IndexError: index 10 is out of bounds for axis 0 with size 10

You try to index outside the range:

for s in range(0, M+1):
    t[s] = t_min + k*s

Change to:

for s in range(M):
    t[s] = t_min + k*s

And it works.

You create t with length of M:

t = np.linspace(t_min, t_max, M) 

So you can only access M elements in t.

Python always starts indexing with zero. Therefore:

for s in range(M):

will do M loops, while:

for s in range(0, M+1):

will do M+1 loops.