I was playing Urgot and one of my items was Manamune. At some point in the late game, I realized that my mana pool was about 3900 but Manamune was only providing 58 AD bonus (with full stacks). So, does Manamune make the AD calculation without its own mana bonus (1000 mana at full cap)? If it does not consider its own mana in the AD calculation, is it still worth it compared to an Infinity Edge (mathematical)?
The short is yes. Manamune does include its own mana in it's AD increasing passive.
It should be noted however, that until you have about 2000 total mana the AD given from Manamune is not worth the cost of creating it.
So for your specific question about Urgot I would recommend grabbing a tear early game, but holding off on upgrading it until you hit 1800-2000 mana. In the interim you can get other items such as a brutalizer or an IE if you are doing really well. But like with all things in LoL your build should be fluid to match the flow of the game.
It's does calculate including it's own mana.
If you had 3900 mana, then you should be getting 3900 * .015 = 58.5 AD. If you had slightly less, it probably rounded down or something. A Manamune is definitely worth it for an Urgot due to the huge mana pool you now get, and the quicker mana regen early game while you have a Tear.
EDIT: Never mind, checked again and realized that the ratio is supposed to be .02, not .015. I'm a bit unsure now. Are you sure that it was only providing 58? O_o