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 now discuss curves and their lengths in more detail. Let be an arbitrary natural number which is fixed throughout this post. Note that in general one needs to distinguish between a parameterised curve, which is a continuous mapping and the curve which is the image of given by Here we shall discuss parameterised curves. Hence, for instance, the parameterised curve with is a circle traversed twice and has therefore length whereas its image is just a circle which has length Continue reading