Differences between revisions 2 and 3
 ⇤ ← Revision 2 as of 2007-06-24 23:34:49 → Size: 1341 Editor: DavidJoyner Comment: ← Revision 3 as of 2007-06-24 23:42:30 → ⇥ Size: 1841 Editor: DavidJoyner Comment: Deletions are marked like this. Additions are marked like this. Line 37: Line 37: SAGE can define piecewise functions like$$\begin{cases} x \ {\mapsto}\ \sin \left( \frac{{\pi \cdot x}}{2} \right) &\text{on (0, 1)}\cr x \ {\mapsto}\ 1 - {\left( x - 1 \right)}^{2} &\text{on (1, 3)}\cr x \ {\mapsto}\ -x &\text{on (3, 5)} \end{cases}$$as follows:{{{sage: f(x) = sin(x*pi/2)sage: g(x) = 1-(x-1)^2sage: h(x) = -xsage: P = Piecewise([[(0,1), f], [(1,3),g], [(3,5), h]])sage: latex(P)}}}

# Differential Equations

## Laplace Transform (LT) methods

### Unit Step Functions

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