this is a bit imprecise, but if you mean "order 2 tensor", it can be represented as a 2D matrix. Order 3 tensor is then 3D matrix, and order n tensor is a nD matrix. A vector is a first order tensor, and a scalar is a zeroth order one. so you could say matlab is natively a tensor math framework.
As for the calculus bit, once you commit to numerical calculus, matlab is well-suited because it becomes simply matrix algebra (after applying some discretization method of choice).
I'm not sure if tools like the symbolic math toolbox let you do analytical tensor calculus.
