Math 121 - Calculus for Biology I Fall Semester, 2002 Lab Subject Index
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Lab Subject Index

This page organizes the available labs according to the subjects used in the computer labs. There is an additional Lab Topic Index that organizes the available labs based on the topics covered in the lecture notes. For a listing of the specific labs that were assigned for the various semesters that this course was taught, then hyperlinks are provided to the lab indexes for Spring 2001, Spring 2002, and Fall 2002 (currently being taught).

The subjects covered in the labs listed below in fairly general categories. Most computer labs are designed to support with hands on learning the concepts in the lecture notes or to have the students demonstrate their understanding of the material presented in the lecture notes.

Graphing Applications, Algebraic Applications, and Derivatives

1. Lines and Quadratic (A1). Introduction to using Excel for editing graphs and Word for writing equations.
2. Intersection of Line and Quadratic (A2). Graphing a line and a quadratic and finding significant points on the graph.
3. Least Squares Fit to a Quadratic (B1). Use an applet to fit a quadratic to three points.
4. Lines and Quadratic (C1). Introduction to Maple for solving equations.
5. Rational Function and Line (D1). Graphing and finding points of intersection, asymptotes, and intercepts.
6. Exponential, Logarithm, and Power Functions (E1). Study the relative size of these functions. Finding points of intersection.
7. Tangent Lines and Derivative (J1). Secant lines are used, then the limit gives the tangent line. Rules of differentiation are explored.
8. 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.

1. Growth of Yeast (C3). Linear model for the early growth of a yeast culture. Quadratic to study the least squares best fit.
2. Bacterial Growth (G1). Discrete Malthusian and Logistic growth models are simulated and analyzed.
3. 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.
4. 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.
5. Continuous Logistic Growth of Yeast (L2). Data from growing cultures of yeast are fitted to a continuous logistic growth model. The growth curve is analyzed to find the maximum growth rate or turning point of the culture.

1. Concentration and Absorbance (B2). Linear model for urea concentration measured in a spectrophotometer. Relate to animal physiology.
2. Olympic Races (B3). Linear model for winning Olympic times for Men's and Women's races.
3. Dog Study (D3). Use an allometric model to study the relationship between length, weight, and surface area of several dogs.
4. 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.
5. 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.
6. Oxygen consumption of Triatoma phyllosoma (J2). Cubic polynomial is fit to data for oxygen consumption of this bug. The minimum and maximum are found.
7. Pulse vs. Weight (K2). A allometric model relating the pulse and weight of mammals is formulated and studied.
8. 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.

1. 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.
2. Malthusian Growth (F2). Data for two countries presented with a discrete Malthusian growth model used for analysis.
3. Malthusian Growth and Nonautonomous Growth Models (F3). Census data analyzed for trends in their growth rates. Models are compared and contrasted to data, then used to project future populations.
4. Immigration and Emigration with Malthusian growth (G3). Find solution of these models. Determine doubling time and when equal.
5. Logistic Growth Model (H2). Simulations are performed to observe the behavior of the logistic growth model as it goes from stable behavior to chaos.
6. 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.
7. 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.
8. 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.

1. Cricket Thermometer (A3). Listening to crickets on the web, then using a linear model for relating to temperature.
2. Island Biodiversity (E2). Fit an allometric model through data on herpetofauna on Caribbean islands.
3. Allegheny Forest (E3). Model volume of trees as a function of diameter or height. Compare linear and allometric models.

1. Weak Acids (C2). Solving for [H+] with the quadratic formula, then graphing [H+] and pH.
2. Planets(D2). Find Kepler's Law using an allometric model.
3. 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.