Maybe I shouldn't have started this blog now, not with everything that's been going on.

On the first day of the third week of the first term in the new school year, I finished the discussions of Chapter One in my Mathematical Methods One class. I continued with the properties of rational exponents, which segued neatly into the properties of all radicals, from which I proceeded to rationalization of radicals in the denominators by multiplying the expression with its conjugate.

It was also a short hop (not that I demonstrated it literally in class) from there to complex numbers seeing that the very definition of a complex number is hinged on the square root of negative one. Here I gave them the standard form of complex expressions, which is a + bi, where the imaginary number could then be treated like a variable.

One of the main operations they had to learn here is factoring values under the radical sign to perfect squares and negative numbers. There was also rationalization of imaginary parts in the denominators of fractions, of course.

I went through the types of operations they could encounter that had to be reverted to standard form, which they all had encountered as polynomial expressions.

In my Differential Equations class afterwards, we expanded our discussion from families of circles, which we discussed during the last meeting, to families of lines and curves, where I gave the general equations of lines, perpendiculars, ellipses, parabolas and hyperbolas, defining them in terms of their centers or vertices, their foci, the directrix line and the asymptotes.

I would have given this to them last meeting but when I asked them for their edition of the calculus book it just gave the assumption that all curves would have their center at the origin and thus was only a special case of conic sections. I even plotted the lines of the derivative, but it didn’t make much sense in the overall scheme of things. It only worked as a somewhat practical application of the elimination of arbitrary constants. In the end of that period I gave them another group exercise based only on the general equation of a circle.

From there we went to removing the arbitrary constants from those equations, the relatively most complicated being where we had went to the third derivative of the equation.

By the time we finished with one example for each, there were only ten minutes left in the period, so since I knew there were only twenty students in that class and they all were present (with the exception of one who was campaigning room to room for the Youth For Christ – it was also Student Organization Recruitment Week after all) I just let them go without an exercise. After all, that gave us all twenty minutes to have lunch before we started our next class, Introduction to Electricity and Magnetism.

In INTROEM, I started on the next chapter, which was about the electric field. This, I related to the electrostatic force in two dimensions that we discussed the previous meeting.

That included a review of summation of forces in two dimensions. We only got to finish the total force on one of three particles in a triangle, so I asked them if they wanted the rest as a group seatwork or as an individual assignment. They chose the latter, so I added another system of particles with four charges in the shape of a square.

This they submitted during the next meeting, when I discussed electric field due to a single particle, then at one point for a system of particles in one dimension (using only two particles as an example), then for two dimensions (using only three particles in a triangle formation as an example. I ended with the special configuration of the electric field due to a dipole, which, even though we got a final expression, was different from the one in the book, but worked just as well, and I gave them another exercise. One student asked if the exercise was individual, so I told the class that it was individual by her request. Next meeting we’ll talk about electric field due to solid objects in familiar easy to analyze shapes.

Thus session 617 comes to a grinding halt. The class is now dismissed.