Differences between revisions 5 and 6
 ⇤ ← Revision 5 as of 2007-06-24 23:43:55 → Size: 1813 Editor: DavidJoyner Comment: ← Revision 6 as of 2007-06-24 23:44:59 → ⇥ Size: 1815 Editor: DavidJoyner Comment: Deletions are marked like this. Additions are marked like this. Line 38: Line 38: $\begin{cases} x \ {\mapsto}\ \sin \left( \frac{{\pi \cdot x}}{2} \right) &\text{on$(0, 1)$}\cr x \ {\mapsto}\ 1 - {\left( x - 1 \right)}^{2} &\text{on$(1, 3)$}\cr$\begin{array}{ll}            x \ {\mapsto}\ \sin \left( \frac{{\pi \cdot x}}{2} \right) &\text{on $(0, 1)$}\\            x \ {\mapsto}\ 1 - {\left( x - 1 \right)}^{2} &\text{on $(1, 3)$}\\ Line 42: Line 42: \end{cases}$\end{array}$

# Differential Equations

## Laplace Transform (LT) methods

### Unit Step Functions

SAGE can define piecewise functions like $\begin{array}{ll} • x \ {\mapsto}\ \sin \left( \frac{2} \right) &\text{on (0, 1)}\\ x \ {\mapsto}\ 1 - {\left( x - 1 \right)}^{2} &\text{on (1, 3)}\\ x \ {\mapsto}\ -x &\text{on (3, 5)} \end{array}$

as follows:

sage: f(x) = sin(x*pi/2)
sage: g(x) = 1-(x-1)^2
sage: h(x) = -x
sage: P = Piecewise([[(0,1), f], [(1,3),g], [(3,5), h]])
sage: latex(P)

## PDEs

### Heat Eqn. Both Ends Insulated

Differential_Equations (last edited 2008-11-14 13:42:08 by localhost)