偏微分方程中的英文单词和短语.docx

偏微分方程中的英文单词和短语偏微分方程Partial Differential Equations第一章 偏微分方程的导出和分类Chapter 1 Derivation and Classification of Partial Differential Equations偏微分方程partial differential equation波动方程wave equation弦string膜film振动方程oscillating equation扰动disturbance张力tension横向振动transversal oscillation弦的自由振动方程free vibration equation of string波wave维数dimension一维波动方程one-dimensional wave equation二维波动方程two-dimensional wave equation三维波动方程three-dimensional wave equation热传导方程heat conduction equation热传导heat conduction非齐次热传导方程nonhomogeneous heat conduction equation齐次热传导方程homogeneous heat conduction equation拉普拉斯方程Laplace equation泊松方程（有源的电势方程）Poisson equation拉普拉斯算子Laplace operator定解问题definite problem定解条件definite problem初始条件initial condition边界条件boundary condition泛函方程functional equation第一类边界条件boundary condition of the first kind第二类边界条件boundary condition of the second kind初边值问题initial boundary value problem混合问题mixed problem柯西问题Cauchy problem初值问题initial value problem边值问题boundary value problem适定问题well posed problem二阶线性偏微分方程second order linear partial differential equation特征方程characteristic equation特征线characteristic line双曲型方程的标准形式standard form of hyperbolic equation超双曲型方程ultra-hyperbolic equation抛物型方程parabolic equation椭圆型方程的标准形式standard form of elliptic equation特里古米方程Tricomi equation椭圆型elliptic type第二章 柯西问题（初值问题）Chapter 2 Cauchy Problems (Initial Value Problems)行波法method of traveling wave达朗贝尔公式DAlembert formula影响区域influence region决定区域determining region特征线法method of characteristic line依赖区域region of dependence球面均值法spherical means method泊松公式Poisson formula降维法method of descent齐次化原理homogenization principle推迟势retarded potential第三章 分离变量法Chapter 3 Methods of Separation of Variables叠加法superposition method自由振动free vibration正弦波sine wave节点node腹点（腹波）antinode驻波stationary wave固有频率eigenfrequency基音fundamental tone泛音harmonic驻波法method of stationary wave分离变量法method of separation variables特征值问题eigenvalue problem特征值eigenvalue特征函数eigenfunction固有函数法（试探法）heuristic method第四章 特征值问题Chapter 4 Eigenvalue Problems贝塞尔方程Bessel equation连带的勒让德方程associated Legendre equation施图姆-刘维尔方程Sturm-Liouville equation贝塞尔函数Bessel function傅里叶-贝塞尔级数Fourier-Bessel series纽曼函数Neumann function勒让德函数Legendre function勒让德方程Legendre equation第五章 边值问题Chapter 5 Boundary Value Problems亥姆霍兹方程Helmholtz equation定态薛定谔方程stationary Schrodinger equation第一边值问题first boundary value problem狄利克雷问题Dirichlet problem第二边值问题second boundary value problem纽曼问题Neumann problem第三边值问题third boundary value problem第四边值问题fourth boundary value problem调和方程harmonic equation内边值问题inner boundary value problem狄利克雷外问题outer Dirichlet problem纽曼外问题outer Neumann problem圆的泊松积分Poisson integral on circular region第六章 格林函数法Chapter 6 Method of Green Function格林第一公式first Green formula格林第二公示second Green formula基本解fundamental solution形式解formal solution源函数source function静电源像法method of electrostatic source image第七章 积分变换法Chapter 7 Method of Integral Transform傅里叶积分Fourier integration傅里叶积分公式Fourier integral formula傅里叶逆变换inverse Fourier transform狄拉克函数Dirac function集中力concentrated force单位阶梯函数unite step function赫维赛德阶梯函数Heaviside step function矩形脉冲函数rectangular pulse function滤波函数filtering function闸门函数sluice function拉普拉斯变换Laplace transform拉普拉斯逆变换inverse Laplace transform反演积分inversion integral拉普拉斯反演积分inversion integral of Laplace黎曼-梅林公式Riemann-Mellin formula赫维赛德展开式法Heaviside expansion method延迟定理法delay theorem method第八章 定解问题的近似解法Chapter 8 Approximate Solutions to Definite Problems差分法difference method差分方程difference equation网络法network method相容性条件compatibility condition同步迭代法synchronous iteration异步迭代法asynchronous iteration method变分方法variation method变分问题variation problem泛函functional零级距离zero-level distance一级距离first-level distancem级距离m-level distance零级领域zero-level neighborhood一级邻域f