I'm teaching Applied Mathematics 105a this semester.  The main content of the course is complex analysis.  The course is taken mainly by undergraduate students in Engineering, Physics, and Applied Mathematics.  There are about 70 people in the class, which makes it the largest class I have taught in the last 10 years. I have never taught a course on complex analysis before, but have used complex analysis in my research, and have taught the method of complex variables in my graduate course on elasticity.