chapter  4
79 Pages

The Inverse Laplace Transform and Application of Laplace Transform

ByBaidyanath Patra

If f(t) belongs to a class A (meaning that it is a piecewise continuous function over 0 ≤ t < ∞ and is of some exponential order), its Laplace transform f ¯ ( p ) $ \bar{f}(p) $ exists. This is denoted symbolically by L [ f ( t ) ; t → p ] = ∫ 0 ∞ e - p t f ( t ) d t ≡ f ¯ ( p ) $$ L[f(t);\,\,t \to p] = \mathop \smallint \limits_{0}^{\infty } e^{{ - pt}} f(t)dt \equiv \bar{f}(p) $$