Math 122 - Calculus for Biology II
Fall Semester, 2000
Lab Index

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San Diego State University -- This page last updated 30-Nov-00

Lab Index

Below is a list of the labs and a brief summary of the problems.

Lab 1 (Help Page)

  1. Polynomial and Exponential (B1). Graphing polynomial and exponential expressions to find intersections, intercepts, and extrema.
  2. Selection in Malthusian Cultures of Bacteria (A2). A culture of two populations growing in a Malthusian manner show a clear dominance of one strain.
  3. Growth of Paramecium populations (C3). Data from cultures of Paramecium are analyzed using the discrete logistic growth model.

Lab 2 (Help Page)

  1. Trigonometric Functions (C1). Differentiation and graphing are explored with two trig functions using Maple.
  2. Optimal Volume (A1). A box is formed from a rectangular piece of paper, and optimal dimensions are determined.
  3. Optimal Foraging (A3). A study of seagulls dropping clams is examined for optimal foraging strategies.

Lab 3 (Help Page)

  1. Feeding a Dog. Review of linear and allometric models from Math 121.
  2. Coughing (B2). Optimization problem for the velocity of air moving through the trachea.
  3. Growth of Paramecium with Ricker's Model. Two methods of fitting data are compared using cultures of Paramecium with Ricker's discrete growth model.

Lab 4 (Help Page)

  1. Graphing Trig Functions. Two cosine functions with different frequencies are summed together, and their graphs are explored.
  2. Length of Day (B3). A cosine function is used to approximate the length of the day over a year.
  3. Cardiac Output. A model examines the optimal energy for pumping blood through the heart.

Lab 5 (Help Page)

  1. Optimal Trough (D1). A trough with a cross-section in the shape of an isosceles trapezoid is optimized for volume.
  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. Fourier Fit to Population (D3). Data on hares gathered by the Hudson Bay company are fit with Fourier series.

Lab 6 (Help Page)

  1. Newton's Method (E1). Newton's method is applied to find the nth root of a number, then used to find points of intersection.
  2. World Population (E2). Fitting the Malthusian growth model to the World population data.
  3. Radiocarbon Dating (E3). Radioactive decay of 14C can be used to date ancient objects, using a simple linear differential equation.

Lab 7 (Help Page)

  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. 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.

Lab 8 (Help Page)

  1. Atmospheric Pressure (F1). A simple model for atmospheric pressure is examined.
  2. Malthusian and Logistic Growth Models (G1). The solutions of these models are explored with their slope fields using Maple.
  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.

Lab 9 (Help Page)

  1. Gravity and Integration. A ball is thrown up and falls under gravity. Rules of integration are investigated with Maple.
  2. Growth of E. coli (H1). Two theories for the growth of the cytoplasm or mass of bacteria are compared.
  3. Flight of a Ball (H3). The flight of a ball in two dimensions is studied for optimal distance and angle of trajectory.

Lab Final (Help Page)

  1. 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.
  2. Insect Population (I2). Polynomials and Fourier series are used to approximate a population survey. Definite integrals are used to find average populations.
  3. Lead Exposure in Children (H2). Differential equations are used to find the level of lead in children during their early years.
  4. Model for Gonorrhea (I5). Euler's method is used to examine a model for the spread of gonorrhea.