Math 55 - Differential Equations
Sample Activities
Instructor: David Arnold
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Activities
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Finding A Model
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Numerical Methods I
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Numerical Methods II
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Modeling the US Population
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Latest version of Chapter 1, with Ken Menkveld's corrections.
Chap1
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Fitting a Logistic Curve to Data
Abstracts and Materials
Finding a Model
Abstract
This activity requires that you visit the periodical stacks at Humboldt
State University to find a model involving differential equations.
Prerequisites
Numerical Methods 1
Abstract
This activity introduces students to solution technique available for the
the numerical solution of first order ordinary initial value problems.
In particular, euler's method, rk2, and rk4 are compared and contrasted.
Because the approach is completely visual, students will need little, if
any, prerequisite material before attempting this activity.
Prerequisites
-
Some familiarity with Matlab's plot command. Also, you will need
to download eul.m, rk2.m,
and rk4.m. The activity also uses Version
2 of the Symbolic Toolbox, a Matlab interface to Maple. However, if you
do not have the Symbolic Toolbox, you can find exact solutions of the IVPS
by hand, then use Matlab's plot command instead of the Symbolic
Toolbox's ezplot command to draw their graphs.
Numerical Methods II
Abstract
This activity introduces students to solution technique available for the
numerical solution of systems of first order ordinary differential equations
with initial conditions. In particular, euler's method, rk2, and rk4 are
compared and contrasted. Because the approach is completely visual, students
will need little, if any, prerequisite material on solving systems of ordinary
differential equations before attempting this activity.
Prerequisites
Some familiarity with Matlab's plot command. Also, you will need
to download eul.m, rk2.m,
and rk4.m. The activity also uses Version
2 of the Symbolic Toolbox, a Matlab 5 interface to Maple. If you do not
have the Symbolic Toolbox, you can use the solutions provided in the activity
to continue with the numerical investigaiton.
Modeling the US Population
Abstract
An introduction to population modeling, from Malthus to Verhulst and the
logistic model. Matlab activities using real data are supplied.
Prerequisites
Some familiarity with Matlab's plot command. Also, you will need
to download one decade semilogarithmic
graph paper. Also, the file uspop.m
contains the US census data used in this activity.
Fitting a Logistic Curve to Data
Abstract
In this activity, we fit a logistic equation to a given set of data.
Prerequisites
Some familiarity with Matlab's plotting commands and array operators, although
the article is completely self contained and should be accessible to anyone
beginning in Matlab. You also need to get the article, "Fitting a Logistic
Curve to Data," by Fabio Cavallini, which appears in the
College Mathematics
Journal, 1993, Volume 24, Number 3, Pages: 247-253.