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The movie follows three [real] black women through the early space program (a mathematician, engineer and mathematician/computer supervisor), over a period of several years. The stories are parallel yet intertwined. There is some recognizable technical detail on real problems solved during the work. I'm wondering if someone could close a loop that was surprisingly left open during the movie (I think):

One of the key problems described was the issue of converting a parabolic path to an elliptical/circular one for orbit insertion and vice versa for re-entry -- for John Glenn's first orbital flight. There apparently was no analytical solution to the problem, but the "eureka" moment was using Euler's method to bridge the two trajectories somehow. While watching I thought I remembered it as a numerical integration tool, but close enough; numerical differential equation solving. The mathematician is shown to have solved it on a blackboard in a movie (I didn't catch the actual math while watching).

Parallel to this is a humor element of the difficult start-up of NASA's first computer, an IBM mainframe. Complete with sledgehammering the door fame out to get the parts into the lab, technicians who couldn't get it to run, etc. The mathematician supervisor recognized this would replace all the human "computers" (human spreadsheet cells) and taught herself and then all the black, female mathematicians she supervised how to use it. The computer got running with her help just as John Glenn's flight was happening.

So here's my question: since Euler's method is numerical, isn't it true that you can only solve iterations at a time on a blackboard and need a computer to do the bulk of the work? The movie pitted the IBM mainframe and human mathematicians as enemies in the movie, even having her check the computer's work directly on this problem (not explaining how the computer came to be working on it). But this would have been an opportunity for bridging between two characters and both winning and resolving a conflict by having the two women collaborate on the problem. On the one hand it seems a real "eureka" moment, (though on the other I would think they would have known a lot about how they could use the computer before they bought it). It seems like a missed opportunity --- if it really happened the way I envision. Anyone know if it did?

[I ordered the book for my mom's birthday next month, so maybe I'll find out...]