function approx = taylor_approx(a,b,srate,degree,func)

%% Construct taylor approximation

%% example:  approx=taylor_approx(-6,6,100,5,'exp');
%% constructs a Taylor approximation of degree 4 of exp(x) with 100 samples per unit
%% time on the interval [-6,6]
syms x;  % symbolic variable
    if strcmp(func,'sin'),
        f=sin(x);
    elseif strcmp(func,'cos'),
        f=cos(x);
    elseif strcmp(func,'exp'),
        f=exp(x);
    elseif strcmp(func,'log'),
        f=log(1+x);
    else
        disp('WARNING: function must be one of sin, cos, log, or exp');
    end
    
    approx=diff(f);

coeffs=fliplr(sym2poly(taylor(f,degree)));
t=a:1/srate:b-1/srate;
y=zeros(size(t));
for i=0:degree-2
    y=y+coeffs(i+1)*t.^i;
end
approx=y;
plot(t,approx);
hold on
    if strcmp(func,'sin'),
        plot(t,sin(t),'r');
    elseif strcmp(func,'cos'),
        plot(t,cos(t),'r');
    elseif strcmp(func,'exp'),
        plot(t,exp(t),'r');
    elseif strcmp(func,'log'),
        plot(t,log(1+t),'r');
    else
        disp('WARNING: function must be one of sin, cos, log, or exp');
    end
    title('Original  f (red) and approximation');


%for i=1:degree