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I used Sage with my advanced math modeling course this semester and did a fair amount of biology in there. Generally, I did not ask the students to do much "from the ground up" coding, although most of them in that group could have. I focused on making worksheets that the students could interact with fairly easily. You can see some samples published at the links below. Most of these use code similar to what Jason mentions above. I've added some options that were needed for my class (nullclines, direction fields, access to the solution coordinates, etc.). This part of the code is lengthy, but it is hidden using "%hide" and automatically executed using "%auto".

Note that the SIR Lab (http://sage.maa.org/home/pub/126/ ) uses the SciPy leastsqrs function to fit the data. This is a useful tool for a course in which you want students to fit data but not have to deal with the details.

Budworm model: http://sage.maa.org/home/pub/110/ Modeling a parachutist: http://sage.maa.org/home/pub/106/ Bifurcations: http://sage.maa.org/home/pub/109/ Solving systems: http://sage.maa.org/home/pub/101/ Linearization: http://sage.maa.org/home/pub/116/ Vector Fields: http://sage.maa.org/home/pub/115/ Advection-Diffusion-Reaction Equation: http://sage.maa.org/home/pub/119/

I used Sage with my advanced math modeling course this semester and did a fair amount of biology in there. Generally, I did not ask the students to do much "from the ground up" coding, although most of them in that group could have. I focused on making worksheets that the students could interact with fairly easily. You can see some samples published at the links below. Most of these use code similar to what Jason mentions above. I've added some options that were needed for my class (nullclines, direction fields, access to the solution coordinates, etc.). This part of the code is lengthy, but it is hidden using "%hide" and automatically executed using "%auto".

Note that the SIR Lab (http://sage.maa.org/home/pub/126/ ) uses the SciPy leastsqrs function to fit the data. This is a useful tool for a course in which you want students to fit data but not have to deal with the details.

Budworm model: http://sage.maa.org/home/pub/110/ http://sage.maa.org/home/pub/110/

Modeling a parachutist: http://sage.maa.org/home/pub/106/ http://sage.maa.org/home/pub/106/

Bifurcations: http://sage.maa.org/home/pub/109/ http://sage.maa.org/home/pub/109/

Solving systems: http://sage.maa.org/home/pub/101/ http://sage.maa.org/home/pub/101/

Linearization: http://sage.maa.org/home/pub/116/ http://sage.maa.org/home/pub/116/

Vector Fields: http://sage.maa.org/home/pub/115/ http://sage.maa.org/home/pub/115/

Advection-Diffusion-Reaction Equation: http://sage.maa.org/home/pub/119/