IS this class very difficult? I asked because it is a grad course but the prerequisite for this class is Calc 3. I am taking as an elective for my math minor and thought this class would useful for applications in physics

7/1/2008 12:56:16 PM

Usually its an easy A, the subject matter is really no more complicated that DEQns or Calc III, but sometimes it could take on a more proofy context depending on the professor. At some other universities the same course is offered for junior or senior undergrads from the same text (Churchill I think, unless something has changed recently).

Calculations you need to know,

- addition
- subtraction
- multiplication
- division
- factoring

But, and here's the fun part, all with complex numbers. Which means lots of

- complex conjugation
- putting things into polar or Cartesian form.

In my humble opinion all of the above things should be taught to middle schoolers (not joking) because a good understanding of basic algebra requires all these manipulations. Anywho, we spent about 1/4 of my course tinkering with such, all be it in a much more methodical manner then you would see in a lower level course.

Beyond that, there is calculus. But again it pretty much works the same way. EXCEPT there is novel new crazy facts that involve how the poles (aka divergences) and certain integrals interact. Think of it this way, a Taylor series relates the coefficients of positive powers of a variable with the derivative of the represented function. If a function has a divergence then a Taylor series fails at the divergence, but perhaps you can capture something with reciprocal powers of the variable... as you might expect by analogy these are related to the integrals of the represented function. This is a phenomenal result because it means you can calculate the integral of certain functions around some divergence by computing the extended power series (well "Laurent series" I think, so many dead math peoples, not to be confused with meth peoples...) and just taking a look at the coefficient of the 1/z term. Danger here: perhaps you don't know the geometric series and associated Calc II tricks in great depth, well you'll remedy that here.

Finally, you can extract real integrals from the complex integrals using certain tricks.

Anyway, its definitely worth taking. It should help with integration in physics if nothing else and besides, more skill with complex arithmatic, algebra and calculus cannot but help make QM less mysterious for most folks. I can't speak for you, you might find the course boring. Its a real possibility if you are looking for a challenge.

[Edited on July 2, 2008 at 1:44 AM. Reason : .]

7/2/2008 1:42:08 AM

I took it as an undergrad, most boring thing I've ever taken. But then, I was a math major and had had significantly more intense classes up to that point, so it might have been interesting if it was my first look at this subject matter. Also, I think the prof was having some family issues so he wasn't teaching all that great that semester.

7/2/2008 5:14:48 PM