Computer Laboratory for
Manual is being developed with much of
the first part completed and online. All labs need to
begin with the Lab
Cover Page. For grading of the Labs and
Lab policy see the Lab
Policy Page. Also, there is a Laboratory Guidelines
page for more details on what is expected. Documentation
is provided to create good
graphs in Excel 2010. Also,
there is additional documentation on what is expected
through the link to the Good
Graph Document. Here are a
couple special Excel spreadsheets: the Graphing
Template and the Discrete
Models. For help with Maple, there are a couple of
Maple help sheets: Maple Help document
Below is a list of the labs and a brief summary of the
Lab 1 (Help page)
of Line and Quadratic (A2). Graphing a line and a
quadratic and finding significant points on the graph.
Thermometer (A3). Listening to crickets on the
web, then using a linear model for relating to
Acids (C2). Solving for [H+] with the quadratic
formula, then graphing [H+] and pH.
Cubic and Rational Functions (CD1). Introduction
to Maple for solving equations. Graphing and finding
points of intersection, asymptotes, and intercepts.
and Absorbance (B2). Linear model for urea
concentration measured in a spectrophotometer. Relate to
of Yeast (C3). Linear model for the early growth
of a yeast culture. Quadratic to study the least squares
Logarithm, and Power Functions (E1). Study the
relative size of these functions. Finding points of
Study (D3). Use an allometric model to study the
relationship between length, weight, and surface area of
Forest (E3). Model volume of trees as a function
of diameter or height. Compare linear and allometric
of Day and Temperature (B5). A sine or cosine
function is used to approximate the length of the day
and average temperature over a year for a particular
Growth and Nonautonomous Growth Models (F4).
Census data for a particular country is analyzed for
trends in their growth rates. Models are compared and
contrasted to data, then used to project future
Growth (F2). Data for two countries presented with
a discrete Malthusian growth model used for analysis.
for Breathing (G2). Examine a linear discrete
model for determining vital lung functions for normal
and diseased subjects following breathing an enriched
source of argon gas.
S. Census models (H3). The population of the U. S.
in the twentieth century is fit with a discrete
Malthusian growth model, a Malthusian growth model with
immigration, and a logistic growth model. These models
are compared for accuracy and used to project future
behavior of the population.
and Height of Girls (I2). Data on the growth of
girls is presented. Allometric modeling compares the
relationship between height and weight, then a growth
curve is created.
Lines and Derivative (J1). Secant lines are used,
then the limit gives the tangent line. Rules of
differentiation are explored.
of Fish (I4). Use von Bertalanffy's equation for
estimating the length of fish with some fish data to
find growth in length of a fish.
consumption of Triatoma
(J2). Cubic polynomial is fit to data for
oxygen consumption of this bug. The minimum and maximum
Female Body Temperature and the Menstrual Cycle (J6).
A cubic polynomial model and a sine or cosine are fit to
data on the female body temperature over one month.
Timing of ovulation is related to points of inflection,
and the maximum and minimum temperatures are found.
Radioactive Isotopes (K6). Certain radioactive
isotopes are used for medical imaging. Exponential
functions are used to study the decay of these isotopes.
The derivative is used to find a maximum and point of
Fourier Fit to Population (D3). Data on lynx or
hares gathered by the Hudson Bay company are fit with a
series of trigonometric functions, providing increasing
accuracy with additional functions.
of Pacific Fish (L1). The von Bertalanffy equation
is used to find the length of Pacific fish, then an
allometric model relates the length to the weight. The
chain rule of differentiation is used to find the
maximum weight gain as a function of age.
Growth (K5). The growth of a tumor is studied by
creating the logistic and Gompertz growth functions from
tumor data, then these models are simulated and compared
to the literature.
Volume (A1). A box is formed from a rectangular
piece of paper, and optimal dimensions are determined.
Trough (D1). A trough with a cross-section in the
shape of an isosceles trapezoid is optimized for volume.
Tent Size (A4). A pyramidal shaped tent is cut
from a square piece of canvas with maximal volume in two
Foraging (A3). A study of seagulls dropping clams
is examined for optimal foraging strategies.
functions for Beetle Populations (L4). The
updating functions for the logistic, Beverton-Holt,
Ricker's, and Hassell's models are compared to beetle
data and studied using the tools from the course.
Discrete simulations are run to compare to data.
Models for Birds (L2). Discrete models for the
growth of a population of birds is studied. The models
that are compared are the logistic growth model,
logistic growth model with emigration, and a cubic model
with the Allee effect.
(F1). A simple model for atmospheric pressure is
Study (F4). Compute the volume and surface area of
different cells, then study their growth with a
Malthusian growth law. Learn more about exponential
growth testing a statement by Michael Crichton.
Logistic Growth Models (G1). The solutions of
these models are explored with their slope fields using
Law of Cooling (G2). Newton's law of cooling is
applied to a situation where a cat is killed by a car,
and the time of death needs to be found.
Lab 12 (Help Page)
in Children (H2). Differential equations are used
to find the level of lead in children during their early
Model (J1). A time-varying Malthusian growth model
is used to help study the declining growth rates in
several European countries.
and Smoking (K1). The cumulative exposure to
cadium is explored over many years. The effect of this
carcinogen is analyzed for a nonsmoker exposed through
diet and a smoker, where Cd is absorbed through the
Extra (Help Page)
in the Salton Sea (J3). The logarithm of the
populations are found, then fit with a quartic
polynomials. Extrema are found to find peak populations.
(C2). Four cosine functions are fit to the October
2000 tide tables for San Diego and analyzed. Minima and
maxima are explored.
Model for Influenza (L3). A discrete
dynamical system with susceptible and infected
individuals is compared to CDC data for the spread of
influenza. The model is used to examine different
strategies to lessen the effect of the disease.
in a Room (I1). Machinery produces CO, which
builds up in a room. Exposure levels are found by
solving a differential equation exactly and numerically.
(J3). The Lotka-Volterra model is studied with
data on a specific predator and prey system. Parameters
are fit to the model, and the model is analyzed.
Biodiversity (E2) Fit an allometric model through
data on herpetofauna on Caribbean islands.
Model for the U. S (F1). Java applet used to find
the least squares best fit of growth rate over different
intervals of history. Model compared to census data.
(G1). Discrete Malthusian and Logistic growth
models are simulated and analyzed.
Growth for a Yeast Culture (H1). Data from a
growing yeast culture is fit to a discrete logistic
growth model, which is then simulated and analyzed.
Model (H2). Simulations are performed to observe
the behavior of the logistic growth model as it goes
from stable behavior to chaos.
of a Ball. Data for a vertically thrown ball is fit,
then analyzed (I1). Average velocities are
computed for insight into the understanding of the
Body Temperature (J4). A cubic polynomial is fit
to data for human body temperature as it varies over a
24 hour period. A maximum and minimum are found.
a polynomial times an exponential (K1). Graphing
the function and its derivative. Maple is used to help
find extrema and points of inflection for this function.
Therapy (K3). Models comparing the differences
between drug therapies. One case considers injection of
the drug, while the other considers slow time release
from a polymer.
Yeast Growth (L2). Data are fit for a growing
culture of yeast. Derivatives are used to find the
maximum growth in the population.
(E3). Radioactive decay of 14C can be
used to date ancient objects, using a simple linear
Improved Euler's Methods (F2). Numerical solutions
of two differential equations are studied.
the Great Lakes (F3). A simple model for build up
and removal of toxic substances from the Great Lakes is
Absorption (G3). Two models for drug absorption
are examined to show the difference between injected
drugs and ones delivered using a polymer delivery
Cell Growth (G4). A culture of cells is growing in
a nonlinear and time-dependent manner. Solutions are
found exactly and numerically.
a Ball (H3). The flight of a ball in two
dimensions is studied for optimal distance and angle of
Logistic Growth (I3). The Malthusian and Logistic
growth models are applied to data for cultures of Paramecium.
for Gonorrhea (I5). Euler's method is used to
examine a model for the spread of gonorrhea.
of E. coli (H1). Two theories for the growth
of the cytoplasm or mass of bacteria are compared.
Flow in an Artery (J4). Poiseuille's law for flow
of fluids is applied to small arteries. Integrals are
used to derive relationships for the velocity of blood
(I2). Polynomials and Fourier series are used to
approximate a population survey. Definite integrals are
used to find average populations.