A layered system of coffee and milk serves as a physical model for temperature gradients in lakes or the atmosphere, where temperature depends on both a temporal and spatial variable. Students create, observe, and collect temperature data of their own, graph the data, and develop mathematical models to fit the data.https://digitalcommons.usu.edu/lemb/1000/thumbnail.jp

Bruder, Andrea

Kohler, Brynja

DigitalCommons@USU

Coffee Thermocline Lab Laboratory Experiences in Mathematical Biology Assessment Items:  Primary assessment of student learning is taken from students' written reports additional assessment items targeting lab objectives are included here.     1. Give two examples of functions of more than one variable arising in real-world contexts. What are the independent and dependent variables of each function?   2. Consider the following graph. Sketch the trace in the 𝑦, 𝑧 −plane.            3. Explain how the level curves indicate the steepness of a graph of a function of two variables.  4. How useful (if at all) do you think will mathematical models be in your future career? Circle one:                                                                                                                                          not at all useful = 0    1    2    3    4 =  extremely useful  Explain your response.  5. Provide two examples of multivariable functions arising in real-life contexts.  What are the dependent and independent variables in each case?   6. The figure below is a map showing curves of the same elevation of a region in Orangerock National Park. We define the altitude function 𝐴(𝑥, 𝑦) as the altitude at a point 𝑥 meters east and 𝑦 meters north of the origin (“Start”).               a) Estimate $A_x (300, 300)$ and $A_y (300, 300)$.  b) What do $A_x$ and $A_y$ represent in physical terms?  7. How useful (if at all) do you think reasoning with limits and partial derivatives will be in your future career?         Circle one:                                                                                                                                          not at all useful = 0    1    2    3    4 =  extremely useful  Explain your response.    

Coffee Thermocline Lab

https://digitalcommons.usu.edu/cgi/viewcontent.cgi?filename=6&article=1000&context=lemb&type=additional

Coffee Thermocline Lab

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