Control Systems
For a transfer function H (s) = P(s) / Q(s), where P (s) and Q (s) are polynomials in s. Then

  degree of P (s) is independent of degree of Q (s).
 the degree of P (s) and Q (s) are same.
 the degree of P (s) is always greater than the degree of Q (s).
 maximum degree of P (s) and Q (s) differ at most by one.

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Control Systems
When deriving the transfer function of linear element

 both initial conditions and loading are taken into account.
 initial conditions are assumed to be zero and the element is assumed to be not loaded.
 initial conditions are assumed to be zero but loading is taken into account.
 initial conditions are taken into account but the element is assumed to be not loaded.

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