Math 122 - Calculus for Biology I Fall Semester, 2007 Lab Topic Index
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Lab Topic Index

This page organizes the available labs according to the topics presented in the lecture notes. There is an additional Lab Subject Index that organizes the available labs based on the subject matter covered in the labs. 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 topics listed below are organized in the order of the lecture notes with most computer labs 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.

Optimization

1. Optimal Volume (A1). A box is formed from a rectangular piece of paper, and optimal dimensions are determined.
2. Optimal Foraging (A3). A study of seagulls dropping clams is examined for optimal foraging strategies.
3. Polynomial and Exponential (B1). Graphing polynomial and exponential expressions to find intersections, intercepts, and extrema.
4. Coughing (B2). Optimization problem for the velocity of air moving through the trachea.
5. Optimal Trough (D1). A trough with a cross-section in the shape of an isosceles trapezoid is optimized for volume.
6. Nutrient Transport (I4). The effects of surface to volume ratio on limiting the growth of a cell is studied.

1. Length of Day (B3). A cosine function is used to approximate the length of the day over a year.
2. Trigonometric Functions (C1). Differentiation and graphing are explored with two trig functions using Maple.
3. Tides (C2). Four cosine functions are fit to the October 2000 tide tables for San Diego and analyzed. Minima and maxima are explored.
4. Sound Waves (D2). A simple model for two superimposed sound waves is presented. Periods, amplitude, minima, and maxima are studied.
5. Fourier Fit to Population (D3). Data on hares gathered by the Hudson Bay company are fit with Fourier series.

1. World Population (E2). Fitting the Malthusian growth model to the World population data.
2. Radiocarbon Dating (E3). Radioactive decay of ¹⁴C can be used to date ancient objects, using a simple linear differential equation.
3. Atmospheric Pressure (F1). A simple model for atmospheric pressure is examined.
4. 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.
5. Growth of E. coli (H1). Two theories for the growth of the cytoplasm or mass of bacteria are compared.

1. Euler's and Improved Euler's Methods (F2). Numerical solutions of two differential equations are studied.
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. Malthusian and Logistic Growth Models (G1). The solutions of these models are explored with their slope fields using Maple.
4. 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.
5. 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.
6. Lead Exposure in Children (H2). Differential equations are used to find the level of lead in children during their early years.
7. 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.
8. Malthusian and Logistic Growth (I3). The Malthusian and Logistic growth models are applied to data for cultures of Paramecium.
9. European Population Model (J1). A time-varying Malthusian growth model is used to help study the declining growth rates in several European countries.
10. Harvesting Fish Populations (J2). The logistic growth model with harvesting is studied for a population of game fish.
11. Spruce Budworm Outbreak (K1). A qualitative analysis of a differential equation that models the outbreak of the spruce budworm.

1. Flight of a Ball (H3). The flight of a ball in two dimensions is studied for optimal distance and angle of trajectory.
2. Model for Gonorrhea (I5). Euler's method is used to examine a model for the spread of gonorrhea.
3. 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.

1. Insect Population (I2). Polynomials and Fourier series are used to approximate a population survey. Definite integrals are used to find average populations.
2. 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.