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{\large\textbf{��5�񐔗����I���K (2010�N11��12�����{)}}
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�S������ ���n����/ TA �����`�j

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\bigskip

\prob
���̌v�Z������B
$$
(1)  \int_{|z|=2}\frac{1}{z^2+1}dz \qquad\qquad
(2)  \int_{|z-1|=1}\frac{e^z}{z^4-1} dz\qquad\qquad\ \\
$$
$$ 
(3) \int_{|z|=2}z^n(1-z)^mdz \qquad
(4) \int_{|z|=\rho}|z-a|^{-4}{dz} \quad (|a|\ne\rho)
$$

\prob
$\gamma$��$\C\setminus\{0\}$����$�P$��$a\ne0$������$C^1$�Ȑ��Ƃ���D���̂Ƃ�
$$
\exp\int_\gamma\frac{dz}{z}=a
$$
�������D�i����Ă��̐��ϕ���$\log a$���`���邱�Ƃ��ł���D�j

\prob
$x$�̑����� $f(x)$�ɑ΂���
$$
F(z)=\int_0^1\frac{f(t)}{z-t}dt
$$
�ƒ�`����i{\bf [26]}�ɂ��$F(z)$��$\C\setminus[0,1]$�Ő����j�D���̂Ƃ�
$$
\lim_{t\downarrow 0}\big(F(x+i t)-F(x-it)\big)=2\pi i\, f(x),\quad x\in (0,1)
$$
��ϕ��H�̕ό`��p���Ď����D(���̓����͈�ʂ̘A���֐�$f(x)$�ɂ��Ă����藧�D)

\prob
$z$�̑�����
$P(z)$�ɑ΂��Đ��ϕ�
\[
 \int_{|z-a|=r} \overline{P(z)} \, dz
 \]
�����߂�D


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���K����
{\tt http://www.ms.u-tokyo.ac.jp/$\sim$hirachi/courses/}
����_�E�����[�h�ł��܂��D�u�`�������ڂ��Ă��܂��D


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