ERROR in teaching of Lecture 1

In the example where we calculate line integral of a vector field along a circular path (without dot product), the solution contained an error: the unit vector in r was taken out of the integral. In cylindrical coordinate, unit vector in r is not CONSTANT; it's direction depends on phi value! Therefore we can't take it out of the integral. Instead, we can decompose it into two vectors in Cartesian coordinate. The axial unit vectors in Cartesian coordinate (along x and y) are CONSTANT regardless of phi; therefore, they can be taken out.

This point is also addressed in the example in Swedish textbook (page 25-26, figure 3.9).

Updates are made in page 9 in Lecture_01-2.pdf, and also Page 10 in the English compendium. Please check.

Best, Max