inverse_laplace_transform_expression
Convert frequency-domain expressions F(s) back into time-domain functions f(t) using inverse Laplace transforms. Ideal for solving differential equations, transfer functions, and pharmacokinetic models.
Instructions
Inverse Laplace transform: F(s) → f(t).
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🆕 PHASE 2 - NOT IN SYMPY-MCP OR NSFORGE v0.2.3!
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Transforms s-domain (Laplace) back to time-domain.
CRITICAL FOR:
- Getting time response from transfer function
- Multi-compartment PK model solutions
- Impulse/step response analysis
- Converting algebraic solutions back to ODE solutions
Args:
expression: Frequency-domain expression F(s)
freq_var: Frequency variable (default: "s")
time_var: Time variable (default: "t")
Returns:
Time-domain function f(t)
Examples:
# Simple pole
inverse_laplace_transform_expression("1/(s + k)", "s", "t")
→ {"result": "exp(-k*t)*Heaviside(t)", ...}
# Two-compartment model (after partial fractions)
inverse_laplace_transform_expression("A/(s + λ1) + B/(s + λ2)", "s", "t")
→ {"result": "A*exp(-λ1*t) + B*exp(-λ2*t)", ...}
# Step response
inverse_laplace_transform_expression("1/(s*(s + k))", "s", "t")
→ {"result": "(1 - exp(-k*t))/k", ...}
# PK: Bolus injection response
inverse_laplace_transform_expression("dose/(V*(s + k))", "s", "t")
→ {"result": "dose*exp(-k*t)/V", ...}
# WORKFLOW: Use with apart_expression!
# 1. apart_expression("F(s)", "s") → partial fractions
# 2. inverse_laplace_transform_expression(...) → f(t)
Input Schema
TableJSON Schema
| Name | Required | Description | Default |
|---|---|---|---|
| freq_var | No | s | |
| time_var | No | t | |
| expression | Yes |
Output Schema
TableJSON Schema
| Name | Required | Description | Default |
|---|---|---|---|
No arguments | |||