Here’s something I just learned and want to share with others and record for my use the next time I need to do this and have already forgotten!
The position and appearance of the figure legend in Maxima plots drawn with plot() (by setting gnuplot_preamble) and in draw() (by setting user_preamble), can be manipulated to any of the gnuplot options listed here.
Here are some examples:
In the back of my calculus book there is a table of famous integrals. Here’s integral number 21 in that table:
From Maxima integrate(), I get
What’s going on?
Both forms give a workable antiderivative for the original integrand:
Furthermore, we believe that both forms are correct because of this helpful identity for hyperbolic sine:
Turns out (thanks to a Barton Willis for pointing me in the right direction) there’s a variable logarc that we can set to make Maxima return the logarithmic form instead of hyperbolic sine:
I haven’t yet encountered cases where this would be a bad idea in general, but I’ll update this if I do.
In the first week of my differential equations course, we study methods of direct integration and separation of variables. I like to emphasize that the absolute values can lend an extra degree of generality to solutions with antiderivatives of the form
As an example, for the initial value problem
it is convenient for treating all possible initial conditions (
However, Maxima omits the absolute values.
For this case, we could consider only the needed interval 
Turns out we can set the Maxima variable logabs to make integrate() include absolute values in cases like this:
But then later in the course, I saw that logabs also impacts the Ordinary Differential Equation solver ode2(). I encountered an example for which Maxima, in particular solve() applied to expressions involving absolute value, didn’t do what I wanted with logabs:true
For the logistic equation
we expect that by separating variables we can obtain the solution
Here’s what happens when we use ode2() with and without logabs:true:
Student Projects in Maxima is an online project to disseminate work by undergraduate students using Maxima to reproduce published results in the sciences and social sciences.
Volume 1, Number 4 (2017) is devoted to Systems of Ordinary Differential Equations for SIR models in epidemiology.
Contents:
Emenheiser, Anna, Virus Dynamics and Drug Therapy
Radermacher, Erin, A Model of the 2014 Ebola Outbreak
Rafai, Sagar, Analysis of Communicable Disease Models
Student Projects in Maxima is an online project to disseminate work by undergraduate students using Maxima to reproduce published results in the sciences and social sciences.
Volume 1, Number 3 (2017) is devoted to Systems of Ordinary Differential Equations for non-chaotic predator-prey and other interacting population models
Contents:
Bhullar, Abhjeet, Lions, Wildebeest and Zebras
Goodin Aunic, Parasitic Nematodes in Grouse
DeFore, Brandon, Breeding Suppression in Predator-Prey
Jerez, Emilio, Predator-Prey with Hawk and Dove Tactics
Bontrager, Eric, Predator-Prey with Prey Switching
Beatty, Ethan, Analysis of Logistic Growth Models
Rice, Gabriel, Pharmacokinetic Mechanism of Ethanol-Benzodiazepine Interactions
Kay, Ian, Radioactive Isotopes
Wile, Jessica, Ebola in Western Lowlands Gorillas
Bailey, John, Kinetic Modeling for Interconnected Reactions
Piet, Joe, Elephant and Tree Population Dynamics
Kim, Judy, A Model for West Nile Virus
Kamalaldin, Kamalaldin, Infected Prey in Polluted Environment
Park, Kayla, Ratio-Dependent Predator Prey Model
Lundy, Liam, Predator Prey in a Single Species with Cannibalism
Orwin, Michael, Interactions of Model Neurons
Schultz, Pete, Photosynthetic Oscillations
Wadhwa, Raoul, Dynamics in an Inflammation Model
Del Olmo, Ricardo, Population Growth and Technological Change
Network Model of Cocaine Traffic in Spain Edited
Kill, Sean, A Logistic Model with Varying Carrying Capacity
McFadden-Keesling, Sophia, Predator Prey Model with a Refuge
Student Projects in Maxima is an online project to disseminate work by undergraduate students using Maxima to reproduce published results in the sciences and social sciences.
Volume 1, Number 1 (2017) is devoted to Chaotic Systems of Ordinary Differential Equations.
Contents:
Thornburg, Eric, Simple Pendulum and Chaos
Bhimani, Kevin, Chaos in a 3-Species Food Chain
York, Lily, A Lattice Model of Epilepsy
Andrews, Steven, 3D Chaotic Model
Rutledge, Tim, A Model of Neuronal Bursting
Student Projects in Maxima is an online project to disseminate work by undergraduate students using Maxima to reproduce published results in the sciences and social sciences.
Volume 1, Number 2 (2017) is devoted to Systems of Ordinary Differential Equations with time-dependent forcing terms, non-continuous inputs, and forcing terms that require knowledge of a past state of the system.
Contents:
Chumley, Qynce, An Office Heating and Cooling Model
Williams, Nick, Baseball Pitch Dynamics
Rizzolo, Skylar, BAC Model for alcohol consumption
Barth, Eric, A model of bladder bacteria proliferation in prostate disease
Barth, Eric, A Model of Pulse Vaccination Strategyi
In MATLAB, I occasionally have need for the plotyy() command for making a plot of two different functions with widely varying scales.
Turns out Maxima draw has an equivalent functionality by setting the option yaxis_secondary:
pause([options]):=block([tsecs],
tsecs:assoc('pausetime,options,0),
if tsecs=0 then
read("Execution Paused...enter any character then CTRL-ENTER")
else(
disp(sconcat("paused for ", tsecs," seconds")),
?sleep(tsecs)),
return("")
);
In MATLAB, I often use the subplot() command to make an array of multiple plots in a single figure.
In Maxima, we can achieve that by generating each of the subplots using gr2d(), and then putting them all together with a call to draw() or wxdraw():
There’s an optional columns argument — the subplots are drawn row-wise in an array with the specified number of columns:
And of course all this works for 3d plots using gr3d():
In Matlab and RStudio, I love the ability to recall a command I’ve already typed using the up arrow key. Today I discovered alt up arrow to do the same in wxMaxima!
This is really the best implementation of function templates I’ve seen in an IDE:
In wxMaxima, if I type inte and then ctrl shift k, I see a popup menu of possible completions. Choosing integrate results in an input cell template that looks like:
integrate(<expr>,<x>)
Pressing Tab highlights <expr> and I simply type the expression to be integrated. A second press of Tab key highlights <x> and I type the name of the independent variable.
But wait, there’s more: this works for any currently defined function—including user defined functions.
**UPDATE** In the newer versions of wxMaxima (since v15.10) Ctrl+Tab and Shift+Ctrl+Tab also trigger autocompletion.
