Math 43
Functions of a Complex Variable
Last updated June 10, 2015 13:11:39 EDT

General Information Syllabus HW Assignments


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Selected Solutions

I will use this page to provide links to selected homework solutions and brief solutions to the exams. These solutions are provided for the benefit of Math 43 students in the spring of 2015. They should not be circulated outside of that class. To do so would be a violation of the honor code.

Since it is hard to avoid making typos, and yes thinkos, on these LaTeX documents, please keep an eye on the modification dates to see if there is a newer version here than the last one you downloaded.

  1. Here are selected solutions for the first homework assignment. (Last modified
  2. Here are selected solutions for the second homework assignment. (Last modified
  3. Here are selected solutions for the third homework assignment. (Last modified
  4. Here are selected solutions for the preliminary exam. (Last modified
  5. Here is a hist-o-gram of the scores on the preliminary exam. There is also data on the average and median scores.
  6. The whole point of having a preliminary exam worth only 60% of the other midterm exam is that students not get too stressed over grades early in the term and before everyone is clear on my expectations. Nevertheless, it is only normal to want some idea of where you stand currently. So if you add your first two homework scores and your exam score you get a number between 0 and 99 (= 75 + 24). Then a crude estimate is that a total of 80 or more would get some sort of A, while totals of 60 or more would get some sort of B. Folks with totals less than 60 would get some sort of C, but should probably also talk to me about how to improve their work.
  7. Here are selected solutions for the fourth homework assignment. (Last modified Sorry to be late in posting these. Let me know in the future if the solutions are not in place Monday afternoon.
  8. Here are selected solutions for the fourth homework assignment. (Last modified
  9. Here are selected solutions for the sixth homework assignment. (Last modified
  10. Here are selected solutions for the midterm exam. (Last modified
  11. Here is a hist-o-gram of the scores on the midterm exam. (Last modified 7:04 pm, May 17, 2015).
  12. The midterm was challenging, but I feel the class did well as a hole. Of course, the final grades in the course will reflect the difficult of the exams. Typically, the median grade is a course like Math 43 will be at least a B+. To give you some idea of where you stand, I am providing some crude guidelines. If you add your scores on the two exam and the five homework assignments grades so far, you get a number out of 260 = 75 + 125 + 60. Totals above 210 would be some sort of A, totals above 160 some sort of B, and totals above 140 are in danger of getting some sort of C. People with lower totals may want to talk to me.
  13. Here are selected solutions for the seventh sixth homework assignment. (Last modified
  14. Here are selected solutions for the eighth and final graded homework assignment. (Last modified
  15. Comments on Final:
    1. In problem 2(b), $n$ is meant to be an integer and the $dx$ in the integral should be a $dz$: $$ \frac1{2\pi i}\int_{|z|=1} \frac1{z^n(z-2)}\,dz.$$
    2. In problem 6, it should read $$|f(z)|\le \frac A{\sqrt{|z|}}\quad\text{for $z\in B_r'(0)$}.$$ The square root in the denominator was inadvertantly omitted. Sorry, as written, the assertion is obviously false. Consider $f(z)=1/z$.
  16. Here is the distribution of scores on the final exam. (Last modified 8:29 am, June 10, 2015).
  17. Your grade in the course is based on the sum of your scores on the priminary exam, the midterm, the homework and the final for a total of $75+125+100+200=500$. With a tiny number of borderline exceptions, your grade was determined as follows:


Dana P. Williams
Last updated June 10, 2015 13:11:39 EDT