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

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. Cricket Thermometer (A3). Listening to crickets on the web, then using a linear model for relating to temperature.

1. Concentration and Absorbance (B2). Linear model for urea concentration measured in a spectrophotometer. Relate to animal physiology.
2. Growth of Yeast (C3). Linear model for the early growth of a yeast culture. Quadratic to study the least squares best fit.

1. Lines and Quadratic (C1). Introduction to Maple for solving equations.
2. Weak Acids (C2). Solving for [H+] with the quadratic formula, then graphing [H+] and pH.
3. Rational Function and Line (D1). Graphing and finding points of intersection, asymptotes, and intercepts.

1. Exponential, Logarithm, and Power Functions (E1). Study the relative size of these functions. Finding points of intersection.
2. Island Biodiversity (E2) Fit an allometric model through data on herpetofauna on Caribbean islands.

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.

1. 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.
2. 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.

1. Tangent Lines and Derivative (J1). Secant lines are used, then the limit gives the tangent line. Rules of differentiation are explored.
2. 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.

1. Oxygen consumption of Triatoma phyllosoma (J2). Cubic polynomial is fit to data for oxygen consumption of this bug. The minimum and maximum are found.
2. 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. 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.
2. Continuous Yeast Growth (L2). Data are fit for a growing culture of yeast. Derivatives are used to find the maximum growth in the population.

1. 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.
2. 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.
3. 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.
4. Olympic Races (B3). Linear model for winning Olympic times for Men's and Women's races.
5. Dog Study (D3). Use an allometric model to study the relationship between length, weight, and surface area of several dogs.
6. Allegheny Forest (E3). Model volume of trees as a function of diameter or height. Compare linear and allometric models.
7. 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.
8. Logistic Growth Model (H2). Simulations are performed to observe the behavior of the logistic growth model as it goes from stable behavior to chaos.
9. 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.
10. Pulse vs. Weight (K2). A allometric model relating the pulse and weight of mammals is formulated and studied.
11. Bacterial Growth (G1). Discrete Malthusian and Logistic growth models are simulated and analyzed.
12. Immigration and Emigration with Malthusian growth (G3). Find solution of these models. Determine doubling time and when equal.
13. Continuous Yeast Growth (L2). Data are fit for a growing culture of yeast. Derivatives are used to find the maximum growth in the population.