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.

I was talking about my Mathematical Methods One lecture last time, for the first day of the seventh week of classes.

This is actually the first time that I’ve discussed this fourth method, which we actually just called The Fourth Method. But it is a good precursor to the three-by-three matrix way of solving for three equations in three unknowns that is one of our later topics.

In my DIFEREQ class after that, I started on the third method for solving differential equations in degree one, which is usable for exact equations – that is, equations whose partial derivative with respect to x, then differentiated with respect to y, is equal to the partial derivative with respect to y, then differentiated with respect to x. I even gave a short review of partial derivatives, including replacing variables other than the one being derived with by constants c with subscripts.

After giving two examples, I decided to test the students’ understanding of the topic by a method I have never tried before, at least as far as I can recall.

This is where we all solved one problem together, and I called one student at a time to complete one step of the solution on the board. I was impressed by how well the students could tell whether the next step they might be asked to do would be a difficult one or an easy one, which shows that they were trying to comprehend the process fully.

In my Introduction to Electricity and Magnetism class after that, I started with Electric Potential, the fourth chapter in our coverage.

I first gave the relationship to potential energy which I hoped they recalled from their mechanics subject, then I proceeded to explain the electric equivalent. It is still the product of force and distance, although the force is now given of course in terms of electrical charge. I also gave the unit (volts, or joules per coulomb) and the definition of potential difference.

Afterwards I introduced equipotential lines, which are perpendicular to electric field lines and where the electric field is equal at all points.

From here I solved to sample problems (one of which proves the path a particle takes in the electric field is irrelevant to its potential), then let them work on one of the checkpoints in the book, where, given lines with assigned potential values, a pair of points on different lines and an arrow indicating the direction, or the initial and final point. This was again one of those where they had to rank the different paths from greatest to lowest potential. As far as I could tell, only one group was able to answer it correctly.

The factory whistle blows on session 637 at this point. For now, class dismissed.