1. The problem statement, all variables and given/known data I just need to be able to change a vector field from spherical to cartesian The question is about verifying stokes theorem (curl theorem) for a given vector field within and on a given path. It says not to use spherical coordinates, but the vector field is given in spherical coordinates. 2. Relevant equations 3. The attempt at a solution I tried using the equations that relate r, theta, and phi to x, y, and z. One thing is, that it gets very messy, and I don't think it's meant to be. Another thing is that I don't know what to do with the unit vectors, as I have components that are (now) functions of x, y, and z but are pointing in the r, theta, and phi directions. I gather if I fixed that up, the messyness would disappear, but I don't know how to do it. I also considered finding the curl in spherical coordinates and then using a Jacobian determinant to evaluate the integral, but I thought this might be kind of cheating. If I can figure out how to change the vector field from spherical coordinates to cartesian I will have no trouble doing the integrals. I have a feeling I would've learnt this in first or second year calculus, but I can't remember :( Any help would be appreciated.