What’s on the Laplace Transforms poster
A 7-row table: f(t) · Its transform F(s).
Defined for s large enough that the integral converges.
- 1 — 1/s
- t^n — n! / s^(n+1)
- e^(at) — 1/(s − a)
- sin ωt — ω/(s² + ω²)
- cos ωt — s/(s² + ω²)
- f′(t) — sF(s) − f(0)
- f″(t) — s²F(s) − sf(0) − f′(0)
The transform turns differentiation into multiplication by s. That is what converts a differential equation into an algebraic one.
Questions about the Laplace Transforms poster
- What’s on the Laplace Transforms poster?
- A 7-row table: f(t) · Its transform F(s). Defined for s large enough that the integral converges. 1 — 1/s; t^n — n! / s^(n+1); e^(at) — 1/(s − a); sin ωt — ω/(s² + ω²); cos ωt — s/(s² + ω²); f′(t) — sF(s) − f(0); f″(t) — s²F(s) − sf(0) − f′(0). The transform turns differentiation into multiplication by s. That is what converts a differential equation into an algebraic one.
- Who is the Laplace Transforms poster for?
- Laplace Transforms belongs to the Mathematics section rather than to a school year, because math is not something one grade owns. Anyone learning differential equations can pin it up — a beginner, a student mid-course, or someone revising years later.
- When should you use the Laplace Transforms poster?
- The derivative rules are the whole point: they bring initial conditions in for free. A wall chart earns its place by being glanceable from where the work is happening, so Laplace Transforms belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
- What other posters go with Laplace Transforms?
- Exact Equations, Existence & Uniqueness and Separable Equations sit alongside Laplace Transforms in the Mathematics section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.Exact EquationsExistence & UniquenessSeparable Equations
- Is the Laplace Transforms poster free to download and print?
- Yes. Laplace Transforms downloads as a free PDF with no account, no email and no watermark, like everything else in the Mathematics section. Print as many copies as you like for a home, a classroom, a library or a tutoring group; reselling the file is the only thing the licence rules out.Read the licence
- What size does the Laplace Transforms poster print at?
- Laplace Transforms is a vector PDF laid out for US Letter, and prints on A4 with Fit to page — the same file, no separate download. Because every mark on it is drawn rather than photographed, it stays sharp enlarged to A3, A2 or A1 at a copy shop. Colour carries emphasis only, so a greyscale print of Laplace Transforms loses nothing.Printing guide
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