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Problem 7. Use a computer (e.g. with Wolframs Mathematica; commands VectorPlot and VectorPlot3D) to visualize the following
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Answer #1

(a)

In[18=f= {-y^ 3, x ^ 3} {-y, x Out[18 In[19= VectorPlot[f, {x, -10, 10}, {y, -10, 10}] 10 Out 19 -10 -10 10

(b)

In125)- f1- -(x A 2+1), -(y^2-1)} Out 25)- {1-x, 1-y2 In 26= VectorPlot[f1, {x, -10,10}, {y, -10,10}] 10 Out[26= -10 -10 5 0

(c)

In 3]= v= Transformed Field[ PolarCartesian, {-r^2,o} , {r, e} -» {x, y}] -xey, Out[33] -y In[34= VectorPlot[v, {x, -10,

In1351- v1 TransformedField[SphericalCartesian, {-r^2,0,0}, {r,e, p}{x, y, z} *V+y?+z? - zx Out[35= - X 1 -Y 1 In[361= Ve

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