都係唔知咩嚟
[數撚圍爐區] 祝手巴日日無工開, 想出紙永遠失敗 (54)
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都係唔知咩嚟
或者簡單D
given
u_x + u_y = 0
你會點solve?
given
u_x + u_y = 0
你會點solve?
Wolfram alpha
唔比用計數機/電腦 
sub 咗
x=唔識打嘅符號
y=(唔識打嘅符號-唔識打嘅符號2)
x=唔識打嘅符號
y=(唔識打嘅符號-唔識打嘅符號2)
然後就唔知點做了
tutor sd咗呢張相俾我
原來佢出錯題目
咁樣先啱
咁樣先啱
你係咪唔知咩叫characteristics 
what is characteristics 
例如 u_x + u_y = 0 條chatacteristics咪 a(t) = (x0 + t, y0 + t)
解1d wave equation會用到
解1d wave equation會用到
The PDE in question can be reduced to an ODE along characteristic lines. If the ODE is nice, you get an invariant quantity along the characteristic lines.
u_x+u_y=0 where subscript denotes partial derivative, 無端端走t出黎?？
444你都識講
將pde變成ode in t lor
將pde變成ode in t lor
Constant a 對我容易D.
u_t+a*u_x=0 where subscript denotes partial derivative.
Let dx/dt=a, then
u_t+dx/dt*u_x=0
And from the definition of total derivative, the equation is now:
u_t+dx/dt*u_x=Du/Dt=0 along dx/dt=a.
No it becomes an ODE:
Du/Dt=0 along dx/dt=a
u=Constant along dx/dt=a
Given an initial condition u0(x), u(t,x)=u0(x-at).
係用characteristic line 將個solution trace返去initial condition.
u_t+a*u_x=0 where subscript denotes partial derivative.
Let dx/dt=a, then
u_t+dx/dt*u_x=0
And from the definition of total derivative, the equation is now:
u_t+dx/dt*u_x=Du/Dt=0 along dx/dt=a.
No it becomes an ODE:
Du/Dt=0 along dx/dt=a
u=Constant along dx/dt=a
Given an initial condition u0(x), u(t,x)=u0(x-at).
係用characteristic line 將個solution trace返去initial condition.
t係吾係independent variable?