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

On the fourth day of week five of classes in the first trimester, I discussed with my Mathematical Methods One students word problems using quadratic equations.

There were two types of examples in their textbook on this that I used. The first described two numbers (usually consecutive, sometimes even AND consecutive or odd and consecutive) and what the sum of their reciprocals added to, thus forcing the students to come up with an equation with the variables in the denominator, which become of degree two when the fractions are removed.

The second type is a work problem, but with one of the times described relative to the other. This is exactly like the problem I told them to disregard in their last quiz, which has a return engagement in their next quiz.

The next types of problems in the book had a “page” with inner margins and outer margins, and the relationship of the area of both. Too complicated, I thought.

So I dug up another book and just got some problems that related the perimeter and area of a rectangle, and the diagonal and sides of a square, as well as the three sides of a right triangle. I also picked some “rows” and “number of units per row” problem, which is a simplified version of the area with the added hint that answers can only be positive integers.

I also gave them the idea that when dealing with word problems, disregard the answers that do not conform to physical reality, such as negative lengths and time working alone which is smaller than time working together.

The students also reported that there are still no test booklets in the bookstore, so just like the Dean suggested when I told him about the dilemma during our faculty meeting last week, the class just contributed for one pad of line papers that during the test I would distribute with the questionnaires.

In my DIFEREQ class afterwards, we were still on the topic of solving differential equations of degree one. This time we moved one step higher in complication, to those that cannot be solved by just separation of variables.

I introduced homogeneous functions in two variables, which, when substituting x and y with lambda x and lambda y, lambda can be factored out and leave the original function. The exponent of lambda is now the degree of homogeneousness.

Determining whether a function is homogeneous or not was the easy part, for me and for them. But I’ll continue this tale next time.

Session 628 has to end here and now. Class dismissed.