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**1. Homework Statement**

When I work in general curvilinear coordinates and in particular for the computation of line and surface integrals, do I need to do anything apart from working through the 'usual steps?'

**2. Homework Equations**

If I am correct, computation of line and surface integrals is typically introduced in cartesian coordinates. In such a coordinate system, some basic parameterisations include those of for a circle of radius r eg. (x,y) = (rcos(t),rsin(t)), 0 <= t <= 2pi.

**3. The Attempt at a Solution**

I know that if I work in say cylindrical or spherical coordinates the expressions for the gradient, divergence and Laplacian are different (and more complicated) than in cartesian coordinates. So do the parameterisations of surfaces and paths become more complicated if I want to compute a line integral in these non-cartesian coordinate systems? If so why would anyone want to use non-cartesian coordinate systems to compute various integrals? Is it because in certain situations, this is the

*only*possible way to compute the integrals?

I'm interested in this because I only really got as far as going through the derivations and computations for alternative forms of the gradient, laplacian etc. I don't feel as if I really learned how to apply useful techniques such as computing integrals in geometries with cylindrical or spherical symmetry apart from trivial cases where the vector field and outward surface normal were both constant.

Any help would be great thanks.