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\centerline
{
\bf Attendance Quiz for  Lecture 19 of Dr. Z.'s Dynamical Models in Biology
class 
}

\bigskip

{\bf Name}: (print!)

{\bf Email}: (print!)

{\bf 1.} Write the Maple command for the following mathematical expressions

$$
\frac{\partial ^2 f}{\partial x^2} +\frac{\partial ^2 f}{\partial y^2} +\frac{\partial ^2 f}{\partial z^2}  \quad,
$$

$$
\int_{-\infty}^{\infty} \int_{5}^{\infty} e^{-x^2/2-y^2/2} \, dx \, dy
$$

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

$$
\frac{dx}{dt}= 5x+7y \quad, \quad
\frac{dy}{dt}= -5x+9y \quad, \quad
x(0)=5 \quad, y(0)=3
$$


{\bf 3.} In the Maple package {\tt DMB.txt}

Let's define
{\tt
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 {\tt A(x)} from {\tt x=2} to {\tt x=30}.?


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