Attendance Quiz for Lecture 19 of Dr. Z.’s Dynamical Models in Biology class

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1. Write the Maple command for the following mathematical expressions

\frac{∂^{2}f}{∂x^{2}} + \frac{∂^{2}f}{∂y^{2}} + \frac{∂^{2}f}{∂z^{2}} ,

∫_{x=−∞}^{∞} ∫_{y=5}^{∞} e^{−x^{2}/2−y^{2}/2} dx dy

2. Write the Maple command to solve the following system of two differential equations with two unknowns functions, with the given initial conditions

\frac{dx}{dt} = 5x + 7y , \frac{dx}{dt} = −5x + 9y , x(0) = 5 , y(0) = 3

3. In the Maple package DMB.txt

Let’s define A:=proc(x):SSSg(HWg(u,v,[[1,x,1],[1,1,1],[1,1,1]]),[u,v])[1][1]:  end:

that tells you the ultimate fraction of the genotype AA if all matings are equally likely except that the mating of Ae with each other is x times more likely then all the other mating. How would you plot a graph of A(x) from x=2 to x=30.?