Math 312
Spring 2006
Homework Assignment 1
Due Friday, January 27.
1. Find the following integrals.
(a)
(b)
(c)
1
dx
xa
1
dx (Hint: Review partial fractions for integrating rational functions.)
x(1 x)
1
1
xb
1
. Use a u-substitution.)
dx, b = 1 (Hint: b
=
Math 312
Spring 2006
Homework Assignment 2
Due Friday, February 3.
1. In some populations, if there are too few individuals, the population may die out. (Perhaps the animals
normally travel in herds, and when the herd is too small, the individuals are eas
Math 312 - Applied Math: Social Sciences
Spring 2005
Homework Assignment 2
Due Friday, February 11
1. Solve the following initial value problems.
dy
= y + et , y (0) = 1
dt
dy
(b)
= 5y + t, y (0) = 4
dt
(a)
2. In class, we saw that expressing the logistic
Math 312
Spring 2006
Homework Assignment 3
Due Friday, February 10.
1. We consider a modication of the SI model. Suppose that infectives eventually recover from the
disease, and once they have recovered, they are immune. The recovered individuals no longe
Math 312 - Applied Math: Social Sciences
Spring 2005
Homework Assignment 3
Due Friday, February 25
1. In this problem we look at solutions to the Romeo and Juliet model.
Lets suppose that the constants in the problem are such that
dR
= J
dt
dJ
= 2R
dt
(1)
Math 312 - Applied Math: Social Sciences
Spring 2005
Homework Assignment 4
* with revised Problem 4 *
Due Friday, April 8
1. The logistic map
xn+1 = rxn (1 xn )
(1)
can be interpreted as a population model with discrete time. We will restrict our attentio
Math 312 - Applied Math: Social Sciences
Spring 2006
Homework Assignment 5
Due Friday, March 3
1. Do Exercise 3.4.2 in the Lanchester Model lecture notes. (The notes are available on the
Math 312 web page.)
2. We consider a naive model of a relationship b
Math 312 - Applied Math: Social Sciences
Spring 2005
Homework Assignment 5
Due Friday, April 22
1. Let
19/20 1/10 1/10
P = 1/20
0
0
0
9/10 9/10
(1)
be the transition matrix of a Markov chain.
(a) Draw the transition diagram that corresponds to this transi
Math 312 - Applied Math: Social Sciences
Spring 2006
Homework 7
Due Friday, April 14
1. Let A be an m m matrix, and let aij be the element of A in row i and column j .
(a) Suppose there is an i such that every entry in the ith row of A is zero except aii