Math 121 - Calculus for Biology I
Spring Semester, 2013
© 2001, All Rights Reserved, SDSU &
Joseph M. Mahaffy
San Diego State University -- This page last updated 19-Apr-13
This hyperlink goes to the Main
Lab Page. There is a hyperlink to Maple on
rohan. All labs need to begin with the Lab Cover Page. For grading of the Labs and Lab policy see the Lab Policy Page. 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
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.
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 temperature.
- Concentration and Absorbance (B2). Linear model for urea concentration measured in a spectrophotometer. Relate to animal physiology.
- Lines and
Quadratic (C1). Introduction to Maple for solving equations.
- Growth of Yeast (C3). Linear model for the early growth of a yeast culture. Quadratic to study the least squares best fit.
- 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,
- 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.
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 (F2). Data for
two countries presented with a discrete Malthusian growth model used
- 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.
- 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.
- Tangent Lines and Derivative (J1). Secant lines are used, then the limit gives the tangent line. Rules of differentiation are explored.
- 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
- 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.
- 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
- Growth 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.
- Oxygen consumption of Triatoma phyllosoma (J2). Cubic polynomial is fit to data for oxygen consumption of this bug. The minimum and maximum are found.
- Female Body Temperature (J5). A cubic polynomial is 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.
- Plankton 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.
- 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.
- Radioactive Isotopes (K6). Certain radioactive isotopes are used for medical imaging. Exponential function are used to study the decay of these isotopes. The derivative is used to find a maximum and point of inflection.
- Logistic 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.
- Tumor 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.
- 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.
- Growth 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.
- Continuous Yeast Growth (L2). Data are fit for a growing culture of yeast. Derivatives are used to find the maximum growth in the population.
- Discrete 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.
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.
- Continuous Logistic Growth of S. aureus (L3). Data from growing cultures of S. aureus are fitted to a continuous logistic growth model. Average growth rates are found and compared to the derivative for the logistic growth model. The maximum growth rate is approximated.
Functions (D4). Introduction to Maple for solving equations.
Examine linear, quadratic, cubic, and rational functions.
- Pulse vs.
Weight (K4). A allometric model relating the pulse and weight of
mammals is formulated and studied.
Growth Model (H2). Simulations are performed to observe the
behavior of the logistic growth model as it goes from stable behavior
- Cell Study
(I3). 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.
Growth (G1). Discrete Malthusian and Logistic growth models are
simulated and analyzed.
and Emigration with Malthusian growth (G3). Find solution of these
models. Determine doubling time and when equal.
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
- Circadian 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.
- Population of
Saw-Tooth Grain Beetle (L1). Discrete logistic model and Ricker's
model for population growth are studied for this beetle population.
Stability analysis of the models are performed.