
Math 121  Calculus for Biology I
Spring Semester, 2007
Lab Index



© 2001, All Rights Reserved, SDSU & Joseph M. Mahaffy
San Diego State University  This page last updated 24Jan07


Lab Index
This hyperlink goes to the Main Lab Page.
This hyperlink goes to the Lab guidelines.
Below is a list of the labs and a brief summary of the problems.
Lab 1 (Help page)
 Lines and Quadratic (A1).
Introduction to using Excel for editing graphs and Word for writing equations.
 Intersection of Line and
Quadratic (A2). Graphing a line and a quadratic and finding significant
points on the graph.
 Cricket Thermometer (A3).
Listening to crickets on the web, then using a linear model for relating to
temperature.
 Concentration and Absorbance
(B2). Linear model for urea concentration measured in a spectrophotometer.
Relate to animal physiology.
 Growth of Yeast (C3).
Linear model for the early growth of a yeast culture. Quadratic to study the
least squares best fit.
 Lines and Quadratic (C1).
Introduction to Maple for solving equations.
 Weak Acids (C2).
Solving for [H+] with the quadratic formula, then graphing [H+] and pH.
 Rational Function and
Line (D1). Graphing and finding points of intersection, asymptotes, and
intercepts.
 Exponential, Logarithm,
and Power Functions (E1). Study the relative size of these functions.
Finding points of intersection.
 Island Biodiversity (E2)
Fit an allometric model through data on herpetofauna on Caribbean islands.
 Malthusian Growth 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.
 Malthusian Growth and
Nonautonomous Growth Models (F4). Census data analyzed for trends in their
growth rates. Models are compared and contrasted to data, then used to project
future populations.
 Weight 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.
 Tangent Lines and Derivative (J1).
Secant lines are used, then the limit gives the tangent line. Rules
of differentiation are explored.
 Logistic Growth for a Yeast Culture (H4).
Data from a growing yeast culture is fit to a discrete
logistic growth model, which is then simulated and analyzed.
 Oxygen consumption of
Triatoma phyllosoma (J2).
Cubic polynomial is fit to data for oxygen consumption of this bug. The minimum and maximum are found.
 Drug 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.
 Graphing 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.
 Continuous Yeast Growth (L2).
Data are fit for a growing culture of yeast. Derivatives are used
to find the maximum growth in the population.
 Graphing 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.
 Flight 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 derivative.
 Model 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.
 Olympic Races (B3).
Linear model for winning Olympic times for Men's and Women's races.
 Dog Study (D3). Use
an allometric model to study the relationship between length, weight, and
surface area of several dogs.
 Allegheny Forest (E3).
Model volume of trees as a function of diameter or height. Compare linear
and allometric models.
 Malthusian Growth and
Nonautonomous Growth Models (F4). Census data analyzed for trends in their
growth rates. Models are compared and contrasted to data, then used to project
future populations.
 Logistic Growth Model
(H2). Simulations are performed to observe the behavior of the logistic
growth model as it goes from stable behavior to chaos.
 U. 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.
 Pulse vs. Weight (K2).
A allometric model relating the pulse and weight of mammals is formulated
and studied.
 Bacterial Growth (G1).
Discrete Malthusian and Logistic growth models are simulated and analyzed.
 Immigration and Emigration
with Malthusian growth (G3). Find solution of these models. Determine
doubling time and when equal.
 Continuous Yeast Growth
(L2). Data are fit for a growing culture of yeast. Derivatives are used
to find the maximum growth in the population.