How Laplace transforms are matched
- Rewrite the time-domain expression into standard pieces.
- Match each piece to a transform table rule.
- Use linearity to combine the transformed terms.
Laplace Transform Calculator
Compute common Laplace transforms.
Use this calculator as a study checker
Enter the problem carefully, review the interpreted input, and compare each step with your own work. Calculus results can depend on notation, variables, bounds, domains, and assumptions.
- Check the method before copying the answer.
- Use the examples below to test nearby problems.
- Read the calculus guides for worked explanations.
Solution
50 study checks todayEnter an expression or choose an example to calculate.
Laplace Transform Examples
What this calculator is for
The Laplace transform converts a time-domain function into an s-domain expression. It is widely used to solve differential equations. Use it to check your setup, compare steps with your own work, and review the meaning of the final expression before copying it into homework.
Manual example
- Problem: \(\mathcal{L}\{t^2\}\).
- Use the rule \(\mathcal{L}\{t^n\}=n!/s^{n+1}\).
- With \(n=2\), the result is \(2/s^3\).
Common mistakes to avoid
- Mixing the time variable \(t\) with the transform variable \(s\).
- Forgetting linearity for sums.
- Using a table rule without checking conditions.
When to double-check the result
Laplace transform answers may have assumptions about growth and initial values. Differential equation applications should include the full equation and conditions.