DSP

电磁学乱七八糟的符号(一)

2019-07-13 18:40发布

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电磁学乱七八糟的符号(一)

@(study)[DSP, markdown_study, LaTex_study]
author:何伟宝

文章目录

chapter1 场量基础

通量ψpsi

ψ=∫sF⃗∙a⃗ndSpsi = int_s vec F ullet vec a_n d S
ψ=∮SF⃗∙dS⃗psi = oint_S vec F ullet dvec S

旋量ΓGamma

Γ=∫lF⃗∙dl⃗Gamma=int_l vec F ullet dvec l
Γ=∮lF⃗∙dl⃗Gamma=oint_l vec F ullet dvec l

矢性微分算符∇ abla

∇=a⃗x∂∂x+a⃗y∂∂y+a⃗z∂∂z abla =vec a_x frac{partial }{partial x}+vec a_y frac{partial }{partial y}+vec a_z frac{partial }{partial z}

拉普拉斯算符∇2 abla^2

∇=a⃗x∂2∂x2+a⃗y∂2∂y2+a⃗z∂2∂z2 abla =vec a_x frac{partial^2 }{partial x^2}+vec a_y frac{partial^2 }{partial y^2}+vec a_z frac{partial^2 }{partial z^2} ∇×(∇×F⃗)=∇(∇∙F⃗)−∇2F⃗ abla imes ( abla imes vec F) = abla( abla ullet vec F) - abla^2 vec F

梯度 grad u

gradu=a⃗x∂u∂x+a⃗y∂u∂y+a⃗z∂u∂zgrad u =vec a_x frac{partial u}{partial x}+vec a_y frac{partial u}{partial y}+vec a_z frac{partial u}{partial z}
gradu=∇u gradu= abla u

散度div F

divF⃗≜lim⁡△V→0∮SF⃗dS⃗△V div vec F riangleq lim_{ riangle V o 0} frac{oint_S vec F d vec S}{ riangle V} divF⃗=∂Fx∂x+∂Fy∂y+∂Fz∂z=∇∙F⃗div vec F=frac{partial F_x}{partial x}+frac{partial F_y}{partial y}+ frac{partial F_z}{partial z} = abla ullet vec F