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 first day of the twelfth week of classes, in my Mathematical Methods One class, I took up the topic of geometric sequences. I skimmed through all the parts that we’ve taken up before in arithmetic sequences: (1) the equation relating the two consecutive elements with the common ratio, (2) the equation with the first element, the nth element, the value of n and the common ratio, (3) the procedure for getting several means between two numbers, (4) the different procedure for getting just one mean between two numbers, and (5) how to get the sum of a sequence from the mean.

I differentiated how an arithmetic sequence increases (when the common difference is positive) as opposed to a geometric sequence (the elements are just all the same sign if the common ration is positive, and alternating in sign if it is negative. When does a geometric sequence increase? When the common ratio is greater than one or between negative one and zero. It decreases when the common ration is less than negative one or between zero and one.

At least one person complained that I was going fast compared to last meeting, until I said that they were already familiar with most of the concepts from the previous topic.

The only hitch, for solving the value of n given the nth element of a geometric sequence, is that in the long method they have to divide by the common ratio several times to get the value of n. The short method required logarithms, which is supposed to be our next topic. Maybe there is a need to change the sequence of topics for this subject in the future, to be clearer.

In my DIFEREQ class afterwards, we had the sixth method for solving differential equations of degree one, which is using the equation for getting the integrating factor from a formula of partial derivatives. If M is the term multiplied to dx and N is the term multiplied to dy, then the integrating factor that is just a function of x is given by the partial derivative of M with respect to y minus the partial derivative of N with respect to x, all over N. If the integrating factor is a function of y alone then the difference is divided by M instead. Then they would proceed just like with exact equations.

We had two examples, and there was another hitch with the derivative of negative dy/y, which turns out to be the absolute value of y, not positive 1/y. Determining if the resulting equation was exact verified this. But there was no such hitch in the exercise that I gave them, that required the exponential of the integral of negative 2dx/x, which is still the reciprocal of x squared.

Since some members of the Council of Recognized Student Organizations had a meeting prior to the class and thus were late, I also gave bonuses to those who were in class on time.

Session 708 receives its own bonus for being in class on time at this point. Class dismissed.