%this line will not work without a call to 'syms'
lim('(1+x/n)^n',n,inf)

%let's declare all of our symbolic variables
syms x n a y z t

%take a limit
lim('(1+x/n)^n',n,inf)

%solve an equation, with 'x' as our variable
solve('x^2-n^2=0',x)

%solve some differential equations, keep in mind that the default variable is 't'
dsolve('Dy=a*y')
dsolve('D2y=-a^2*y','y(0)=1','Dy(0)=2*a','x')

%take a derivative
diff(tan(x))

%integrate some functions, let's see how smart MATLAB is...
int(x^n)
int(sin(x),x,0,pi/2)
int(besselj(1,z))

%you can even declare symbolic matrices!
A = sym(A)
A = [0 1; -1 0];
G = expm(t*A)
g = eigs(G)

