function ydot = sect_5_1_ode_fn_part_a(t,y)
% SECT_5_1_ODE_FN_PART_A - returns the time derivative needed to integrate the covariance evolution equations 
%
% Written by:
% -- 
% John L. Weatherwax                2005-08-14
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

% the common terms for all parts (ignores the measurement term -P H^T R_C^{-1} H P):
ydot = sect_5_1_ode_fn(t,y);

% extract the components:
y = y(:); 
p11 = y(1);
p12 = y(2);
p22 = y(3);

% add in the measurement term (-P H^T R_C^{-1} H P): 
%
ydot(1) = ydot(1) - p12^2; 
ydot(2) = ydot(2) - p12*p22;
ydot(3) = ydot(3) - p22^2;