I don't think it's implied that complex analysis is required for reading these notes. The author writes that he expects students will take a course on complex analysis "at some point" but as far as I can tell he doesn't do anything requiring complex analysis in these notes (e.g. every search for "complex" turns up something unrelated to complex analysis, and the word "contour" (as in contour integral) doesn't appear in the notes at all).
I'll take your word for it. In that case, the notes can't very well be said to take you to the graduate level. There's no point in skating over arguably the most beautiful and interconnected area of mathematics (by which I mean complex analysis) in an effort to get to some nominal level of mathematical advancedness.
