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此文件可在网址 math.shekou 下载 - PowerPoint PPT Presentation

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第一章 一些典型方程和定解条件的推导

§1.1 基本方程的建立

u

T'

M'

a'

ds

M

a

T

N'

N

x

x

x+dx

O

(1.3)式称为一维波动方程.

i

i+Di

LDx

CDx

v

v+Dv

x

x+Dx

L—每一回路单位的串联电感;C—每一单位长度的分路电容.L—每一回路单位的串联电感;C—每一单位长度的分路电容.

i

i+Di

LDx

CDx

v

v+Dv

x

x+Dx

i

i+Di

LDx

CDx

v

v+Dv

x

x+Dx

i

i+Di

LDx

CDx

v

v+Dv

x

x+Dx

J—传导电流面密度,r—电荷的体密度.

(1.15)与(1.16)称为三维波动方程. 用标量形式表示可写成

u是E(或H)的任意一个分量, 而

2u=0 (1.19)

n

DS

M

V

S

n

DS

M

V

S

k为热传导系数. 从时刻t1到t2, 通过曲面S流入区域V的全部热量为

c—物体的比热, r—物体的密度.