1
Math 2370, Midterm Exam, Fall 2008
Instructor: D. Swigon
NAME: _
Show all your work, justify your results.
Number and sign every page.
Problem 1: (20 points) Consider the linear space V of 2 by 2 ma
2.4.7 There are many ways to solve this problem. Here is an example.
(a) Examples of f4(x) dynamics for r = 2.5, 3, 3.5, 4.
(Graphs obtained using XPP app for iPad).
(b) The plot of f4(x) shows that t
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Math 1360, Practice Problems I, Fall 2011
Instructor: D. Swigon
Problem 1: Analyze the map xn1 2 xn /(1 xn ) . (Find fixed points and their stability. Check
whether the system has a 2-periodic orbit.)
Math 1360, Fall 2011
Homework #5 SOLUTIONS
Instructor: D. Swigon
Problem 1:
The solution of the initial value problem is given by
p(t ) p0 e rt
Let y(t ) ln p(t ), y0 ln p0 . The transformed solution
Math 1360, Practice Problems II, Fall 2011
Instructor: D. Swigon
Problem 1: Consider an age-structured population model with constant with death rate that
increases linearly with time and a constant b
Math 1360, Fall 2011
Homework #5
Instructor: D. Swigon
Consider the data set for the growth of the population of Paramecium aurelia in Table 2.1 on
page 11 of the book. The data can be modeled using d
Math 1360, Fall 2011
Homework #7
Instructor: D. Swigon
due Wednesday Nov 30
Problem 1: Let
1 1 / 3 1 / 3
P 0 1 / 3 2 / 3
0 1 / 3 0
be the transition matrix for a Markov chain with three states.
(a)
Math 2370 Fall 2008
Quiz #3
Problem 1: Let P be the linear space of all polynomials over IR , U the subspace of P containing
polynomials divisible by t 4 and W be the subspace of P spanned by p1 (t )
Math 2370 Fall 2006
Quiz #8
I
Problem 1: Let V be a finite dimensional linear space over C and T L(V , V ) be a map such
that the nullspace and range of (T I ) obey
N T I RT I = cfw_0 for all C
I
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