Yes, as Tom says, Prof Ng has set everything up here so that no calculus is required to take these courses, but that means we have to take his word for things in a lot of cases.
But if you have the math background, there is a lot of info available out there. E.g. here’s a paper from Yann LeCun’s group that shows some interesting results relative to local minima and the fact that they aren’t generally a serious problem.
And here is a Quora thread which is relevant, which is also linked from other forum posts here.