"usage"= "Kelvin[u, x] gives the Kelvin transform of u, "<> "thought of as a function of x." KelvinM::"usage"= "KelvinM is the modified Kelvin transform, "<> "as defined in Chapter 7 of Harmonic Function Theory." Laplacian::"usage"= "Laplacian[f, x] gives the Laplacian of f "<>"with respect to x." Multiple::"usage"= "Multiple is an option for AntiLaplacian. "<> "The default value is None. The value Norm^2 produces the "<> "unique antiLaplacian that is a polynomial multiple of "<> "Norm[x]^2, where x is the variable." Neumann::"usage"= "Neumann[f, g, x] solves the "<> "Neumann problem of finding a function of x whose "<> "outward normal derivative (on the unit sphere) is f "<> "and whose Laplacian is g." If[$VersionNumber < 5,Norm::"usage"="Norm[x] gives the Euclidean norm of x."] NormalD::"usage"= "NormalD[f, z] gives the outward normal derivative of f, "<> "as a function of z, with respect to the unit ball." Orthonormal::"usage"= "Orthonormal is an option for BasisH. "<> "The default value is None. The value Ball produces a "<> "basis that is orthonormal with respect to volume measure "<> "on the ball. The value Sphere produces a "<> "basis that is orthonormal with respect to surface area "<> "measure on the sphere." \!\(Partial::"\<usage\>"\ = \ \*"\"\<Partial[f, \!\(x\_j\)] gives the \ partial derivative \>\"" <> \*"\"\<of f with respect to \!\(x\_j\).\>\""\) \[CapitalPhi]::"usage"= "\[CapitalPhi][z] is the modified reflection defined in "<> "Chapter 7 of Harmonic Function Theory." PoissonKernel::"usage"="PoissonKernel[x, z] gives the Poisson kernel for the \ unit ball." PoissonKernelH::"usage"= "PoissonKernelH[x, y, t] gives the "<> "Poisson kernel for the upper half-space." Quadratic::"usage"="Quadratic is an option for Multiple "<> "in AntiLaplacian and for Region in Dirichlet." Region::"usage"="Region is an option for Dirichlet." S::"usage"="S is the south pole." Schwarz::"usage"= "Schwarz[x] gives the maximum of |u[x]|, where "<> "u ranges over all harmonic functions on the unit ball with "<> "u[0] = 0 and |u| < 1." SetDimension::"usage"="SetDimension[x, n] sets the Dimension of x to n." Singularity::"usage"= "Singularity is an option for AntiLaplacian. "<> "The default value is None." Sphere::"usage"= "Sphere is one of the values that may be assigned to the option "<> "Orthonormal." SurfaceArea::"usage"= "SurfaceArea[n] gives the surf
评论
    相关推荐
    • Mathematica_Mainbook.rar
      这是Mathematica软件的作者所著的关于Mathematica软件使用最权威,最详尽的教程。
    • Mathematica在“平抛运动”教学中的应用.rar
      Mathematica在“平抛运动”教学中的应用
    • mathematica-modeling.zip
      数学建模,这是我数学建模的哦资料,知道吗,不一定有用
    • netting-theory_pudn.zip
      Mathematica code for filament winding of cylindrical pressure vessel with semispherical domes (netting theory)
    • mathematica合集
      Geometric Optics_ Theory and Design of Astronomical Optical Systems Using Mathematica.pdf Group Theory in Solid State Physics and Photonics Problem Solving with Mathematica.pdf Groups and Manifolds...
    • qi_functions_list (QI package mathematica).pdf.zip
      QUantum Information package for mathematica. version 0.3.27
    • The Mathematica Book 5ed
      Mathematica Version 5 introduces important extensions to the Mathematica system, especially in scope and scalability of numeric and symbolic computation. Building on the core language and extensive ...
    • sage-game-theory
      “为Magma,Maple,Mathematica和MATLAB创建可行的开源替代方案” 版权所有(C)2005-2014 The Sage Development Team Sage库为GPLv2 +,随附的软件包具有兼容的OSS许可证(请参阅COPYING.txt)。 超过400人为...
    • Mathematica Symbolic Toolbox for MATLAB
      Using the MathLink communication standard supplied with Mathematica and the MEX facility of MATLAB we write a toolbox that provides MATLAB users with all of the symbolic and high-precision numeric ...
    • SIM800C_MQTT.rar
      使用SIM800C模块,使用MQTT协议,连接中国移动onenet平台,能实现数据的订阅、发布、存储等