1.3 KiB
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.