Math 416

Complex variables. This is a course that explores the theory and applications of complex analysis as extension of Real analysis.

The course is taught by Professor. John E. McCarthy mailto:mccarthy@math.wustl.edu

Some interesting fact is that he cover the lecture terribly quick. At least for me. I need to preview and review the lecture after the course ended. The only thing that I can take granted of is that many theorem in real analysis still holds in the complex. By elegant definition designing, we build a wonderful math with complex variables and extended theorems, which is more helpful when solving questions that cannot be solved in real numbers.

McCarthy like to write $\zeta$ for $z$ and his writing for $\zeta$ is almost identical with $z$, I decided to use the traditional notation system I’ve learned to avoid confusion in my notes.

I will use $B_r(z_0)$ to denote a disk in $\mathbb{C}$ such that $B_r(z_0) = \{ z \in \mathbb{C} : |z - z_0| < r \}$. In the lecture, he use $\mathbb{D}(z_0,r)$ to denote the disk centered at $z_0$ with radius $r$. If $\mathbb{D}$ is used, then it means the unit disk $\mathbb{D}=\{z:|z|<1\}$. You may also see the closure of the disk $\overline{B_r(z_0)}$ and $\overline{\mathbb{D}}$, these are equivalent definition.

I will use $z$ to replace the strange notation of $\zeta$. If that makes sense.