Real Analysis and Complex Analysis

[calculo2718]

I was wondering if it is too ambitious to take both Real Analysis and Complex Analysis in the same semester.

Thanks.

 

[micromass]

What are the prereqs for the courses? Do you meet the prereqs? What book do they use?

Are you comfortable with proofs?

 

[calculo2718]

What are the prereqs for the courses? Do you meet the prereqs? What book do they use?

Are you comfortable with proofs?

The pre-reqs are Multivariable Calculus and differential equations

for complex analysis they use Complex Variables and Applications by James Ward Brown and Ruel V. Churchill, eighth edition, McGraw-Hill, 2009.

for real analysis they use Boundary Value Problems and Partial Differential Equations, Fifth Edition, by David L. Powers, Elsevier Academic Press, 2006.

 

[micromass]

for real analysis they use Boundary Value Problems and Partial Differential Equations, Fifth Edition, by David L. Powers, Elsevier Academic Press, 2006.

Are you sure that's the real analysis book?? That book doesn't sound very much like real analysis to me.

Are these the only math courses you'll take? If so, you'll probably be fine.

 

[Mandelbroth]

The pre-reqs are Multivariable Calculus and differential equations

for complex analysis they use Complex Variables and Applications by James Ward Brown and Ruel V. Churchill, eighth edition, McGraw-Hill, 2009.

for real analysis they use Boundary Value Problems and Partial Differential Equations, Fifth Edition, by David L. Powers, Elsevier Academic Press, 2006.

I can say that I've personally read Complex Variables and Applications (by James Ward Brown, et al.) in its third edition. I remember enjoying it, though I seem to remember its section on Riemann surfaces was fairly disappointing. I don't know what I'd expect in its eighth edition, but I get the feeling it is still an excellent introduction to complex analysis.

I'd say you should be fine taking both. If you've got multivariate calculus down, you should be pretty good. Plus, more proofs means more fun.

You need to take differential equations before you take real and complex analysis? I find this interesting, since I often find using methods from real/complex analysis very helpful in solving differential equations. For example, you need to use complex analysis to compute a function's inverse Laplace transform, unless you are given a table. I feel like they should be taught beforehand.

 

[TomServo]

I'm finishing up complex analysis over the Summer semester using that same book (eight edition). It's fine but the binding is crap, and I bought a brand new copy. I was already comfortable with complex numbers from taking qm and Fourier series, but Fourier series had nothing to do with the class. My teacher covered some stuff on solving third and fourth degree polynomials and Riemann sphere stuff that wasn't in the book. While the lectures were very proofy and sometimes tedious, the actual tests and quizzes were comparable to the homework problems, and this was a teacher who had a reputation for being very hard.

I'm not sure I know what the point of taking both real analysis and complex analysis is, seems to me that you should just take complex analysis since a lot of real analysis stuff you probably already covered in your calc classes.

 

[WannabeNewton]

...since a lot of real analysis stuff you probably already covered in your calc classes.

That material is but the foothold of real analysis.

 

[hsetennis]

II'm not sure I know what the point of taking both real analysis and complex analysis is, seems to me that you should just take complex analysis since a lot of real analysis stuff you probably already covered in your calc classes.

The point is to formalize the material and delve deeper into it. My complex analysis class also used Brown and Churchill. I can't really say anything bad or good about it; it's pretty popular and gets the job done. However, considering its content, I don't think it's possible to teach a challenging proof-based class solely with the textbook (hence many professors supplement it with their own material). Real analysis is of paramount importance for a math major. Even if your college does not require it, YOU NEED IT.

 

[lurflurf]

Those books are not very theoretical, so it is unlikely the class is. The only real concern is there is some overlap, so if they are intended to be taken in a certain order there might be a lot of "as you recall.." in which you do not recall. This is also unlikely as neither is prerequisite of the other.

You need to take differential equations before you take real and complex analysis?

Many programs designate differential equations a first year course and analysis a second year course. One might argue about that, but taking every class last is not workable. Also the naming is silly the second year analysis course often should really be called calculus.

 

[mathwonk]

I want to echo micromass' concern. That PDE book does not look at all like a book for someone starting to learn real analysis. Is it perhaps a computational approach, sort of the opposite flavor of a theoretical real analysis course?

The complex book too is a new version of the classic applied type book, a rewrite of Churchill's original. These are not books I use with math majors. I suggest talking to the prof and asking how proof oriented it is.

 

[Theorem.]

I don't think this will be problematic if you take the right steps and put the effort in. That depends on you. In regards to the textbook I would have to agree with Mathwonk and Micromass... That does not seem like a book for a real analysis class and seems quite unusual and I would do what Mathwonk suggests: contact the profs. If you are looking at getting a formal mathematics education, in part through these courses, maybe this is an odd path. It's hard to tell.