## Spring 2020!

I'm fresh off of the JMM meetings where I helped with one of the Minicourses on SIMIODE.  I met some great new people and reconnected with old friends (not age, but how long I've known them.)  This is a great community - I'm always learning new things.  I also came back with some knowledge of #vnps (Vertical Non Permanent Surfaces) that I am testing out in my typically quiet courses.  It worked great my first day in Calc III -- but more on that later.  For the most part, I will focus on my Differential Equations class in this blog.  I plan on blogging each Wednesday to talk about what transpired during the previous week (class is Tuesday/Thursday).

My DE class is small this semester - 6 students.  I am teaching the night section.  The daytime section is at about 20 students.  At a community college, there are some semesters where a lot of night-only students sign up, and other semesters where it's more typical day students.  I told them to stick with no more than 3 tables and to sit in even numbers, since they'd be working in pairs.

After the brief syllabus talk (I've attached my syllabus here for those interested), we dove straight into the m&m scenario, first without immigration, and then with.  Both of those files are also uploaded here.  Being close to Valentine's Day, I had red. pink and white m&m's that were stamped with grey letters -- no horrible yellow m&m's to avoid!  Students worked in pairs -- the first case without immigration worked quickly and easily.  Everyone was happy with the fact there were no m&m's at the end.  I took their data and typed it into MATLAB (a 1 credit MATLAB class is a pre/co req for our Differential Equations class.)

• % without immigration
• x=0:5;
• y1=[20 11 6 3 0 0];
• y2=[20 11 7 3 1 0];
• y3=[20 9 2 2 1 1 0];
• plot(x,y1,'o')
• hold on;
• plot(x,y2,'+')
• plot(x,y3,'.')

I talked about steady state and transient solutions, the difference between discrete and continuous data, and why everyone didn't have the exact same result.  We then went through creating a DE model, first discrete and then going to continuous.  We talked about this being a separable equation.

Then we moved to immigration.  When asked how many m&ms the steady state solution would be, some did correctly guess 20.  I started one group with 50, one at 20, and one at 0. The issue with having a small class is one group lagged behind the other two, so there was a bit of a pacing issue that I don't usually get in a more full class.  We came up with the DE for this model, and then - after explaining this was no longer separable and now linear - we used MATLAB to solve and graph to show the family of curves.  That annoying +C in Calc II that just seemed annoying when professors fussed about forgetting?  Turns out it matters in DE :-)

• % with immigration
• hold off
• a1=dsolve('Dy=-0.5*y+10','y(0)=0');
• a2=dsolve('Dy=-0.5*y+10','y(0)=10');
• a3=dsolve('Dy=-0.5*y+10','y(0)=20');
• a4=dsolve('Dy=-0.5*y+10','y(0)=30');
• a5=dsolve('Dy=-0.5*y+10','y(0)=40');
• a6=dsolve('Dy=-0.5*y+10','y(0)=50');
• fplot(a1,[0 10])
• hold on
• fplot(a2,[0 10])
• fplot(a3,[0 10])
• fplot(a4,[0 10])
• fplot(a5,[0 10])
• fplot(a6,[0 10])
• hold off

I put links to Overleaf (an online LaTeX editor) on my Blackboard site.  If someone turns in any assignment (homework, projects, etc.) with LaTeX, they get one bonus point.  It's a great skill to have, but I don't have time to teach it in class, but last semester over half the class learned it on their own or in office hours for the bonus point.  Bribery sometimes works!

1. Down with yellow m&m's!!!  Hurrah for "plus C"!!!!

Different starting pops is great idea so they can see the convergence is independent of initial condition.

Good percentages on students learning LaTEX and Matlab. This will suit them well.

Thank you for sharing ALL you offered here. Sounds like a great and power packed start.

Where were you some 56 years ago when I took DE?  Wait don't answer that :+)