Teaching tools.  Lectures, instruction chapters, computer programs.

Measurements of [Ca2+] and [H+] with dyes.

IDL Programs.  (Use at your own risk).

Demonstrating Fourier transforms, convolution, and filtering


Demonstrates inverse Fourier transform by use of the definition and by FFT.  N, number of points in function, must be even.  The coefficients Ck are located in positions 1,...,N/2, the C-k in N-k,...,N/2 + 1.  C0 is in position 0.


Demonstrates filtering techniques by Fourier transform and by convolution.  Note the difference between the functions used in "Fourier convolution" and in direct convolution.


Similar to previous, but demonstrating the use of a differentiator.


Simple Markovian state models with oscillatory solutions. 


3-state ring model.  Its solutions are oscillatory when its selectable rate constants violate micro-reversibility.


Finds rate constants for oscillating solutions of 3-state ring.


A ring model with more states.  Great oscillations!


Analysis of Ca sparks.


Calculates calcium transients ([Ca2+](x,t)) from line scan fluorescence records .