(This question was proposed during the area51 phase.)
It's common for chemistry/biology/physics majors to be required to take certain calculus courses. At my school, chem/bio students must take up through Calc II (integration, separable diff eqs, infinite sequences/series) and physics students up through Calc III (vector calc). We don't have the resources necessarily to develop a separate "Calc for science students" course. Yet, this semester, I find myself with a section of 25 students entirely from other science majors.
I'd like to appeal to the interests of these students and, hopefully, demonstrate that calculus can be both useful and interesting for them. Alas, many textbook applications are somewhat contrived, or don't represent the way the students will have to handle data/problem-solving in their actual scientific work (i.e. the numbers are too "round", the modeling function is already given with no motivation as to its applicability/accuracy, etc.), while other application problems are just too difficult to assign, given the range of abilities in the class.
Do you have any in-class activities or take-home assignments that demonstrate a calculus concept/technique in the context of a scientific problem and have effectively appealed to the interests of science majors in your course?
I am specifically curious about activities/assignments you have used before, and would like a description of how you think it was effective (and what could be improved, if need be), and to whom it appealed. I don't want this thread to be full of "Try something with topic X, that might work."