流函数、势函数的存在条件各是什么?它们是否都满足拉普拉斯方程形式?
<img src='https://img2.soutiyun.com/ask/2021-02-03/981198730930672.png' />是两个格,f:L->S是格同态,试证明j的象点集合是S的子格.
函数y=C-sinx(其中C为任意常数)是微分方程<img src='https://img2.soutiyun.com/ask/uploadfile/6693001-6696000/76c14d8aecc7af50292b8b9e94b078bf.png' />的( ).
试判断下列函数在分界点x=0处是否可导?如果可导,则该函数的导数f’(0)是下列四个结论中的哪一个()。<img src='https://img2.soutiyun.com//1/2021-06-20/993065591395231.png' />
设<img src='https://img2.soutiyun.com/ask/2020-12-15/976910006079741.png' />为同一区间上的可导函数,证明
满足方程f(x)+2<img src='https://img2.soutiyun.com/shangxueba/ask/17673001-17676000/17675800/201510261646105063.jpg' />f(x)dx=x<sup>2</sup>的解f(x)是:()
证明柯特斯系数满足<img src='https://img2.soutiyun.com/ask/2020-08-04/965384831848618.png' />
设是满足的实数,试证明方程在(0,1)内至少有一实根。
求下列参数方程所确定的函数的三阶导数<img src='https://img2.soutiyun.com/ask/2020-08-06/965553991550217.png' />
利用Γ函数和B函数的关系,证明<img src='https://img2.soutiyun.com/ask/2021-01-19/979914972490034.png' />
设参数方程<img src='https://img2.soutiyun.com/shangxueba/ask/17670001-17673000/17670789/2015102617291875238.jpg' />,确定了y是x的函数,且f′(t)存在,f(0)=2,f′(0)=2,则当t=0时,dy/dx的值等于:()
设参数方程<img src='https://img2.soutiyun.com/shangxueba/ask/17670001-17673000/17672290/2015102617310076340.jpg' />,确定了y是x的函数,f″(t)存在且不为零,则d<sup>2</sup>y/d<sup>2</sup>x的值是:()
设f(x)为连续函数,且满足等式<img src='https://img2.soutiyun.com/shangxueba/ask/51381001-51384000/51383367/97672305236883.png' />则<img src='https://img2.soutiyun.com/shangxueba/ask/51381001-51384000/51383367/976723063701479.png' />=().
在半平面y> 0内求解拉普拉斯方程的第一边值问题<img src='https://img2.soutiyun.com/ask/2020-09-21/96955493800503.png' />
悬链线方程为: <img border="0" alt="" src="//up.zaixiankaoshi.com/questions/image/39/8783255_0.jpg">可见悬链线方程含双曲线函数,计算复杂。在档距
系统的开环传递函数为<img src='https://img2.soutiyun.com/ask/uploadfile/5400001-5403000/08172de8426e22acf0dd8e15a54e3139.png' />,则闭环特征方程为( )。
设矩阵满足方程<img src='https://img2.soutiyun.com/ask/uploadfile/10923001-10926000/62839ccf0758320892b8a63233c10674.jpg' />
设函数<img src='https://img2.soutiyun.com/shangxueba/ask/51060001-51063000/51061013/970054070213009.png' />求方程f(x)=0的根。
某原电池,当有1mol电池反应发生时,其体积变化为ΔV,试证明在等温条件下,该电池可逆电动势随压力的变化遵循下列关系:<img src='https://img2.soutiyun.com/ask/2020-12-22/97751383724922.png' />
若<img src='https://img2.soutiyun.com/latex/latex.action' />,<img src='https://img2.soutiyun.com/latex/latex.action' />试证明时域卷积定理<img src='https://img2.soutiyun.com/latex/latex.action' />和频域卷积定理<img src='https://img2.soutiyun.com/latex/latex.action' />
在轴对称位移问题中,试导出按位移求解的基本方程。并证明可以满足此基本方程。
6、平面势流的流函数与流速势函数均满足拉普拉斯方程。
证明:若f为函数,则<img src='https://img2.soutiyun.com/ask/2020-08-12/966099742187747.png' />
有一以理想气体为工作物质的热机,其循环如图所示,试证明热<img src='https://img2.soutiyun.com/ask/2020-12-21/977425781975255.png' />