function dxdtau = deriv01(tau,x)

% function deriv01(tau,x) supplies the ODE definitions
% needed by m-file ex01.m
% ex01 calls the standard MATLAB function ode45()
% and ode45() calls deriv01()

% x is the dependent variable, fractional conversion
% in deriv01.m, x is a 1x1 array, that is, a scalar
% tau is the independent variable, space time

% dxdtau holds the current value of the derivative
% dxdtau is a 1x1 array with only one element, that is, a scalar
% dxdtau = dx/dtau

% declare "global" variable shared with file "ex01.m"
% its value is assigned in file "ex01.m"
global k

% x is a scalar so .* not needed below

% calculate derivative
% dxdtau = dx/dtau

dxdtau = k * (1 - x);

% dxdtau value is returned by this function to the calling routine

% end of function