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

Going back to talking yesterday about my lecture in mechanics for the second meeting on the second week of classes, I rationalized to the students the detriment of relying on the tables, which is when they might be asked to find out the value of the velocity or the displacement when the value of time is in the hundreds or thousands.

Another instance is if they are given the velocity or displacement and they are supposed to get the time, and looking it up in the table, they find that it’s not exact but between two whole number values.

That’s when I introduced to them the rest of the formulas for getting any quantity involved with constant acceleration (initial velocity, current velocity, displacement, and current time). There are five equations in all, involving only four quantities each or with one missing.

I gave five examples for constant acceleration, where part of the steps included making sure that the units were consistent before the substituted them in the formulas, as much as possible using all of the given, and how the definition of “rest” and “deceleration” affects their values (initial velocity is zero and acceleration is negative, respectively).

Lastly, I also prepared a list of the shortcuts they could use for constant velocity problems. There turned out to be twelve possible equations they could use for this, which students have already preferred not to memorize to the half-dozen steps that I gave them before.

The analysis took a whole page, and seeing all that text, I guess the average student’s brain was already biased against it. At least I was able to present both choices to them.

In the first meeting of my Electromagnetic Theory class for the second week of classes, we took up the two methods for the multiplication of vectors, which is the scalar or dot product and the vector or cross product.

It turned out to be still part of the review, because the one student I asked before if they had taken it up in David’s class or even in Maila’s turned out to be absent when it was discussed in Maila’s Geometric Applications class.

But of course, Maila’s approach was theoretical while mine was towards the specific use in examples in electricity and magnetism.

For the scalar product it was easy because given the three components of each vector “multiplied” the numeric value is equal to the sum of the product of the components along the same axes. This is because the expression involves the cosine of the angle between the two vectors, which is zero for the same axes and 90 degrees for different ones. And since the cosine of a perpendicular angle is zero, all the non-parallel angles cancel out.

Since the scalar product has two formulae, only one of which involves the angle, this is also used as an indirect method for solving for the angle between two vectors, even if they are both in three-dimensional space.

The teacher of the next class is already outside. We’ll end here for now. Dismissed.