In this blog entry you can find lecture notes for Math2111, several variable calculus. See also the table of contents for this course. This blog entry printed to pdf is available here.

We discuss in what sense the scalar line integrals do not depend on the orientation of the curve.

Let us start with integrals where is a Riemann integrable function. Let and let be such that let for and We can now form the Riemann sum

By considering the limit where such that we obtain the Riemann integral Continue reading