Math help: PDE or Complex Variables?

[Trapped In an EW Box]

Do you guys/girls know which is probably going to be the most useful - partial differential equations or basic complex variables?


Sorry for yet *another* math question...any help would be appreciated! Thx

[doubtful]

Pde....

[asianeconomist]

A typical Complex Variable course will include topics like Path Integrals, Fourier Transforms, Bessel functions.....None of this will come in handy in the 1st 2 year of your PhD. However, you might be learning/ doing some proofs: Cauchy's Integral theorem....

On the other hand, PDE's are essentially linked to optimization. Hence, go for the PDE course.

[can_econ]

PDEs are more useful for finance or theory, complex variables are used in time-series analysis so complex analysis would be helpful if you wanted to do econometrics. So what's more useful depends.

[doubtful]

you do Fourier transforms and Bessel functions even in PDE....

[econandon]

Originally Posted by can_econ

PDEs are more useful for finance or theory, complex variables are used in time-series analysis so complex analysis would be helpful if you wanted to do econometrics. So what's more useful depends.

what can_econ said

[treblekicker]

Originally Posted by can_econ

PDEs are more useful for finance or theory, complex variables are used in time-series analysis so complex analysis would be helpful if you wanted to do econometrics. So what's more useful depends.

Not that I am questioning you, but I am just wondering how complex analysis is used for in time-series.

[israelecon]

Originally Posted by treblekicker

Not that I am questioning you, but I am just wondering how complex analysis is used for in time-series.

i was wondering the same thing

[puecon]

Originally Posted by israelecon

i was wondering the same thing

I wonder about this too. I want more specifics. If all you need is to know just some manipulation of complex functions like say sine or exponential then that does not justify taking a potentially very difficult math course. For that, just read the first two chapters of a complex analysis text. On the other hand, if working in time series requires understanding of something like Cauchy's Theorem, then perhaps taking this course could be justified. (I somehow doubt though). You certainly don't need complex analysis to _take_ a time series course and do time series analysis of your data.

Regarding PDEs, this course is probably nice to have for general math/calculus knowledge, but still not required even for asset pricing people. My understanding is that you need to solve PDEs in order to do things like pricing the actual derivative securities, e.g. a very practical applied math question. (BUT WHY would economists POSSIBLY want to do something like that? :-)

[doubtful]

I have been studying time series for 5 years and I never got the impression I needed complex analysis... functional analysis I agree... or maybe I am just a bad student.. eheheh