Student "edition" found at {csi dot journalspace dot com}.

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

On the fourth day of the ninth week of classes I started out with my Mathematical Methods One lecture. It was a topic not exactly covered in the text book, or if it was, it wasn’t in a “form” that I found or believed the students could appreciate.

It was about getting factors for polynomial expressions of degree three or higher. So far we have only taken up factoring for polynomials of degree two or one, and we also discussed the special products.

The limitation for this current lesson is that the factors (or at least all but two of them) are of the form (x – r). They could get the factors by trial and error by using the constant in the expression, or the term that is multiplied to the variable raised to the power of zero. These they could use as their r, and if the remainder is zero from synthetic division, then it is a factor. I also discouraged them from using r is equal to positive or negative one, because that is a factor of all constants.

I reminded them that when they got to an expression of degree two, they could use the factoring methods that we used last time, which did not necessitate the coefficient of x in the factor to be one.

I gave them examples up to degree five for this one, which I’m proud to say I randomized from spreadsheet software. That application seems to fill my need right now for computational pseudo-programming.

In my DIFEREQ class afterwards I continued with the fourth method of solving differential equations of degree one, which is after determining linearity. I had found out how we were supposed to solve the problem we ended on last time. If in homogeneous equations we could use either x = vy or y = vx depending on which is easier to integrate, we could also use dx/dy + P(y)x = Q(y) if the equation is not linear in dy/dx + P(x)y = Q(x). Then the exponential of the integral of P(y) dy would be the integrating factor.

Afterwards I gave them exercises by pair, which, because it used the integral of the exponential that we have not had all that much before (but they have learned in their Differential Calculus class) they had to relearn all over again. That was their main stumbling block.

In my Introduction to Electricity and Magnetism lecture class, I gave a very detailed example of resistors in series and parallel, of which they are already familiar in the lab. This time, using a practice-based situation where six resistors whose values are given are connected to a known voltage source, they had to solve for the individual currents and voltages as well as the total resistance. Then I gave them an assignment of another circuit almost as complicated with seven resistors.

This is where I have to erase the chalkboard for session 688. Class dismissed.