Exam 1 Math 1360 Fall 2015
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit
Exam 1 Math 1360 Fall 2015
Work each problem on a separate page
Staple in upper LH corner when you hand in
Make plots BIG and clear
Full justifications are needed for credit.
1. a. What are the 3 assumptions of Richardson’s model of arms races?
b. Write down his model and identify which assumption yiealds each term.
2. Consider the system below.
a. Sketch the nullclines, trajectory directions, equilibria, and a few repre- sentative trajectories.
b. Pick one equilibrium [NOT BOTH!]. Find the linearization matrix there and classify the equilibrium.
x′ = x2 + y2 − 1 and y′ = 2y.
3. The town of Cutbait Wyoming lists the census data below. Assume a logistic model.
a. Plot the data and
b. use the plot to predict its long term, persistent population. Explain!
lpopulat(year)ion 6347(1970) 5986(1980) 5772(1990)] .
4. Consider the pendulum like equation below.
a. Write it as a first order sustyem using x = θ, y = θ′ .
b. Find its first integral. Is the system conservative? Explain.
2023-09-25