Math 122 - Calculus for Biology I Fall Semester, 2007 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 Fall 2000, Fall 2001, 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 Differential Equations

1. Optimal Volume (A1). A box is formed from a rectangular piece of paper, and optimal dimensions are determined.
2. Optimal Trough (D1). A trough with a cross-section in the shape of an isosceles trapezoid is optimized for volume.
3. Polynomial and Exponential (B1). Graphing polynomial and exponential expressions to find intersections, intercepts, and extrema.
4. Trigonometric Functions (C1). Differentiation and graphing are explored with two trig functions using Maple.
5. Newton's Method (E1). Newton's method is applied to find the n^th root of a number, then used to find points of intersection.
6. Euler's and Improved Euler's Methods (F2). Numerical solutions of two differential equations are studied.

1. Selection in Malthusian Cultures of Bacteria (A2). A culture of two populations growing in a Malthusian manner show a clear dominance of one strain.
2. Cell Study (F4). 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.
3. Growth of E. coli (H1). Two theories for the growth of the cytoplasm or mass of bacteria are compared.
4. Nutrient Transport (I4). The effects of surface to volume ratio on limiting the growth of a cell is studied.

1. Coughing (B2). Optimization problem for the velocity of air moving through the trachea.
2. Newton's Law of Cooling (G2). Newton's law of cooling is applied to a situation where a cat is killed by a car, and the time of death needs to be found.
3. Drug Absorption (G3). Two models for drug absorption are examined to show the difference between injected drugs and ones delivered using a polymer delivery system.
4. Lead Exposure in Children (H2). Differential equations are used to find the level of lead in children during their early years.
5. Model for Gonorrhea (I5). Euler's method is used to examine a model for the spread of gonorrhea.
6. Blood Flow in an Artery (J4). Poiseuille's law for flow of fluids is applied to small arteries. Integrals are used to derive relationships for the velocity of blood in arteries.

1. Growth of Paramecium populations (C3). Data from cultures of Paramecium are analyzed using the discrete logistic growth model.
2. Fourier Fit to Population (D3). Data on hares gathered by the Hudson Bay company are fit with Fourier series.
3. World Population (E2). Fitting the Malthusian growth model to the World population data.
4. Malthusian and Logistic Growth Models (G1). The solutions of these models are explored with their slope fields using Maple.
5. Insect Population (I2). Polynomials and Fourier series are used to approximate a population survey. Definite integrals are used to find average populations.
6. Malthusian and Logistic Growth (I3). The Malthusian and Logistic growth models are applied to data for cultures of Paramecium.
7. European Population Model (J1). A time-varying Malthusian growth model is used to help study the declining growth rates in several European countries.
8. Harvesting Fish Populations (J2). The logistic growth model with harvesting is studied for a population of game fish.
9. Predator-Prey (J3). The Lotka-Volterra model is studied with data on lynx and snowshoe hares. Parameters are fit to the model, and the model is analyzed.
10. Spruce Budworm Outbreak (K1). A qualitative analysis of a differential equation that models the outbreak of the spruce budworm.

1. Optimal Foraging (A3). A study of seagulls dropping clams is examined for optimal foraging strategies.
2. Pollution in the Great Lakes (F3). A simple model for build up and removal of toxic substances from the Great Lakes is studied.
3. Carbon Monoxide in a Room (I1). Machinery produces CO, which builds up in a room. Exposure levels are found by solving a differential equation exactly and numerically.

1. Length of Day (B3). A cosine function is used to approximate the length of the day over a year.
2. Tides (C2). Four cosine functions are fit to the October 2000 tide tables for San Diego and analyzed. Minima and maxima are explored.
3. Sound Waves (D2). A simple model for two superimposed sound waves is presented. Periods, amplitude, minima, and maxima are studied.
4. Radiocarbon Dating (E3). Radioactive decay of ¹⁴C can be used to date ancient objects, using a simple linear differential equation.
5. Atmospheric Pressure (F1). A simple model for atmospheric pressure is examined.
6. Flight of a Ball (H3). The flight of a ball in two dimensions is studied for optimal distance and angle of trajectory.