So far, we have looked at the general theory theory and tools for working with curvilinear coordinates, as well as doing integrals in curvilinear coordinates. This is already enough for a lot of interesting applications in vector calculus.

However, there is still one thing we are missing that's crucial for a solid understanding of vector calculus - how do the various vector operators like the gradient, divergence, curl and Laplacian work in curvilinear coordinates?

That is the topic we are diving into in this lesson. The key idea we'll discover is that the interpretation and geometric meaning of all the vector calculus operations remain exactly the same as discussed previously, but their form looks different when expressed in different coordinates.