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Some of the Shockwave animations are created using Macromedia Director 6, so they require the latest
Shockwave plug-in. Download and follow the simple directions.

Dixon's Population Pages.
Exponential Growth;
Pages 1 to 4.

Nonlinear Terms and Outbreaks;
Pages 5 to 9.

Nonlinear Terms and Chaos;
Pages 10 to 13.

Matrix Models;
Pages 14 to 18.


Elaborate simulation of evolution.
Page 19: Mathematical Sex
and Violence Simulator.
Background Mathematical.
Visual and Interactive Calculus Primer.
Derivatives and Extrema.
This log review will open a separate window.
Quicky log review.

Using a DE to approximate the future.
Thinking about Differential Equations.
Magnification approach to tangent planes.
Partial Derivatives.
More of this.
Partial Derivatives and Extrema.

Grey stuff dissolves into white stuff.
Diffusion Simulation.
A bug seeking nutrients.
Gradient.

Mathematical Look at a Synaptic Junction.
Page 2. ... Page 3. ... Page 4. ... Page 5. ... Page 6. ... Page 7.
Mathematics and the Genome.
This is a 50 page site constructed Autumn 1996.

The author of the above pages announces

Tutorial Modules


Lonberg's Pages.

A note to High School Students and Teachers re the value of this site.
In the common view of the sciences, physics and chemistry 
are thought to be heavily dependent on mathematics, while 
biology is often seen as a science  which only in a minor way 
leans on quantitative methods.  Therefore students intending 
to study biology generally do not feel a need to prepare themselves 
with courses in mathematics. Once that may have been true, 
but today the situation has substantially changed.
In contemporary biology there are many areas which depend heavily on rather advanced mathematics. This site demonstrates a few of these. In models of populations, with and without predators, iteration of a difference equation is a technique which enables the biologist to predict the effect of different parameters on the growth of the population. Similar techniques can be used to build simple and complex models of the propagation of disease. Students who do not have a fundamental grasp of differential equations will not be able to understand these powerful tools. The examples on this site are only a small selection of the areas of biology in which mathematics plays a crucial role.
Because of the importance of mathematics in contemporary biology it is vital that prospective students of the biological sciences get as good a background in mathematics as they can. The math courses that are taken in high school form the basis of a student's mathematical future. Thus all students who are thinking that they may study a biological science should avail themselves of all the math courses which are open to them while they are in high school. Four full years of high school math are a requirement for any student who might want to pursue a career involving biology. Only with this preparation will they be able to take the advanced mathematics courses in college that they will need to be sucessful in any biological field.

Frank Lonberg, High School Teacher, October 1997

Link to Frank's pages below: Nice Java Applets.
Discussion of Differential Equations
and Iteration applied to Population.
Susceptible-Infected-Recovered Model;
Differential equations applied to disease.


Casey's Neuron Pages.
Mike's Menu.
Discussion of the Action Potential and Central Pattern Generators.



Bye bye Toy.