Proving cylinder is a Manifold

Question

I need to prove that a cylinder in $R^3$ is a Manifold by using the definition.

So basically I have to show that It is locally diffeomorphic to an open subset of $R^2$.

Can anyone help me with that. I am new to the subject.

Thanks & regards

Answer 1

Hint

Use the fact that a circle is a one dimensional manifold based on the mapping $t \mapsto (\cos t, \sin t)$ and that $(u,v) \mapsto (\cos u, \sin u, v)$ is a parameterization of a cylinder.