I recently discovered MAPLE. What a wonderful tool to relearn all that math you once knew and to learn new things. The examples below may have a typo or 2 in the pdf but all the MAPLE code works, including simple animations, and was developed on MAPLE 2024
You can download all 10 examples here: Ten MAPLE Examples
I start with an Introduction to MAPLE using a money compounding example. Euler’s method is derived graphically and is programmed in MAPLE.
The Falling Body problem shows how to solve problems starting with F = m x a. Taking this technique into 2 dimensions if the X-Y Projectile Motion problem with air resistance.
Next is the Logistic Equation and Population Growth example. A source for the equation is given and then several examples are worked out.
The Mass Spring 2nd order differential equations are developed and solved. The concept of damping is derived and the results are plotted.
Next are several mixing tank examples. This starts with the first equation I learned in engineering school: Accumulation = Input – Output. Then we expand to multiple mixing tanks with an example from the University of Utah where the flux or flow/volume is equal for each pond. Naturally, for the next example, the constraint of equal flow is removed.
One of my favorites is the Pendulum Problem. This examples shows the simplified linear equation and sets up the nonlinear precise equation which is solved numerically. We then add damping, solve, and then animate the solution.
Finally, as an electrical engineer I needed to include an example. Here, we explore the behavior of an R-L-C circuit and how its damping can change its behavior. We then set R = 0 to see a resonant circuit.
specialtyengineering.org 