How does the ideal of heroic citizenship change from Greek mythpoetic tradition through the emergence of Greek tragic drama to the stoicism of Roman imperialism. What elements remain the same in this development of the ordeal and what elements undergo alteration or adaptation? What, in the end, is the essence of the heroic ideal?
Here's a brief sketch that could be a lot more thorough—but it should at least give you a place to start!
Greek heroes from the mythopoetic tradition like Achilles, Odysseus, Heracles, and Theseus are deeply individualistic characters. They single-handedly change the course of wars (they start them and they end them). Armies march on their whim. They are subject only to the gods and the greater strength or cunning of other heroes (or occasionally fate).
As Greek theater reaches its peak around 500 BCE, its heroes begin to take on new form. Oedipus and Agamemnon are blind (in Oedipus's case literally) to the machinations around them. They unknowingly walk to their own doom, unable to escape fate, no matter—or occasionally because of—how hard they try. (Achilles at least knew what was going to happen to him and chose to face it head on.)
Roman imperialism brings us Aeneas, a stoic hero whose determination and courage depend on him remaining calm and determined in the face of massive obstacles (storms, deaths, enemies). He is a less emotional character than Odysseus (who also faces massive obstacles on his journey), characterized by (mostly) unwavering determination. He is the support of all those around him, and not even fate can do more than delay him from reaching his goals.