Laplace Transform
The image of a function and the original from an image, using a table and partial fractions.
What to find:
Function:
x
Original: sums of c·tⁿ·e^(at)·sin(bt) or cos(bt) with rational numbers. Image: a fraction in p whose denominator factors. Example: t^2 e^(−3t), (p + 3)/(p^2 + 3p + 2).
This calculator finds the direct and inverse Laplace transform using a table, properties and partial fractions.
| f(t) | F(p) |
|---|---|
| 1 | 1/p |
| tⁿ | n! / pⁿ⁺¹ |
| eat | 1 / (p − a) |
| sin bt | b / (p² + b²) |
| cos bt | p / (p² + b²) |
Functions outside the table are not solved, and the calculator says so plainly.
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