laplace_transform_expression
Convert time-domain functions to s-domain using Laplace transform for ODE solving, stability analysis, and transfer functions. Returns F(s) with convergence conditions.
Instructions
Laplace transform: f(t) → F(s).
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🆕 PHASE 2 - NOT IN SYMPY-MCP OR NSFORGE v0.2.3!
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Transforms time-domain functions to s-domain (Laplace domain).
CRITICAL FOR:
- ODE solving (time → algebraic in s-domain)
- Stability analysis (poles in s-plane)
- Transfer functions (system response)
- Compartment model analysis
Args:
expression: Time-domain expression f(t)
time_var: Time variable (default: "t")
freq_var: Frequency variable (default: "s")
Returns:
Laplace transform F(s) with convergence conditions
Examples:
# Exponential decay
laplace_transform_expression("exp(-k*t)", "t", "s")
→ {"result": "1/(s + k)", "convergence": "Re(s) > -Re(k)"}
# Compartment elimination
laplace_transform_expression("C0*exp(-k*t)", "t", "s")
→ {"result": "C0/(s + k)", ...}
# Step function response
laplace_transform_expression("Heaviside(t)", "t", "s")
→ {"result": "1/s", "convergence": "Re(s) > 0"}
# Dosing with absorption
laplace_transform_expression("D*ka*exp(-ka*t)", "t", "s")
→ {"result": "D*ka/(s + ka)", ...}
# PK: Convert ODE to algebra
# dC/dt + k*C = 0 → s*C(s) - C(0) + k*C(s) = 0
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 | |||