Week 8 Homework List

As always, a self contained ipynb solutions should be uploaded to Canvas along with a pdf copy. Each Question shall be clearly displayed inside the same notebook. Headers and formating will be graded

Question 1

Consider a tank with volume 300L containing a salt solution. Suppose a solution with 3.5kg/L of salt flows into the tank at a rate of 12L/min. The solution in the tank is well-mixed. Solution flows out of the tank at a rate of 15L/min. If initially there is 20kg of salt in the tank.

Plot two graphs showing the amount of salt in the tank and the concentration of the salt at any time t

Question 2

Use the code from this week to plot various solutions illustrating the dynamics of the competing species

$$ \frac{dx}{dt} = (1-x-y)x $$$$ \frac{dy}{dt} = \frac{3}{4}(1-\frac{4}{3}y-\frac{2}{3}x)y $$

Question 3

Use the code from this week to plot various solutions illustrating the dynamics of the competing species

$$ \frac{dx}{dt} = 2x(1-\frac{x}{2})-xy $$$$ \frac{dy}{dt} = y(\frac{9}{4}-y^2) -x^2y $$