%FINDING Z
xvec=0.1:0.1:5.0;
jmax=10;
jvec=0:1:jmax;
[xmat,jmat]=meshgrid(xvec,jvec);
summandvec=(2.*jmat+1).*exp(-jmat.*(jmat+1).*xmat);
Z=sum(summandvec);
Zapp=1./xvec;
DZ=abs(Zapp-Z)./Z; %difference in Zapproximate and Z"exact"
    %Plotting things:
subplot(3,2,1); plot(xvec,Z,xvec,Zapp,'x');
title('Z "exact" and Z approx');
a=legend('Z "exact"','Z approx');
xlabel('X');
ylabel('Z');
subplot(3,2,2); plot(xvec,DZ);
xlabel('X');
ylabel('D');
title('Difference (D) in Zexact and Zapp');
%FINDING U
xvec1=0.1:0.1:4.9;
U=0.-diff(reallog(Z));
Uapp=0.-diff(reallog(Zapp));
DU=abs(Uapp-U)./U; %difference in Uapproximate and U"exact"
    %Plotting things:
subplot(3,2,3); plot(xvec1,U,xvec1,Uapp,'x');
title('U "exact" and U approx');
b=legend('U "exact','U approx');
xlabel('X');
ylabel('U');
subplot(3,2,4); plot(xvec1,DU);
xlabel('X');
ylabel('D');
title('Difference (D) in Uexact and Uapp');
%FINDING Cv
xvec2=0.1:0.1:4.8;
C=diff(1./xvec1).*diff(U); %My attempt to take dU/dT.  I'm not sure this is correct, because the graphs are very different.
Capp=1;
DC=abs(Capp-C)./C;
    %Plotting things:
subplot(3,2,5); plot(xvec2,C,xvec2,Capp,'x');
title('Cv "exact" and Cv approx');
h=legend('Cv "exact"', 'Cv approx');
xlabel('X');
ylabel('Cv');
subplot(3,2,6); plot(xvec2,DC);
xlabel('X');
ylabel('D');
title('Difference (D) in Cv,exact and Cv,app');