Is a Differential Equations course necessary to understand everything in a Complex Variables course?

Question

I can take Complex Variables (for engineering) without going through a diff eqs course at my university. However, the Complex Variables Syllabus says we will study the Laplace Transform, etc. Do you think I could survive this course without knowing much about differential equations. I already took Calc 1 through Calc3.

Answer 1

I dont know what a "complex variables" course is in your university, however I have done complex analysis (maybe the two coincide) and advanced differential equations (both at undergrad). There is only one thing that the two had in common which is solving a PDE (and maybe fourier series, but im not too sure). This is solving your laplace, wave and heat equation. The hardcore understanding of pdes were done in my advanced differential equations course, however i felt that without that course id still be able to solve those pdes in my complex analysis course because they were relatively simple. Maybe it will be the same for you as well.

Answer 2

So to answer your question, no a differential equations course will not replace your complex variables course (assuming its similar to my complex analysis course). Complex analysis has alot more than solving a pde. Please reply to this if you want more detail