mathmatica

Question

求这页面上的五个题所需函数命令可以直接复制的，mathmatice的

Answer 1

1. 解方程组:

   Solve[
   {
    2 x1 + x2 - 5 x3 + x4 == 8,
    x1 + 4 x2 - 7 x3 + 6 x4 == 0,
    x1 - 3 x2 - 6 x4 == 9,
    2 x2 - x3 + 2 x4 == -5
   },
   {x1, x2, x3, x4}
   ]
   

2. 计算矩阵A的转置B和A与B的乘积:

   A = {
   {-2, 5, -1, 3},
   {1, -9, 13, 7},
   {3, -1, 5, -5},
   {2, 8, -7, -10}
   };
   B = Transpose[A];
   AxB = A.B
   

3. 定义函数并求偏导数:

   f[x_, y_] := Log[Sqrt[x^2 + y^2]] + ArcTan[y/x]
   dfdx = D[f[x, y], x]
   d2fdxdy = D[dfdx, y]
   

4. 计算定积分:

   NIntegrate[Sin[Sin[x]], {x, 0, 3}]
   integral2 = Integrate[x^2 + y^2, {x, 0, 1}, {y, 1 - x, Sqrt[1 - x^2]}]
   

   因为integral1无法找到解析解，所以用得是数值积分NIntegrate。

5. 解微分方程:

   dsolve = DSolve[y''[x] + 2 y'[x] + y[x] == 0, y[x], x]