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{\large ���wI���K�@��P�O��@2007�N11��13���z�z} 

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�S�� ���n����CTA �O�p �~
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{\tt http://www.ms.u-tokyo.ac.jp/$\sim$hirachi/courses/sugaku-I-2007/}
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{\bf ���.}
��� $[a,b]$��̘A���֐� $f(x)$�̃O���t$G=\{(x,f(x))\in\mathbb{R}^2:x\in[a,b]\}$�̖ʐς͂O�ł��邱�Ƃ������B

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{\small
�ȉ��̖����ł���͈͂ŉ���, 11��20��13���܂łɃA�h�~�j�X�g���[�V�������̃��|�[�g��o�{�b�N�X�ɒ�o���邱��. 
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\prob �ȉ��̔���������������.
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(a) $\displaystyle\frac{dy}{dx}=ky(1-y) \quad k\not=0$

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(b) $\displaystyle \frac{dy}{dx}+y=\sin x $


\prob $\mathbb{R}^2$���̓_��$\{P_n\}_{n=1}^\infty$�����������
�W�� $A=\{P_n:n=1,2,3,\dots\}$�̖ʐς͂O�ł��邱�Ƃ������B
�܂�$\{P_n\}_{n=1}^\infty$���������Ȃ��Ƃ��ɂ͂ǂ��Ȃ邩�H

\prob $f(x,y)$��L�E�̈�$D$��̘A���֐��Ƃ���B���E$\partial D$�̖ʐς��O�ł���Ƃ�$D_+=\{(x,y)\in D: x\ge0\}$, $D_-=\{(x,y)\in D: x\le0\}$�̋��E�̖ʐς��O�ł���$$
\iint_D f(x,y)dxdy=\iint_{D_+} f(x,y)dxdy+\iint_{D_-} f(x,y)dxdy
$$ 
�����藧���Ƃ������B



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