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[再寄小读者之数学篇](2014-05-27 偏导数的计算)

已知  

u(x,t)=1210dηx+t?ηx?t+ηf(ξ,η)dξ,
<script id="MathJax-Element-1" type="math/tex; mode=display">\bex u(x,t)=\cfrac{1}{2}\int_0^1\rd \eta \int_{x-t+\eta}^{x+t-\eta}f(\xi,\eta)\rd \xi, \eex</script> 且 f(ξ,η)<script id="MathJax-Element-2" type="math/tex">f(\xi,\eta)</script>, fξ(ξ,η)<script id="MathJax-Element-3" type="math/tex">f_\xi(\xi,\eta)</script> 连续. 试求 ?2u?t2??2u?x2<script id="MathJax-Element-4" type="math/tex">\cfrac{\p ^2u}{\p t^2}-\cfrac{\p ^2u}{\p x^2}</script>.