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

Continuation, Advanced Mathematics, first session, seventh week of classes, third trimester: for the operations performed on the dependent variable of a signal graph, I had to emphasize to the students that in amplitude scaling, the fundamental period remains unchanged.

I also showed my class the basic operations performed on the independent variable. There were only three: time scaling, reflection or flipping, and time shift.

For time scaling, I showed them through three examples that the period decreases when the scaling factor is positive, and increases when the factor is negative.

For flipping, I had to specify a half wave example rather than the full wave I used in the previous examples, just to emphasize that the symmetry or axis of reflection is vertical and not horizontal. For horizontal flipping, it’s actually just amplitude scaling with a scale factor of negative one. The amplitude and the period are still the same.

The last operation, time shifting, meant moving the signal either up or down the horizontal scale, while keeping both amplitude and the period again.

To wrap up the lecture I talked about the precedence of applying both time shifting and time scaling to the same function. Unlike normal mathematical operations, where the multiplication (time scaling) is applied first, here the addition (time shifting) is applied first, then the time scaling, which occurs around the constant point of the zero origin.

I, admittedly, don’t see the point of it yet but it was in the lecture notes, so I included it.

For my mechanics lecture session, first meetings for the seventh week of classes, I taught them how to apply the two dimensional vectors to our already familiar equations of force, acceleration and velocity.

I made a “cockroach”-shaped graph showing all the variables from the magnitude and direction of the individual forces, to their x and y components, to the x and y components of the summation of forces, and from those to the x and y and resultant forms of the acceleration, velocity and displacement.

I also listed all the equations in all their forms, like using the Pythagorean relation for getting the resultant acceleration, velocity etc.

There were eight unique equations (counting the five for constant acceleration as one) and including the one that stated the angles or direction for final summation of forces, acceleration, velocity and displacement are the same.

I told them that the thirteen formulas (including the quadratic derivation) would be given in the exam, but it was still up to them to know which form to use when.

The first example I gave used the summation of forces canceling out, or equating to zero. This was to show that even if the magnitudes of the forces do not add up to zero, but the summations of their components can.

The rest of this tale will have to wait until the succeeding post, as well as the happenings in the Open Campus. I’m all done for this period.