It has been my experience that sophomores prefer the structure that is provided by a textbook. Thus, I have chosen a fairly general textbook on applied mathematics (E. Kreyszig, Advanced Engineering Mathematics, eighth ed., J.W. Wiley, 1200 pages) and have rearranged the topic order within the book to fit the needs of course. Extra material pertaining to materials science specifically will be created and placed on the web.
I have identified 66 sections of the book (330 pages in total) as required reading. Spreading the over 22 lectures is 15 pages of reading time per lecture which I would conservatively estimate as one hour of outside reading per lecture. There are 27 lectures in total, about 5 lectures will utilize outside material. After outside reading, this leaves about 2-3 hours a week for homework.