The Digestive Process of Sheep (UMAP)

This unit introduces a differential equations model for the digestive processes of sheep. Students describe the digestive processes of ruminants, explain how the assumptions of the model are translated into equations, discuss what support there is for the validity of the model, and discuss some possible conclusions to be drawn from the model.

Table of Contents:

1. THE PROBLEM
1.1 Description of the Digestive Process
1.2 The Experiment
1.3 The Data

2. THE MODEL
2.1 The Functions r(t), a(t), and d(t)
2.2 The Assumptions

3. THE SOLUTIONS OF THE EQUATIONS
3.1 Solving for r(t)
3.2 Solving for a(t)

4. COMPARISON OF THE MODEL'S PREDICTIONS WITH THE EXPERIMENTAL DATA
4.1 Solving for d(t)
4.2 The Formula for the Amount of Feces
4.3 Least Squares Fit
4.4 How Good is a Good Fit?
4.5 Fitting the Graph of f(t) to the Data

5. CONCLUSIONS

6. REFERENCES

7. ANSWERS TO EXERCISES