A=[1 2;3 4]

% The following command is used to calculate the eigenvalues and
% eigenfunction of matrix A

[V,D]=eig(A)


%The following command is used to calculate inverse of matrix A
B=inv(A)


% Define transfer function of zero pole gain system: G=(2s-1)/(s^2+5s+6)=2(s-0.5)/((s+2)(s+3))

G1=tf([2 1],[1 5 6])
G2=zpk(0.5,[-2 -3],2)

%Step response of the system

step(G1)

%impulse response

impulse(G1)

%ltiview will open a step response plot. If you want any other plot, right
%click on the graph and specify the plot that you want to analyse.

ltiview(G1)

%lsim command will open a GUI in which you can design any kind of input.
%Here we will choose step signal.

lsim(G1)




%%%%%%%%%%%%%%%%%%%%%
%%%symbolic commands%%


syms x
f= x*log(x/(1+x))

%differentiation

df=diff(f,x)
simplify(df)

%evaluate df at x=1

subs(df,x,1)

%Indefinite integration

IntF=int(df,x)

%definite integral

IntF2=int(df,x,1,2)

%nth order taylor series about x0

x0=0.5;
n=3
taylor(f,x0,n)

% gradient of f

df=jacobian(f,x)

% solving of an ODE dy/dx=y^2 y(0)=1;

dsolve('Dy=y^2','y(0)=1')