PSC
Math 216-01
Program Code and CAS
Worksheets for Differential Equations
- Maxima is a free,
open-source computer algebra system.
- euler.wxm - Euler's method
- ieuler.wxm - Improved Euler's method
- rk4.wxm - Classic 4th-order Runge-Kutta
method
- rk5.wxm - Butcher's 5th-order Runge-Kutta
method
- ode_taylor.wxm - Symbolically
determines the Nth order Taylor method and numerically implements it
- Sage
is a free, open-source, computer algebra system that can be run online
without installing any software on your personal computer. It
can also be downloaded and installed, but I don't recommend this option
for students. Once you've created a Sage account, you can
upload and use the following notebooks:
- Direction_Fields.sws - plot
slope fields for a 1st-order DE
- Euler.sws -
use Euler's method or improved Euler's method to approximate solutions
- DE_Exact_Solution.sws
- Symbolically find exact solutions of 1st order DEs
- RK4.sws - use
the classic 4th-order Runge-Kutta method to approximate solutions
- Classic_RK4sys.sws
- use the classic 4th-order Runge-Kutta method to approximate solutions
of systems of ODEs
- Lua is
a free, open-source programming language that is available for almost
every conceivable platform. It is perfect for the type of
programming we will need.
- euler.lua -
Euler's method
- ieuler.lua - Improved Euler's method
- rk4.lua - Classic 4th-order Runge-Kutta
method
- rk4sys.lua - Classic 4th-order
Runge-Kutta method for systems of ODEs
- rk5.lua - Butcher's 5th-order Runge-Kutta
method
- Scilab is free and open
source software for numerical computation providing a powerful
computing environment for engineering and scientific applications.
Scilab is an excellent alternative to Matlab.