Now of course there is an important difference between the length of a path and the displacement vector of the corresponding path. Thus there is also an equally important semantic difference to be made between the two concepts.

Let us define for a parametric function such that describes the motion of an object, as was traditionally done countless years back, the distance in time as:

For the same function we have the displacement vector defined as:

Please, please, science is not like litterature; if you want us to calculate the displacement vector, tell us to calculate the “displacement vector”; if you want us to calculate the distance along a path, then you can use the word “distance”. For the sake of scientific rigor, respect the conventions and don’t try to make fancy ambiguous sentences.

Seriously, it’s not like it would kill you. As of me, on the other hand, we never know! I might end up having lost a crucial 6% in an examination paper, and because of such ambiguity, I might not end up going to McGill two years from now, at which point I might or might not be part of a car accident in Moncton. Now I understand the probability of that happening is rather scarce, but let’s just play it on the safe side, shall we?

The approximation method for calculating the area under a curve is named after Bernhard Riemann, who was one of the pioneers of modern integration theory.

If we take a function so that on an interval , where is a continuous function and :

1. We divide the interval in subsections of width equaling . This operation is called a partition of the interval .
2. We evaluate at the right end-point of the th subsection for .
3. we write the sum of areas of the rectangles, which we write:

   

4. Since we expect the approximation of to get more and more accurate as gets smaller, we say that the area delimited by the curve, the axis and the lines of equations and are equal to the limit of when (or ). We then write

   
   If that limit exists. this means we can approximate with an arbitrary degree of precision with small enough, or large enough.

Wow, this is going to be a long term for me, seeing as I already did all this stuff back in highschool. At any rate, at this point I should probably try to focus more on chemistry, or even biology.

Anyway, that’s it for today, I might add images to this article later if I feel like it, or even some variations of the Riemann method of approximation, like the middle-sum or the trapezoidal rule… I don’t think it is absolutely critical information however, so I realize it’s probably not worth the effort.

Sometimes the most unfathomable things are not the problems presented to you, but indeed your answers to them. Why is it that some people are more prone to doing stupid mistakes than others? It always seems like there are some who never make any mistakes. While this might be true of my Half-Windsor knots or of my impeccable bookcase (or even my CD collection), I often question why it is that the human brain is, err —well—, so stupid.

After all, one only needs to look at the prestigious figures of the past that managed to carve their names in history to see just how stupid we are (ohh yes!). After all, their numbers are scarce within our populous species…

The best example of what is expressed in this post should be a mundane representation of our failure to fully master ourselves. Take, for example, a problem from my last mathematics exam:

To which I promptly answer…

If , then .

What is it that makes us do so many mistakes? What exactly is wrong with our innate cognitive process that we have to be forgetful, that we lack focus or that we are so logically incompetent? I would sure like to know, because that mistake brought me down from an A+ to an A-. Not acceptable at all when you think my laptop running Maple 12 could have gotten a perfect grade on this. We question the mere existence of intelligence in robotic contraptions, yet we are so painfully aware of our own handicap.

I don’t know about you, but I need a Redbull.

Oh, how joyful is that time of year when you need to register your university schedule! It’s that time of year when you realize how much you’ve just spent in scholarship fees — and how close the time is when you need to pay it all again. Fear not, however! It’s also that time when you get to pick the courses you would like most. Right. Well so it’s supposed to be.

The problem with this is that I am still missing 2 courses due to administrative issues…

What happens at Université de Moncton is that all second-year students get to register their classes at 7:00 AM one day, and all the first year students get to register at the same time the next day. For some reason an important number of 2nd graders got their courses backwards the year before and need to take first year courses in order to meet all the requirements for med school. That’s all very fine and well, but that also means that it saturates the courses first graders need to take, resulting in lots of frustration and anger.

Add to that the general incompetence of a powerless administrative bureaucracy, and you get a system that doesn’t work and a system that relies on top decision makers to micromanage each student’s affairs…

But enough on that. The administration will fix everything up so I can focus on my next post!