The yellow flowering plant on the right above is canola. We can't grow it around Whitehorse.
Or can we? How do farmers decide? If we can't grow it now, might climate change enable us to
grow it someday soon? It all depends on the accumulation of heat by the plant. And
accumulations are measured by integrals, our final calculus topic.
Integrals measure areas,
and are calculated using antiderivatives
The heading above says it all. That's it. That's the week. 😅
If we have a function that represents a physical quantity (weight, rainfall, electric
current) then the area beneath that function measures the total accumulation of the quantity
over time. We call that amount the integral.
It turns out that the integral over an interval is the
difference between the values of the function's antiderivative at the endpoints. So
the new skill this week is antidifferentiation. That is such a mouthful that we usually say
integration instead.
Beware! The main point of confusion in this week's material is that while we have
spent the last two weeks taking derivatives we now need to switch direction and ‘untake’ them,
that is to go backwards from a derivative to the function it came from. Not getting the two
directions confused is this week's main challenge.
Don't forget about Exercise set 7!
It's due by the start of class tomorrow.
Also: Don't forget about the Biodiversity Forum!
Interesting talks and free food, this Friday evening 7 - 9 pm, and Saturday 9 am - 4 pm. Free, but you need to register through Eventbrite:
This week will complete our tour of calculus topics. Next week we'll move on to something
completely different: probability. It's an area of discrete (as opposed to continuous)
mathematics. After probability we'll look at graph theory, which is about using arrow
diagrams to model connectivity (and nothing to do with graphs of functions). Because our
final two topics are so different from what we have been doing, they give you a fresh start
for the home stretch of the course (and time to sort out any earlier topics that have been giving you trouble before the final exam 😉).
That's all for now!
See you in class,
Tim
Measurements are supposed to be objective, but even measurement has subtleties, e.g. if we do not agree on what we are measuring!
