Is the course "Complex Variables with Applications" taken after Differential Equations? Is this course applied or pure math? Can someone recommend me a good textbook for this course?
Without the course contents, the title could mean anything from high school up to grad school level.
If you mean this http://ocw.mit.edu/courses/mathematics/18-04-complex-variables-with-applications-fall-2003/index.htm or something similar, it says Differential Equations are a prerequisite.
The theory part of that MIT course is pure math - similar courses are sometimes called Complex Analysis. For the application part, the clue is in the word "applications".
There is no Math Czar (at least not in the US) who dictates to colleges and universities that "thou shalt require Differential Equations as a prerequisite for Complex Variables." At the college where I work, the prereqs for Complex Variables are the calculus sequence and the intro to proofs class ("Transition to Advanced Mathematics").