Math 114.01 and 114.02

Plan for Week 3

Week 3 (January 25 - January 29).

We will begin the week by examining the concept of differentiation for complex-valued functions of a complex variable. We will continue this on Wednesday. Then we will turn to the complex transcendental functions. These functions will be the focus of the lab on Friday.

Homework originally due for Wednesday, January 27. This will now be collected on Monday, February 1.

  1. Calculate the derivatives of each of the following functions. Then express the derivative in terms of its real and imaginary parts.
  2. Verify the Cauchy-Riemann Equations for the function f(z) = z3.

  3. Let f be a differentiable function on the open set O. Suppose that u is the real part of f and v is the imaginary part of f. Assume that u(x,y) and v(x,y) have continuous second partial derivatives in O. Show that both u and v are harmonic functions, i.e., that

    uxx + uyy = 0 for all x + iy in O and

    vxx + vyy = 0 for all x + iy in O

Homework due on Monday, February 1.


Section 17.7: 1, 2, 3, 5, 7, 9, 11, 15, 18

Lab Activity for Friday, Janurary 29

Work through the module "Complex Transcendental Functions" -- in the Engineering Mathematics section, and answer all the questions in Parts 1 and 2 and Question 4 in the Summary. Your report will consist of your completed worksheet emailed to 114-1 or 114-2 with the names of the team members on it. The report is due by Wednesday, February 3. You should email a copy to the second partner and to your acpub addresses. I will return the graded report to the addresses on the original submission.

Lawrence C. Moore < lang@math.duke.edu>

Last modified: January 26, 1999