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I am teaching calculus for undergraduate students in humanities departments.
Will Powerpoint presentations be better than using marker and whiteboard? Will students learn more efficiently?
I am using computer-based presentations only to describe 3D functions and constrained optimizations.
There are different kinds of 'learning types'. Some people learn best by listening and talking, some people learn best by understanding the material with the help of pictures, and some learn best by writing things down.
The 'classical method' of presenting formulas, proofs and theorems by writing them down gives the students the time to write it down themselves, and to digest the content.
On the other hand, using computer-based illustrations will help students who are not familiar working with formulas. For this particular course, well-designed plots can help to understand the idea behind certain definitions and theorems. For instance, you can show that, in order to show convergence of a sequence, it doesn't suffice to check the first few elements. Consider three series like $$a_n = \frac{1000}{n} - 1, \quad b_n= \sin\left(\frac{n}{900}\right), c_n= \frac{n}{1000},$$ where you can see that their behavior shouldn't be judged on the first 10 or 100 elements. And with a plot, you could just show the pictures (eg for 10, 100 and 1000 elements) and discuss them, and maybe show the actual definitions of the series after that.
I think that for a maths for humanities course you can't be illustrative and accessible enough, so using computer graphics is a good idea. You should however be wary that using slides instead of writing stuff down may speed up your lectures towards non-understandability.
I think the main thing to remember, regardless of which method you choose, is that you are the most important part of the presentation. You could spend hours/days/weeks/months preparing the best slides ever, but if the delivery is no good, then it will all be for nothing.
Slides can certainly be an important accessory, but they should only ever be there to provide support for you, and for what you are saying; it should never be the other way round.
The ultimate fear in this context (as the presenter) is to cause death by powerpoint, so it is incredibly important to 'mix things up'; slides are ok for some content now and again, but you have to keep the audience engaged. You could, for example, aim to transition between slides, board work, and (if room space, time, institutional ethos allow) group work.
