Which major for applied math PhD? I am still in the process of choosing which major in the SEAS of my school I should pursue.

I want to go into an applied math PhD program after undegrad, so must I choose applied mathematics as my major? Or can I pursue electrical engineering or mechanical engineering? A double major isn't an option.

Any thoughts?
I don't mean to be rude but JeffE's answer (which I cannot comment on-site as I don't have the necessary reputation) 


  Whatever.
  Your major won't matter as much as your demonstrated potential for research in applied mathematics, which you can develop in almost(?) any engineering discipline.


is so off-base, it's like saying that majoring in English gives you license to do a PhD in any field that involves writing in the English language.

Engineering is certainly not a substitute for applied mathematics, and the transition can be very harsh. 


First of all, you need to localize yourself. Applied mathematics in the US is different from applied mathematics in the UK, which is different from applied mathematics in France. Similarly, applied mathematics at Harvard (which would not be with mathematics, but SEAS) would be different from applied mathematics at Courant at NYU or in the Mathematics department at Princeton (who don't have an applied mathematics department, but rather a Program)
In any case, you will be expected to know all the core mathematics curriculum that pure mathematicians take in their first two years. From here, it will depend on what subfield of applied mathematics you're interested in. For example, if you are applying to a subfield that involves the classical mathematical physics (like solid or fluid mechanics), then you would need classes on those. 
Engineering classes are vastly different from mathematics classes in almost all the mathematical topics. There might be some overlap in terms of, for example, fluid mechanics, but even then there is a big distinction between engineering fluid mechanics and mathematical fluid mechanics. For instance, mathematical fluid mechanics would involve more rigorous reductions and derivations of the Navier-Stokes equations (exploring techniques in asymptotic analysis, for instance). 
There is some possibility of jumping from an engineering degree to an applied mathematics PhD, but again, this would depend on the country and the university and the department. If you want to examine the difference, look at the applied mathematics department at Cambridge University and compare to the applied mathematics group at the Courant Institute in NYU. Also, examine the PhDs of current faculty.