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Properties of Laplace Transform
| Linearity Property | A f1(t) + B f2(t) ⟷ A F1(s) + B F2(s) |
|---|---|
| Integration | t∫0 f(λ) dλ ⟷ 1⁄s F(s) |
| Multiplication by Time | T f(t) ⟷ (−d F(s)⁄ds) |
| Complex Shift Property | f(t) e−at ⟷ F(s + a) |
| Time Reversal Property | f (-t) ⟷ F(-s) |
- What are the conditions for Laplace transform?
- What is the application of Laplace transform?
- What are the types of Laplace transform?
What are the conditions for Laplace transform?
Note: A function f(t) has a Laplace transform, if it is of exponential order. Theorem (existence theorem) If f(t) is a piecewise continuous function on the interval [0, ∞) and is of exponential order α for t ≥ 0, then Lf(t) exists for s > α.
What is the application of Laplace transform?
The Laplace transform can also be used to solve differential equations and is used extensively in mechanical engineering and electrical engineering. The Laplace transform reduces a linear differential equation to an algebraic equation, which can then be solved by the formal rules of algebra.
What are the types of Laplace transform?
Laplace transform is divided into two types, namely one-sided Laplace transformation and two-sided Laplace transformation.
