Using MAPLE and PHASER on Lab Assignments in ODE Course

Ponidi
ponidi@makara.cso.ui.ac.id
B. Alhadi
alhadi@makara.cso.ui.ac.id
Department of Mathematics
Faculty of Mathematics and Natural Science
University of Indonesia
Depok (16424) - Indonesia

Abstract

ODE is one of elementary course in Mathematics. Previously, we have done our course in ODE by using class lecture only, and focused our subject in how to solve and find the exact solution by introducing and using various classical methods from textbooks. Nowadays, regarding additional subject that the course must cover not only one equation of ODE but also system equations of ODE (linear and non-linear), we have supplemented it with lab assignment by using MAPLE and PHASER. With these tools we hope the students will get more substance subjects of ODE, beside theoretical solving technique they will also acquire real world interpretation from simulation of ODE solutions.

We use MAPLE to all of ODE subjects to show and to compare between theoretical solution (exact solution) and numerical solution (from Maple). The students can see various behavior of solutions depend on parameters, initial and boundary value of ODE. With these behavior the student can interpret the real means of the solutions. In addition, to solve and to simulate the system of ODE, it is more convenient by using PHASER then MAPLE. Considering our freshmen class that has minimal skill in programming, we decided to use PHASER for system of ODE. PHASER has available with many standard packages for linear and non-linear system of ODE. The students can easily switch between linear and non-linear system of ODE by choosing suitable menus and by changing evaluation parameters.

As the result we found the increasing of academic atmosphere, and positive feedback from the students. It can be detected with more enthusiastic, enjoyable and involving student in class and laboratory. Beside that, we see that MAPLE and PHASER are comfortable and interesting to be used in our mathematics course, especially for freshman class in ODE course. The students also have new experienced and perception about modeling, solving methods, simulations, and real interpretation on ODE solutions.