Differences between revisions 4 and 5
 ⇤ ← Revision 4 as of 2007-06-24 23:43:24 → Size: 1815 Editor: DavidJoyner Comment: ← Revision 5 as of 2007-06-24 23:43:55 → ⇥ Size: 1813 Editor: DavidJoyner Comment: Deletions are marked like this. Additions are marked like this. Line 38: Line 38: $$\begin{cases} \begin{cases} Line 42: Line 42: \end{cases}$$ \end{cases}$# Differential Equations ## First order DEs ### IVPs, Direction Fields, Isoclines ### Direction Fields, Autonomous DEs ### Separable DEs, Exact DEs, Linear 1st order DEs ### Numerical method: Euler (or Constant Slope) ### Applications (Growth/Cooling/Circuits/Falling body) ## Higher order DEs ### IVPs/General solutions, Basic theory ### Numerical methods for higher order DEs ### Constant coefficient case: Undetermined Coefficients ### Application: springs (free, damped, forced, pure resonance) ### Application: Electrical Circuits ## Laplace Transform (LT) methods ### Inverse Laplace & Derivatives ### 1st Translation Thrm ### Partial Fractions, completing the square ### Unit Step Functions SAGE can define piecewise functions like$\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)