Lab 1: Oscillations in Differential Equations
Throughout this course, you have seen systems that oscillate. The purpose
of this lab is to take a closer look at such systems and to review important Sag
1. The thyroid hormones thyroxine (T4) and triiodothyronine (T3) regulate
the metabolism of almost all tissues in the body. The thyroid is stimulated
to produce these by a third hormone, thyrotropin (
LS 30A
Midterm Study Guide
Instructor: Sharmila Venugopal
Feedback

Identify the types of feedback, interpret what happens to a variable if positive versus
negative feedback is present
Function prope
1. (7 pts) Giant pandas are an endangered species native to China. Set
up a discrete time matrix model of a panda population based on the
following assumptions:
 . / :i
o A panda gives birth to one c
1. (15 pts) Consider a model of the population of Moose (M ) and Wolves
(W ) on Isle Royale, based on the following assumptions:
Without the wolves around, the Moose population grows logistically,
wi
1. (15 pts) Consider a model of the population of Moose (M ) and Wolves
(W ) on Isle Royale, based on the following assumptions:
Without the wolves around, the Moose population grows logistically,
wi
l. (8 pts) In a population of tribbles, the percapita birth rate is 40% per
day, and the immigration rate is 70 tribbles per day. Due'to overcrowd
ing, there is a percapita emigration rate of 20% per
1.
(10 pts) Rabbits and sheep compete for resources in an ecosystem. Let
R be the rabbit population, and S the sheep population. Construct a
model based on the following assumptions:
(a) The rabbit po
W. Conley
LS 30B, Lecture 1
Tue, Jan 31, 2017
Midterm
Version A
Last Name:
First Name:
Student ID:
Signature:
Lab Section:
1A (Tue 810)
1B (Tue 1012)
1C (Tue 122)
1D (Tue 24)
1E (Wed 1012)
1F (Wed 122
Student ID:
1. A farmer cultivates bees for honey, and has many acres of Wildflowers from
Which the bees can collect honey. These both grow so successfully that he
eventually decides to get some goa
J. Shevtsov
LS 30A
Mon, Aug 24, 2015
Midterm
Last Name:
First Name:
Student ID:
Signature:
Instructions: Do not open this exam until instructed to do so. You will have 1 hour and
50 minutes to complet
1. (10 pts) A patient receiving an IV morphine drip will have a certain
level of morphine in their blood system, and a certain level of the drug
in their cerebrospinal fluid. Consider a model of this
1. The lifespan of a unicorn can be divided into three distinct stages: magic
eggs (E), glitterponies (P), and sages (S).
(a) (6 points) Set up a discrete—time matrix model for the unicorn pop—
ulati
1. (12 pts) Glucose (G) and insulin (I) in the bloodstream interact in the
following ways:
0 The pancreas produces insulin at a rate that increases with the current blood
glucose level, but only up to
AE
2’,
All;
1. (8 points) Frogs go through three life stages: eggs, tadpoles, and adults.
Assume the following:
. Each adult lays 200 eggs each year.
. Each year 23% of eggs survive to become tadpoles
1. (10 pts) The assumptions below describe a very basic model of a viral
infection in vertebrate animals. This model considers only the number
of viruses (V), the number of cells infected by the virus
1. The lambda phage is a virus that infects E. coli bacteria, and can operate
in one of two modes: an active (lytic) mode in which the virus produces
many copies of itself until the host cell bursts a
1. (10 pts) A patient receiving an IV morphine drip will have a certain
level of morphine in their blood system, and a certain level of the drug
in their cerebrospinal fluid. Consider a model of this
OneClass
OneClass
1. (10 pts) During a measles epidemic, the population can be divided into
three groups: those susceptible to the disease (S), those who are cur
rently infected (I), and those who ha
LS 30B, Mathematics for Life Scientists
Winter 2017
General Description: In this course, you will learn how to design, study, and run mathematical
models, particularly ones that apply to the study of
W. Conley
LS 30B, Lecture 1
Thu, May 22, 2014
Midterm 2
Last Name:
First Name:
Student ID:
Signature:
Lab Section:
Lab 1A
Mon 46
Lab 1B
Tue 111
Lab 1C
Tue 13
Lab 1D
Wed 122
Instructions: Do not open t
1. An infectious disease is spreading through the population of mountain
lions that you are studying in the Grand Canyon. Set up a model that
tracks the number of healthy mountain lions and the number
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