Describe in your bid:
I have designed and integrated reference designs for many power supplies and chargers, there are many minimum component count Applicaition Specific IC's already designed and reference layouts provided by many IC manufacurers for charging any kind of battery topology. So your need for calculus is overkill due to the designed into the chip brains, to smart charge. These chips are able to determine the batteries health and determine the type of charge required. If this is going into a product make sure you do not go with some discrete unproven design but rather a reference design that has allready been totally scrutinized by the finest engineers like the Texas Instruments families, Linear Technologies makes great products also but they typically run hot, Maxim is good but a bit pricey. I can supply previous layouts upon request and am Highly profesional and will hit you with many questions prior to commncement of work if chosen and present you with at least three options with costs.