Online Laplace Transform Calculator
Compute Laplace and inverse Laplace transforms with step-by-step solutions
Calculator
Please enter a valid function
Examples:
sin(t)
cos(2*t)
e^(-5*t)
t^2
3*t^3
dirac(t)
Transform Result:
Step-by-Step Solution:
Common Laplace Transforms
| Function f(t) | Laplace Transform F(s) |
|---|---|
| 1 | 1/s |
| t | 1/s² |
| t^n | n!/s^(n+1) |
| e^(at) | 1/(s-a) |
| sin(ωt) | ω/(s²+ω²) |
| cos(ωt) | s/(s²+ω²) |
| t*sin(ωt) | 2ωs/(s²+ω²)² |
| t*cos(ωt) | (s²-ω²)/(s²+ω²)² |
How It Works
The Laplace transform converts a function of time into a function of complex frequency. Our calculator uses these steps:
- Parse Input: Interpret your function notation
- Identify Components: Recognize exponents, trigonometric functions, constants
- Apply Transform: Use appropriate method based on function type
- Simplify: Reduce the expression to simplest form
- Provide Steps: Show detailed step-by-step solution
For inverse transforms, the process is reversed using inverse Laplace transform techniques.
FAQs
What is a Laplace transform?
The Laplace transform is an integral transform that converts a function of a real variable t (often time) into a function of a complex variable s (complex frequency). It is used to simplify differential equations into algebraic equations.
How do I calculate the Laplace transform of a function?
The Laplace transform of a function f(t) is defined as F(s) = ∫₀^∞ f(t)e^(-st) dt. Our calculator automates this process, handling the complex integration for you.
Can this calculator handle piecewise functions?
Yes, our Laplace transform calculator supports piecewise functions. You can define different expressions for different intervals.
Does the calculator show step-by-step solutions?
Yes, after calculating the transform, you can see detailed step-by-step solutions explaining how the result was obtained.
What is the Laplace transform of t?
The Laplace transform of t is 1/s². You can verify this using our calculator by entering "t" as the function.
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Created by Sadiq Saleem | Reviewed by Team TheEducationistHub