MATH 371 Problem Set 3 (Due Monday, October 20)

1. Find an admissible parametrization for each of the following smooth arcs or smooth closed curves:

a) The circle of radius 5 centered on 3-2i.

b) The semicircle with endpoints at 2-i and 2+i passing through 3.

c) The ellipse .

2. Find admissible parameterizations for each part of the following contour:

The square of side with a vertex at 1+i , its next vertex at 2+2i , traversed counterclockwise.

3. Let be the contour defined as the square of side 1 with vertices at 0,1,1+i, and i , traversed counterclockwise.

Compute each of the following:

a)

b)

c)

4. Let r be a given positive real number and the circle centered on 0 of radius r, with positive orientation.

Compute each of the following:

a)

b)

c)