I recently began to use your MathStudio app in my iPad.
I am currently learning to use, and found that your mathstudio app will serve excellently in my electrical engineering lectures (e.g., microwave engineering).
But I found some issues with your results.
If you perform VectorPlot(x,y), the resulting length of vector arrows should be proportional to the magnitude of the vector. The lengths of arrows in the plot are the same everywhere. This issue was observed with other mathstudio examples in the manual. This is correctly displayed with the Wolfram Alpha calculations.
The contour plot is not working at all with the current version.