这是一份UCL伦敦大学 MATH006101作业代写的成功案例
By inspection,
$$
T(x, y)=10+7.5(y-x)
$$
the real part of
$$
F(z)=10-7.5(1+i) z .
$$
A systematic derivation is as follows. The boundary and boundary values suggest that $T(x, y)$ is linear in $x$ and $y$,
$$
T(x, y)=a x+b y+c
$$
From the boundary conditions,
$$
\begin{aligned}
&T(x, x-4)=a x+b(x-4)+c=-20 \
&T(x, x+4)=a x+b(x+4)+c=40
\end{aligned}
$$
By addition,
$$
2 a x+2 b x+2 c=20
$$
Since this is an identity in $x$, we must have $a=-b$ and $c=10$. From this and
$$
-b x+b x-4 b+10=-20 .
$$
MATH6101 COURSE NOTES ：
On the $u$-axis both arguments are 0 for $u>1$, one equals $\pi$ if $-1<u<1$, and both equal $\pi$, giving $\pi-\pi=0$ if $u<-1$.
$w-a=z^{2}$. Hence Arg $(w-a)=\operatorname{Arg} z^{2}=2 \operatorname{Arg} z$. Thus (a) gives
$$
T_{1}+\frac{2}{\pi}\left(T_{2}-T_{1}\right) \operatorname{Arg} z
$$
and we see that $T=T_{1}$ on the $x$-axis and $T=T_{2}$ on the $y$-axis are the boundary data.