Comprehensive Laplace Transform Table Dataset
This dataset provides a comprehensive table of 39 Laplace Transform pairs, mapping functions from the time domain (f(t)) to the s-domain (F(s)). It includes categories, conditions, and descriptions.
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💡 Key Takeaways
- Access 39 essential Laplace Transform pairs for quick reference.
- Explore common functions and their s-domain equivalents.
- Download the complete table in multiple convenient formats.
- Leverage this data for engineering, physics, and mathematics studies.
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Showing 20
of 39
⚠️ Showing first 20 of 39 records. Download the file for complete data.
| Category | f(t) (Time Domain) | F(s) (s-Domain) | Condition | Description |
|---|---|---|---|---|
| Basic | 1 | 1/s | s > 0 | Unit step (constant) |
| Basic | t | 1/s² | s > 0 | Ramp function |
| Basic | tⁿ | n!/s^(n+1) | s > 0, n ≥ 0 | Power function |
| Basic | t² | 2/s³ | s > 0 | Quadratic |
| Basic | t³ | 6/s⁴ | s > 0 | Cubic |
| Basic | √t | √π/(2s^(3/2)) | s > 0 | Square root |
| Exponential | e^(at) | 1/(s-a) | s > a | Exponential |
| Exponential | t·e^(at) | 1/(s-a)² | s > a | Exponential ramp |
| Exponential | tⁿ·e^(at) | n!/(s-a)^(n+1) | s > a | Exponential power |
| Exponential | 1 - e^(-at) | a/(s(s+a)) | s > 0 | Exponential decay from 1 |
| Trigonometric | sin(ωt) | ω/(s²+ω²) | s > 0 | Sine function |
| Trigonometric | cos(ωt) | s/(s²+ω²) | s > 0 | Cosine function |
| Trigonometric | tan(ωt) | Complex | - | Tangent (no simple form) |
| Trigonometric | t·sin(ωt) | 2ωs/(s²+ω²)² | s > 0 | Ramp sine |
| Trigonometric | t·cos(ωt) | (s²-ω²)/(s²+ω²)² | s > 0 | Ramp cosine |
| Trigonometric | sin²(ωt) | 2ω²/(s(s²+4ω²)) | s > 0 | Sine squared |
| Trigonometric | cos²(ωt) | (s²+2ω²)/(s(s²+4ω²)) | s > 0 | Cosine squared |
| Damped | e^(-at)·sin(ωt) | ω/((s+a)²+ω²) | s > -a | Damped sine |
| Damped | e^(-at)·cos(ωt) | (s+a)/((s+a)²+ω²) | s > -a | Damped cosine |
| Hyperbolic | sinh(at) | a/(s²-a²) | s > |a| | Hyperbolic sine |
🔧 Use Cases
- Import the CSV file into your Python scripts or simulation software to automate calculations involving Laplace Transforms.
- Use the Excel file to filter and sort specific transform pairs, create custom reference sheets, or integrate into engineering reports.
- Print the PDF version for quick offline reference during exams, lectures, or practical problem-solving sessions.
- Integrate this dataset into educational platforms or e-learning tools to provide students with a structured learning resource.