Math 43
Functions of a Complex Variable
Last updated June 17, 2019 14:18:35 EDT
Announcements:
- Generally speaking, this page, rather than
the canvas
page, will contain most of the information you need for the
course.
- By popular demand, the final format will be Take-Home
and due at 11am on Monday, June 8th.
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.
- Here are selected solutions
for the first homework assignment. (Last modified
- Here are selected solutions for the
second homework assignment. (Last modified
- Here are selected solutions for the
third homework assignment. (Last modified
- Here are selected solutions for the
preliminary exam. (Last modified
- Here is a hist-o-gram of the
scores on the preliminary exam. There is also data on the average
and median scores.
- 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.
- 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.
- Here are selected solutions for the
fourth homework assignment. (Last modified
- Here are selected solutions for the
sixth homework assignment. (Last modified
- Here are selected solutions for the
midterm exam. (Last modified
- Here is a hist-o-gram of the
scores on the
midterm exam. (Last modified 2:18 pm, June 17, 2019).
- 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.
- Here are selected solutions for the
seventh sixth homework assignment. (Last modified
- Here are selected solutions for the
eighth and final graded homework assignment. (Last modified
- Comments on Final:
- In problem 2(b), $n$ is meant to be an integer and the $dx$ in
the integral should be a $dz$: $$ \frac1{2\pi i}\int_{|z|=1}
\frac1{z^n(z-2)}\,dz.$$
- 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 $f(z)=1/z$.
- Here is the distribution of
scores on the final exam. (Last modified 2:18 pm, June 17, 2019).
- 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:
- $\ge 444$: A
- $\ge 420$: $A{-}$
- $\ge 400$: $B{+}$
- $\ge 350$: $B$
- $\ge 320$: $B{-}$
- $\ge 250$: $C$
- $D$
Dana P. Williams
Last updated June 17, 2019 14:18:35 EDT