Has done for the integrity the course and the university and
The primary goal of this assignment is to
● provide you with experience using concepts of proportionality and geometric similarity to logically derive a mathematical model of mammalian heart pulse rates vs weight, use existing data to derive model parameters, and then evaluate the model with respect to the provided data as well as any other data you may find.
Construct a mathematical model relating pulse rate to body weight. Assume that the amount of energy available is proportional to the blood flow through the lungs, which is the source of
oxygen. Assuming the least amount of blood needed to circulate, the amount of available energy will equal the amount of energy used to maintain the body temperature.
Some data from A.J. Clark, Comparative Physiology of the Heart (New York: Macmillan, 1977), p. 99, plus some from my own estimates.
To derive the mathematical model, you should
To help you out, I am going to give you some ideas to think about, hoping to keep you from going too far astray. However, you should provide justification for any assumptions, which may require you to do some research. Just using my “suggestion” below does not constitute properly derived assumptions. Also, you should keep in mind that not all of my suggestions are necessarily relevant for you to derive a model.
Some things to consider
● Relate the blood flow rate to the surface area of the organism
● Relate the blood flow rate to pulse rate and the weight of the organism
● Use concepts of geometric similarity, with some of the above, to derive a model that shows the heart rate pulse to be proportional to some function of the weight
●
Use the available data to evaluate our derived model and to compute model parameters (which will obviously be “tuned” for the data that you have available)You should show your work in detail, neatly and clearly. Again, you have several examples of similar work available in your textbook and from lectures. For those of you who might want to use LaTeX for your equations, the proportionality symbol is \propto
| ● |
|---|
In past assignments most of you did very well and I tended not to use the rubrics when grading, but in this assignment I will, so it would be to your advantage to review some of the points I look for.
Summary of what to submit
Warning on Plagiarism
Please remember the aggressive warnings I gave about plagiarism at the beginning of the course. It is simply wrong to take somebody else’s work and try to make it look like your own, new work. Every assignment must be an original work created by you. It is, of course, permissible and encouraged to collaborate with others in the class, but you should make it very clear in your report who you collaborated with and in what capacity.
If you have any concerns about whether what you are doing is a violation or not, then you should post questions about it to the course discussion forum for clarification. In the long run, you will probably do much better if you invest the time to do the work yourself, than if you have to suffer the consequences of violating these standards.