5B said:Bonus Action
A spell cast with a bonus action is especially swift. You must use a bonus action on your turn to cast the spell, provided that you haven’t already taken a bonus action this turn. You can’t cast another spell during the same turn, except for a cantrip with a casting time of 1 action. (emphasis mine)
I don't think so.
I think the Eldritch knight can cast one cantrip and one non-cantrip a round with Action Surge.
Thaumaturge.
I don't think so.
I think the Eldritch knight can cast one cantrip and one non-cantrip a round with Action Surge.
Thaumaturge.
I think the OP is asking about the additional action from Action Surge, which doesn't seems to be a bonus action. In fact, in Basic it is said that with Action Surge "you can take one additional action on top of your regular action and a possible bonus action".
So it sounds like the Eldritch Knight (or a Fighter 2/Wizard X) can cast 2 spells in that round, but if she uses the bonus action for a swift spell, apparently she can cast only that one (plus a cantrip).
At 7th level, the EK could cast a spell, cast a cantrip, and attack once, if she uses an Action Surge.
Uhm... I don't know what happens at 7th level. But for the combination spell+cantrip+attack, I think it's required that the spell is "swift".
Alternatively she can cast a non-swift spell, and cast another non-swift spell using Action Surge (and neither has to be a cantrip).