Should I take Complex Analysis? Am I ready?

[RJLiberator]

Here's my situation:
Summer 2015, I am majoring in math and physics.

I am taking a 4-week course on DIFF EQ right now, and completely loving it and doing extremely well. Just finished my set of Calc 1, 2, and 3, and an intro to advanced math course (proof-writing basics).

Diff EQ is a 220 level course, while Complex analysis is a 417 level course.

I have not yet taking Linear Algebra 320, Abstract Algebra 310, Analysis 1 313, Analysis 2 414

I will be taking Linear Algebra in the Fall, and other courses as I go, however, it would virtually cost me nothing to add on Complex Analysis 417 to my summer schedule and they do not offer any other math courses that I need to take for the Summer.

I see that the only pre-req is Calc 3, which I have completed. I know that Complex Analysis is great for physics.

Am I ready to take Complex Analysis even tho I have not had the other math courses? Is it extremely difficult to the point where taking Physics II and Complex Analysis at the same time would cause me problems?

Thank you.

 

[RJLiberator]

For reference: https://www.physicsforums.com/threa...alysis-before-taking-complex-analysis.700565/

Good conversation here.

But would like posts on my personal situation.

 

[jtbell]

What are the official prerequisites for Complex Analysis, according to your university's catalog or web site?

 

[RJLiberator]

Only Calculus III is the pre-requisite.

I just completed it, spring 2015 and performed well.

 

[Arsenic&Lace]

My university has several CA courses, one which is basically like elementary calculus except with complex numbers (i.e. mostly computational problems, very few if any proofs), and several which concentrate on proofs.

It sounds like the course you are looking at is like the former, in which case it will both be useful and doable, as opposed to difficult and useless.

 

[JorisL]

I glanced at the explanations real quick here. (yay google)
I'm not sure what to think, the powerful Rouché's theorem is mentioned. I don't like the description they give though.
It should be mentioned if it is proof-based.

It really depends on the lecturer I suppose, some like a really formal method of teaching others try to give more of an intuitive approach (when possible).
I advise to contact a teacher if possible.

[...]
It sounds like the course you are looking at is like the former, in which case it will both be useful and doable, as opposed to difficult and useless.

The lather part of this statement I don't (fully) agree with. I can't give an immediate example for complex analysis.
However there is Stokes' theorem (Gauss' divergence theorem is a special case)
It is important to know the exact mathematical necessities to apply it.

The following example/language used might not be totally clear for RJLiberator

Spoiler

You need (roughly) that the n-form you're integrating is bounded on your volume otherwise it breaks down.
You can (and should) encounter this when looking at a covariant formulation of electromagnetism.

It's easy to say that you invoke a certain identity/theorem assuming it works. But it can break down even with the (apparently) well behaved equations you often deal with in physics. I made such a mistake a while back and didn't bother to check explicitly. Because of that I got a wildly different result

 

[Arsenic&Lace]

It's not difficult to figure out how to apply Stoke's theorem, and it doesn't require a course in advanced vector calculus. Proofs also don't necessarily improve one's ability to understand how to use a theorem; this depends on the proof and the theorem. In every case I can think of (i.e. that is relevant to a physicist), the intuition for the proof is enough to understand the conditions.

But there's nothing wrong with taking a proofy CA course if the OP likes proofy courses.

 

[vela]

I see that the only pre-req is Calc 3, which I have completed. I know that Complex Analysis is great for physics.

Am I ready to take Complex Analysis even tho I have not had the other math courses? Is it extremely difficult to the point where taking Physics II and Complex Analysis at the same time would cause me problems?

You're probably fine preparation-wise for complex analysis. After all, the only pre-requisite listed is Calc 3. One thing to keep in mind is that upper-division courses tend to be more intense than lower-division courses, and the increased difficulty is amplified by the shorter summer schedule. As long as you are aware of what to expect, you'll probably be fine.

Whether the course is actually useful for a physicist, that's a different question. If it's geared more toward applying math to solve problems, it would be very useful. If it's primarily concerned with proving the various theorems, perhaps not so much. That said, it never hurts to know the material at a more rigorous level than you might learn it in a math methods course for physicists.

 

[JorisL]

It's not difficult to figure out how to apply Stoke's theorem, and it doesn't require a course in advanced vector calculus. Proofs also don't necessarily improve one's ability to understand how to use a theorem; this depends on the proof and the theorem. In every case I can think of (i.e. that is relevant to a physicist), the intuition for the proof is enough to understand the conditions.

But there's nothing wrong with taking a proofy CA course if the OP likes proofy courses.

You are right, wanted to soften the language of the useless stuff a bit.
I've noticed that a lot of my fellow students, like me, benefit from proofs to see why you need certain conditions.

But don't take my words for a general wisdom. I'm more mathematical minded lately.
This are mostly my reasons for embracing more mathematical sophistication.
This might have been sparked by a course on phase transitions from a measure theory perspective which gave a lot of insight into the nature of thermodynamics as well

 

[neosoul]

I took Complex Analysis this semester, and thought I would not do well in the course. In my opinion, complex analysis is almost like calculus, but it uses complex numbers instead of real numbers. Be sure to do practice problems. Even the ones that are not done or assigned by the teacher. If you did well in Calculus I, II, and III as well as differential equations you will do well. I did very well without taking differential equations first.

 

[RJLiberator]

Excellent responses. It seems I am already to go for this course in the summer. Perhaps I will report back here mid-way through for future reference.

 

[RJLiberator]

Just to update this thread with the conclusion: It was a very intense course, I love intense courses and did extremely well here. There were times when I was wondering what was going on, but overall - the resources online were at a surplus and it was easy to catch up when needed. My professor was fantastic which also helped, but overall great course.

Thanks again guys.