Do airline pilots identify failed engines in the same way as light aircraft pilots? Do the two old adages of light multi-engine flying, namely "Dead foot, dead engine" and "Raise the dead", still apply when flying transport-category aircraft?  Or do airline pilots need to rely on their engine instruments in order to figure out which engine's kicked the bucket?

For those who aren't familiar with those memory aids, they are from page 12-21 (186 in PDF versions) of the FAA AFM:


  There are two time-tested memory aids the pilot may find useful in dealing 
  with engine-out scenarios. The first, “Dead foot–dead engine” is used to 
  assist in identifying the failed engine. Depending on the failure mode, the 
  pilot won’t be able to consistently identify the failed engine in a timely 
  manner from the engine gauges. In maintaining directional control, however,
  rudder pressure will be exerted on the side (left or right) of the airplane 
  with the operating engine. Thus, the “dead foot” is on the same side as the 
  “dead engine.” Variations on this saying include “Idle foot–idle engine” and 
  “Working foot–working engine.”
  
  The second memory aid has to do with climb 
  performance. The phrase “Raise the dead” is a reminder that the best climb 
  performance is obtained with a very shallow bank, about 2° toward the
  operating engine. Therefore, the inoperative, or “dead” engine should be
  “raised” with a very slight bank.
Yes, the dead foot, dead engine does apply (but not as much as you might think), and, yes, airline pilots need to rely on their engine instruments in order to figure out which engine has failed, especially when you're flying a 4-engine aircraft. Actually, and with obvious prejudice, I prefer to say that the Flight Engineer will use the engine instruments to tell the Captain which engine has failed. Couldn't resist that.

Sudden loss of power on 727-100s and 747-100s/-200s is not nearly as noticeable as, say, on a Cessna 310. If you lose the middle engine (#2) on a 727, all you're going to notice is the loss of 1/3 of your power. Even the loss of engines 1 or 3 will not produce much yaw because they're mounted close to the aircraft centerline.

On the transport-category aircraft I flew it was unlikely that your foot would notice an in-flight engine failure because you took your feet off the rudder pedals as soon as you lifted off and didn't put them back on until short final. Adverse yaw was taken care of by the yaw damper.

If the loss of an engine came during descent at flight idle, the pilots might not notice it unless there is an obvious alert of some kind. We had one quit on us descending into Miami once and neither I nor the f.o. noticed it. Our alert was the f.e. saying something like, "We just lost #3." My increased work load consisted of simply saying something like, "See if you can get it running again. If it doesn't light off, forget it."

If you deliberately shut down an engine, you of course know which engine it is. That happened to me once. Again another vote for f.e.s. This one informed me that the oil pressure was dropping and oil temp climbing on one of the engines. He recommended shutting it down, which we did.

Generally speaking, when you lose an engine suddenly without warning when climbing out, I think the thing to remember is to take your time, fly the airplane with the configuration you have, and work the checklist for the situation at hand. That checklist will have procedures to ensure you shut down the engine that has failed, not one that's still operating. In other words, just do what you do in the sim every 6 months.