%% Synaptic conductance model to simulate an EPSP
 clear; clf; hold on;

%% Setting some constants and initial values
 tau_syn=1; c_m=1; g_0=1; E_syn=10; delta_t=0.01; 
 I(1)=0; v(1)=0; g(1)=1;

%% Numerical integration using Euler scheme
 for t_step=2:10/delta_t
    g(t_step)= (1-delta_t/tau_syn) * g(t_step-1);
    I_syn(t_step)= g(t_step) * (v(t_step-1)-E_syn);
    v(t_step) = (1-delta_t/c_m*g_0) * v(t_step-1) ...
                 - delta_t/c_m * I_syn(t_step);
 end

%% Plotting results
 t=(1:10/delta_t)*delta_t;  
 plot(t,v); plot(t,g*5,'r--'); plot(t,I_syn/5,'k:') 
