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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 types of Laplace transform?
- What Laplace transform is used for?
- What is the property of the first derivative of the Laplace transform?
What are the types of Laplace transform?
Laplace transform is divided into two types, namely one-sided Laplace transformation and two-sided Laplace transformation.
What Laplace transform is used for?
The Laplace transform is one of the most important tools used for solving ODEs and specifically, PDEs as it converts partial differentials to regular differentials as we have just seen. In general, the Laplace transform is used for applications in the time-domain for t ≥ 0.
What is the property of the first derivative of the Laplace transform?
First Derivative
The first term in the brackets goes to zero (as long as f(t) doesn't grow faster than an exponential which was a condition for existence of the transform). In the next term, the exponential goes to one. The last term is simply the definition of the Laplace Transform multiplied by s.
