On second thoughts, we will probably not cover the following. If you go on to a further calculus course, the following will generally be taught from the beginning. By leaving this out we can cover exponential and logrithmic functions more thoroughly.
In this class we will go over lots of examples from previous classes,
and cover points students had difficulties with, so you should be well
prepared for the exam.
Main Part of class
This is what I had been planning to do, but we will have a review class instead.
In lecture 2, we saw a special case of finding area using the idea of limits, and saw how the area of a circle can be found from a limiting process; we rearange the pieces, and in the limit, the rearanged shape becomes a rectangle, so we can easily find the area:
Parts of circle rearranged:
Smaller divisions can be rearranged to give something closer to a rectangle:
So the area of the circle is the same as the area of the limiting rectangle, which is base*height = r * pi*r = pi r2
In general, we can't divide things up like we can with the circle. We need a method that will work for a wider variety of shapes; the idea is to divide into strips. The area measured by the strips is not quite as big as the area under the curve, but as the strips get thiner, the area of the strips gets closer to the real area:
In this class we will cover some ideas from chapter 10, and some of the notation from chapter 11. Since we are only going to cover quite a selective part, I will probably give a hand out based on these chapters, saying exactly what you are expected to learn.
The following questions from the text book should be done for practice, but are not to be handed in for marking.
The following questions from the text book should be handed in Wednesday ?
Please send corrections to spelling mistakes, and any other comments, to me.
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