When recently teaching Calculus II to college students, I instructed my students to read and be ready to work through the first 8 or so questions of James Walsh's climate modeling differential equations packet: http://www2.oberlin.edu/math/faculty/walsh/UMAPclimate.pdf
I enjoy this text, because:
1) these problems are well within the reach of students in any Calc II class that addresses examples of the simplest kinds of ODEs (separable, linear first-order, etc.),
2) the questions attack the ODE from different angles, allowing the students to understand the ODE from different perspectives and to integrate new and old mathematical skills, and
3) the familiarity that the long-form nature of this richly contextual problem engenders in the students allows them to translate their mathematical observations and deductions into scientific interpretations. Most of my students are science majors, so this is a win-win.
I capped off this unit in my Calc II class with a speculative question on a take-home quiz that had the students qualitatively examining the the energy-balance ODE for the atmosphere of Mars and making a predictive scientific interpretation for the dust storm phenomena observed by the Mariner 9 probe in 1971. Admittedly, I did perhaps prepare them a little heavy-handedly for answering that question on the quiz, but otherwise, I was fairly satisfied with how well this unit went over with the class.
I would like to utilize more long-form, multi-step, skills-integrating applied mathematics problem packets like this in my calculus classes, and was wondering what you all had uncovered on the internet or had written yourselves that is in the vein of the Walsh packet? I am especially interested in Calc III (multi-variable calculus) applications, but all calculus topics are fine.