Math 121 - Calculus for Biology I Spring Semester, 2010 Lab Index
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Lab Index

This hyperlink goes to the Main Lab Page. There is a hyperlink to Maple on rohan and an additional Help Page for the use of Maple (by Brendan Fahy).

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. Lines and Quadratic (C1). Introduction to Maple for solving equations.
2. Concentration and Absorbance (B2). Linear model for urea concentration measured in a spectrophotometer. Relate to animal physiology.
3. Weak Acids (C2). Solving for [H+] with the quadratic formula, then graphing [H+] and pH.

1. Rational Function and Line (D1). Graphing and finding points of intersection, asymptotes, and intercepts.
2. Growth of Yeast (C3). Linear model for the early growth of a yeast culture. Quadratic to study the least squares best fit.
3. Dog Study (D3). Use an allometric model to study the relationship between length, weight, and surface area of several dogs.

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.
3. Allegheny Forest (E3). Model volume of trees as a function of diameter or height. Compare linear and allometric models.

1. Malthusian Growth (F2). Data for two countries presented with a discrete Malthusian growth model used for analysis.
2. 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.
3. 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.

1. 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.
2. 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.
3. 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. 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. 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.

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. 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.
3. 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.

1. 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.
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.
3. 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.
   

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. 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.
3. 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.

1. Continuous Yeast Growth (L2). Data are fit for a growing culture of yeast. Derivatives are used to find the maximum growth in the population.
2. Updating 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.

1. Graphing Functions (D4). Introduction to Maple for solving equations. Examine linear, quadratic, cubic, and rational functions.
2. Pulse vs. Weight (K4). A allometric model relating the pulse and weight of mammals is formulated and studied.
3. Logistic Growth Model (H2). Simulations are performed to observe the behavior of the logistic growth model as it goes from stable behavior to chaos.
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. Bacterial Growth (G1). Discrete Malthusian and Logistic growth models are simulated and analyzed.
6. Immigration and Emigration with Malthusian growth (G3). Find solution of these models. Determine doubling time and when equal.
7. 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.
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.
9. 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.
10. 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.