Math help

[ParadigmShifter]

This thread reminds me of this (true, honest) story...

Two mathematicians are in a bar. The first one says to the second that the average person knows very little about basic maths. The second one disagrees, and claims that most people can cope with a reasonable amount of maths. The first mathematician goes off to the washroom, and in his absence the second calls over the waitress. He tells her that in a few minutes, after his friend has returned, he will call her over and ask her a question; all she has to do is answer, "One third x cubed." She agrees, and goes off mumbling to herself. The first guy returns and the second proposes a bet to prove his point. He says he will ask the blonde waitress an integral, and the first laughingly agrees. The second man calls over the waitress and asks, "What is the integral of x squared?" The waitress says, "One third x cubed." Then, while walking away, she turns back and says, "Plus a constant!"

 

[Bluemofia]

Reminds me of this other math joke that my math teacher told us.

e^x was in a party all alone. His/her/its friend x^2 came over, and asked: "e^x, why don't you integrate?" e^x responds: "Well I would, but it won't make a difference."

Meh. There's the +C, but oh well. Then she told us that if we didn't get the joke by now (it's like a week before AP exams), then we're screwed for the exams.

 

[Catharsis]

at Integral's avatar. What is that, maths? Maths in an avatar is just sick.

 

[ParadigmShifter]

Says the sick statistics boy, too interested in position and spread. You may have a large residual, but does anyone want to manipulate your polynomial expressions?

 

[Integral]

Catharsis...At least I don't have the normal distribution walking around with me...

X~N(0,1)...bah.

Integral

 

[Catharsis]

Says the sick statistics boy, too interested in position and spread. You may have a large residual, but does anyone want to manipulate your polynomial expressions?

Oh yeah, I'm into deviation; I'm into the chain rule.

Catharsis...At least I don't have the normal distribution walking around with me...

X~N(0,1)...bah.

Integral

That's improper, Integral. There are limits to my patience, you know.

 

[ParadigmShifter]

At least you fixed your avatar so it wasn't a load of nonsense with x as one of the limits of the integration as well as the integrand, Integral. I prefer indefinite integrals myself, or ones taking bounds towards a discontinuity or infinity.

EDIT: I wonder if this real maths link I saw the other day will be allowed? I think it is funny anyway.

http://mathworld.wolfram.com/TitsGroup.html

EDIT2: The wikipedia entry is actually better than the mathworld one though, if you are interested in the classification of finite simple groups

http://en.wikipedia.org/wiki/Tits_group

 

[Godwynn]

You probably haven't gotten to integration yet, which is the harder half of calculus IMO.

It's coming, I looked ahead in the book. Next chapter.

 

[ParadigmShifter]

Integration is not nice. Differentiation is easy and can be taught to 4 year olds if you really want to. Integration is a whole new kettle of fish. Many integrals don't have closed form algebraic solutions, nasty. They can only be calculated numerically (which is pretty easy though [apart from getting the numeric stability and accuracy], now we have computers).

 

[History_Buff]

Integration isn't really that nasty. Or I've gone through two years of Engineering Calculus, and they haven't bothered to show us the hard . .. .. .. . yet (I've no doubt it gets rediculous at the high levels, but so does everything in Math).

All you have to do is get your limits straight, and then either integrate it yourself, or toss it into a computer. Only once was I ever asked to numerically integrate something by hand.

 

[West 36]

I wish I was a derivative so I could lie tangent to you curves
Thanks to everyone for making me feel like a kindergartener in a... IDK! I feel stupid, but math is not my strong point.
DEATH TO THE MATHS

 

[Bluemofia]

2 questions.

W, U and V are vectors.

W = ||U||V + ||V||U

Prove W bisects the angle formed by vectors U and V.

I know the logic behind it, but I can't mathematically prove this.

---------------------

Cross Products
W, V, and U are vectors

U X V = U X W, U =/= 0

Does V = W? Why?

My main question on this one is, if W has shifted its location, is it still W? Or is it some other vector?

 

[Japanrocks12]

wait a sec

int(dx/x)

doesn't that become ln|x|? just curious

and yeah, you can't neglect the constant of integration (C)

 

[Integral]

Japanrocks: yes, int(1/x dx) is ln|x| + C. He was trying to integrate by parts.

 

[Bluemofia]

Yes, yes.

Now onto Analytical Geometry part of Calculus questions. I didn't feel like starting a new thread, so I revived this one.

 

[Truronian]

1) w = |u||v|e_u+|u||v|e_v

= |u||v|(e_u+e_v)

(e_u+e_v) is the trivial bisector, so w is a bisector.

2) v and w are parallel.

Different vectors, same direction.

 

[Bluemofia]

What does the eu and ev mean?

And is 2 true or false?

 

[History_Buff]

2 is true, but unfortunately not 10 chars long.

 

[Bill3000]

My main question on this one is, if W has shifted its location, is it still W? Or is it some other vector?

If the orientation of the vector has changed, but not the magnitude, then it is a different vector. Vectors do not change on the physical position of their location. (Unless it is in a vector field, obviously)

 

[El_Machinae]

http://online.math.uh.edu/HoustonACT/videocalculus/

To all people who've taken calculus or are taking calculus: Here is a video tutorial broken into parts to help you review. It might not be the best source to learn the original material (you need a prof who can walk you through it better) but it's a different perspective teaching the same material. Beautifully, it's broken into ~20 minute segments. If you're having trouble with a concept, or want help reviewing, it's the way to go.

Plus, you can pause it, meaning you can work through the examples on your own first.

(each video will take a couple minutes to load)

El_"tutorials on the web"_Machinae