On the Laplace transform of delta function

Delta function is an important function in mathematics and physics. In this paper, the Laplace transforms of δ(t)and δ(t-τ)have been discussed in detail. After the Laplace transform of δ(t)is analyzed, the author has found that three aspects should be taken into account, i.e. τ→0+, τ→0- andτ=0; and it is the same with the Laplace transform of δ(t-τ). Then the results of the Laplace transform of Delta function have been obtained in a rigorous and comprehensive sense.

Delta function is an important function in mathematics and physics. In this paper, the Laplace transforms of δ（t） and δ（t- τ） have been discussed in detail. After the Laplace transform of δ（t） is analyzed, the author has found that three aspects should be taken into account, i.e. τ→ 0＋, rτ→0- andτ = 0 ; and it is the same with the Laplace transform of δ（t - τ）. Then the results of the Laplace transform of Delta function have been obtained in a rigorous and comprehensive sense.