From ab8cc85adde879fb963c94d15675783f2cf4b183 Mon Sep 17 00:00:00 2001
From: dos-reis <gdr@axiomatics.org>
Date: Tue, 14 Aug 2007 05:14:52 +0000
Subject: Initial population.

---
 src/input/laplace.input.pamphlet | 59 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 59 insertions(+)
 create mode 100644 src/input/laplace.input.pamphlet

(limited to 'src/input/laplace.input.pamphlet')

diff --git a/src/input/laplace.input.pamphlet b/src/input/laplace.input.pamphlet
new file mode 100644
index 00000000..07b072a2
--- /dev/null
+++ b/src/input/laplace.input.pamphlet
@@ -0,0 +1,59 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input laplace.input}
+\author{The Axiom Team}
+\maketitle
+\begin{abstract}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\section{License}
+<<license>>=
+--Copyright The Numerical Algorithms Group Limited 1994.
+@
+<<*>>=
+<<license>>
+
+-- some laplace transforms
+
+)cl all
+f n == t**(n-1)*exp(-a*t)/factorial(n-1)
+
+-- L(f n) is 1/(s+a)^n
+f 2
+laplace(%, t, s)
+f 5
+laplace(%, t, s)
+sin(a*t) - a*t*cos(a*t)
+laplace(%, t, s)
+(cosh(a*t) - cos(a*t))/(2*a**2)
+laplace(%, t, s)
+exp(-a*t) * sin(b*t) / b**2
+laplace(%, t, s)
+sin(a*t) * cosh(a*t) - cos(a*t) * sinh(a*t)
+laplace(%, t, s)
+(exp(a*t) - exp(b*t))/t
+laplace(%, t, s)
+2/t * (1 - cosh(a*t))
+laplace(%, t, s)
+2/t * (1 - cos(a*t))
+laplace(%, t, s)
+(cos(a*t) - cos(b*t))/t
+laplace(%, t, s)
+-- we handle some very limited form of special functions
+a*Ci(b*t) + c*Si(d*t)
+laplace(%, t, s)
+exp(a*t+b)*Ei(c*t)
+laplace(%, t, s)
+-- we keep unknown transforms as formal transform in the answer
+sin(a*t) - a*t*cos(a*t) + exp(t**2)
+laplace(%, t, s)
+
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
-- 
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