# Are Complex Analysis and Complex Variables the same thing?

1. Oct 26, 2014

### Math10

Is Complex Analysis and Complex Variables the same thing? Is Complex Analysis pure or applied math? Is Complex Variables pure or applied math? What's the prerequisite of Complex Analysis and Complex Variables? Are they useful for the field of computer science?

2. Oct 26, 2014

### FactChecker

Both terms are probably referring to the same thing -- complex analysis. The subject can be either theoretical or applied, depending on what the class emphasis is. Complex analysis was developed to solve many physics and engineering problems. It is basic for understanding feedback control systems, ideal fluid flow (irrotational, incompressable), temperature distributions, electrostatic potentials, etc.

I am not aware of any direct applications to computer science. Electrical Engineering will almost certainly require it.

3. Oct 27, 2014

### Math10

Thank you. But what's the prerequisite for this course?

4. Oct 27, 2014

### FactChecker

You should check the prerequisites that are listed for any course you are considering. The school will list them.

5. Oct 28, 2014

Okay.

6. Nov 1, 2014

### mathwonk

to do complex analysis, you need to understand continuity, integration theory, power series, and some plane topology. Some courses will try to teach all this in the course, but it helps to review your Riemann integration, and not just as antidifferentiation, but as limits of Riemann sums, especially applied to path integrals. It also helps to understand stereographic projection, e.g. lines and circles in the plane and their relation with circles on the sphere. One also usually makes more use of differentials, things like dz, dx, dy than in real calculus. And review your partial derivatives, and green's theorem from advanced calculus. Of course review algebra of complex numbers.

7. Nov 1, 2014

### Math10

Okay, thanks.