Angličtina pro matematiky II
COURSE MATERIALS WEEK V.
Listening lecture 5
Decide whether the statements are true or false.
1) Almost all students have heard about vectors before.
2) In the first week there will not be many new things to learn.
3) If the students have problems with vectors, they can go to instructor´ s house and ask him.
4) Vector has both direction and size.
5) If we are in the plane, we use x-y-z axis.
6) Vector quantity is indicated by an arrow above.
7) In the textbooks it is in bold because it is easier to read.
8) A vector hat points along the z axis and has length one.
9) The notation >a1, a2 is in angular brackets.
10) The length of a vector is a scalar quantity.
What is the nationality of the professor?
So, let's see, so let's start right away with stuff that we will need to see before we can go on to more advanced things. So, hopefully yesterday in recitation, you heard a bit about vectors. How many of you actually knew about vectors before that? OK, that's the vast majority. If you are not one of those people, well, hopefully you'll learn about vectors right now. I'm sorry that the learning curve will be a bit steeper for the first week. But hopefully, you'll adjust fine. If you have trouble with vectors, do go to your recitation instructor's office hours for extra practice if you feel the need to. You will see it's pretty easy.
So, just to remind you, a vector is a quantity that has both a direction and a magnitude of length. So -- So, concretely the way you draw a vector is by some arrow, like that, OK? And so, it has a length, and it's pointing in some direction. And, so, now, the way that we compute things with vectors, typically, as we introduce a coordinate system. So, if we are in the plane, x-y-axis, if we are in space, x-y-z axis. So, usually I will try to draw my x-y-z axis consistently to look like this.
And then, I can represent my vector in terms of its components along the coordinate axis. So, that means when I have this row, I can ask, how much does it go in the x direction? How much does it go in the y direction? How much does it go in the z direction? And, so, let's call this a vector A. So, it's more convention. When we have a vector quantity, we put an arrow on top to remind us that it's a vector. If it's in the textbook, then sometimes it's in bold because it's easier to typeset.
If you've tried in your favorite word processor, bold is easy and vectors are not easy. So, the vector you can try to decompose terms of unit vectors directed along the coordinate axis. So, the convention is there is a vector that we call hat that points along the x axis and has length one. There's a vector called hat that does the same along the y axis, and the hat that does the same along the z axis.
And, so, we can express any vector in terms of its components. So, the other notation is between these square brackets. Well, in angular brackets. So, the length of a vector we denote by, if you want, it's the same notation as the absolute value. So, that's going to be a number, as we say, now, a scalar quantity. OK, so, a scalar quantity is a usual numerical quantity as opposed to a vector quantity. And, its direction is sometimes called dir A, and that can be obtained just by scaling the vector down to unit length, for example, by dividing it by its length.
Word study:
There are some examples of mnemonics in English used in maths. Try to guess what they refer to.
a) The alligator has to open its mouth wider for the larger number.
b) I Viewed Xerxes Loping Carelessly Down Mountains.
I Value Xylophones Like Cows Dig Milk
I Value Xylophones Like Cows Dig Milk
c) Tweedle-dee-dum and Tweedle-dee-dee,
Around the circle is pi times d,
But if the area is declared,
Think of the formula π "r" squared.
Around the circle is pi times d,
But if the area is declared,
Think of the formula π "r" squared.
d) Apple pie are square.