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Chapter 5 Surfaces

We've seen previously how to describe curves: parametrically, implicitly and explicitly. Now we are going to describe surfaces, and similarly will do so parametrically, implicitly and explicitly. Our first major application is surface area, which is analogous to arclength of a curve from previously. Then in the next section - as you might guess - we will then have surface integrals analogous to line integrals, and then big theorems about vector fields and surfaces just as we had Green's theorem which was about vector fields and curves.