A question blatantly inspired by my old question here: What would be the impact of a modern programmer and laptop being dropped into World War II, possibly breaking Enigma? I had so much fun with the idea that I went back and reread it today and noticed that I focused a lot of my question on Enigma, but others suggested uses based entirely off of its raw number crunching ability alone.
Thus let's try an altered version of the same scenario that focuses only on that second part. Again, our time traveler somehow falls through time, unexpectedly, while headed to his last final for college. Unlike the previous question he didn't have his computer with him. However, he does have his graphing calculator and a cheap smartphone, along with a newly purchased 12 pack of batteries and his smart phone charger (I'm waiting to see how safe it will be to charge the smartphone though)
He's fallen in time to right about the time when WW2 was starting in Europe, but he is in his home in the United States. He somehow manages to get in contact with someone high enough in the government or military to be able to put him into contact with those who would be interested in him and convince this person of what his calculator can do.
He is relatively intelligent and was about to receive his bachelor's degree in software engineering, and has a decent 'dabbler level' understanding of physics, science, history of computers/software development, etc. However, his hardware knowledge is limited to what he had to learn for his degree, not enough to tell them how to build a computer. In addition while he is familiar with many aspects of his graphing calculator he has never done any real programing for either the calculator or phone, and has no way to look up the API for either now; heavily limiting his ability to program anything complex, but allowing him to manage at least basic scripts on his graphing calculator.
To keep the focus on computation power, and keep him from being too game breaking, assume that the time traveler has very little interest in most history, and particular was not interested in war history. He has a below average knowledge of WW2, and while he may have vague knowledge of a few key battles existing: D-Day, Pearl Harbor, Midway, etc. he remembers little specifics and in particular has no idea about the time-frame for these events. Between his limited historical knowledge, his uncertainty of what he does know, and the timeline changing as he interacts with it he has little to offer in way of direct intelligence about the war or what to avoid.
His long term goals are the increase of quality of life and general benefit of humanity (regardless of their home country) and to accelerate the development and adoption of technology. His short term goal, more relevant to this question, is the ending of WW2 as quickly as possible with minimal lost of life, which he considers best done by aiding the Allies war effort to speed up the Axis defeat and thus minimize the lives lost during a drawn out war.
What can the the traveler do with his two powerful computational devices to affect WW2? Where are his resources best allocated to maximize their benefit?
Any suggestions for how he can also drive his longer term goals, enhancing tech and quality of life, at the same time he is working towards ending the war are welcome! I'm interested in any answer for helping the war effort, but if some option meet those long term goals at the same time all the better.