Math Problem (Calculus)

[Max™]

Log functions blew my mind for a while until I realized they were just a meatgrinder, put in this number, out comes that number.

Very neat seeing it worked out though, Euler's Number still vexes me a bit, helpful to read over this shit while thinking it through.



Regarding infinite quantities: it isn't that they're large, it is that they're a different class of numbers entirely from what we usually think of as big numbers.

A big number minus a big number is a small number.

An infinite quantity minus an infinite quantity is still infinite.

I can't help but try to turn them into circles though, Cantor must have been utterly insane to have such an intuitive grasp of the concept.

[Trajan]

Log functions blew my mind for a while until I realized they were just a meatgrinder, put in this number, out comes that number.

Very neat seeing it worked out though, Euler's Number still vexes me a bit, helpful to read over this shit while thinking it through.



Regarding infinite quantities: it isn't that they're large, it is that they're a different class of numbers entirely from what we usually think of as big numbers.

A big number minus a big number is a small number.

An infinite quantity minus an infinite quantity is still infinite.

I can't help but try to turn them into circles though, Cantor must have been utterly insane to have such an intuitive grasp of the concept.

There are some people; Cantor, Euler, and in the 20th century Godel and Ramanujan, who were just so smart that it's ridiculous.

[Woozie]

An infinite quantity minus an infinite quantity is still infinite.

An infinite quantity minus and infinite quantity can be anything. It can be 1, 2, 0, -5, infinity, -infinity, etc. It's very easy to manipulate expressions to make infinity minus infinity equal whatever you want. In general, "infinity minus infinity" is meaningless all by itself because infinity is not a number or a quantity, and the minus sign is usually defined as a relationship between two quantities. So technically, infinity minus infinity is undefined.

[Max™]

Well, yeah, it is only defined if you're speaking of countable infinities, I was just giving an example of the natures of infinities which seem paradoxical at first.

[Mojo]

Round 2

The definition I was given for a trend line was a line where the sum of squares of the distances from the line was minimized for that set of data. I've been trying to find a way to calculate this and have gotten this far (this is for a linear trend line.)

http://i27.tinypic.com/2zthve0.png

I don't know how to solve for both b and m at the same time.

[Woozie]

Well, yeah, it is only defined if you're speaking of countable infinities, I was just giving an example of the natures of infinities which seem paradoxical at first.

Oh okay, I misunderstood. And yeah, Cantor is a freakin genius for even attempting to find such relations between infinite sets, let alone for him being successful.

[Melchiah]

Try the chain rule?

Though if you aren't up to derivatives yet, wouldn't help you.

[Mojo]

I used the chain rule to derive the solution I ended up with. It's accurate although I can't solve for both m and b with any set of data. I'm not sure if there are more steps I need to take or if there is an alternate approach to the problem that doesn't result in this.

[Melchiah]

It's been a few years since I took differential calculus, but as I recall, limits are taught as a way to conceptualize the derivative.

Your solution seemed pretty involved for a Cal I(I'm assuming this is Cal I) limit problem, I'm tempted to think this might be some math professor's pet problem.

[Mojo]

It's not a problem that's been assigned to me by anybody, mostly just something that I'm curious about. It arose in a chem class where we're taking a set of observed data and calculating a trend line using Excel.

[Melchiah]

Reaction rates?

[Mojo]

Calculating enthalpy of vaporization.

[Galois]

You're on the right track to solving for both m and b, but you also need to take the partial derivative with respect to b and minimize that, in addition to working with the partial derivative with respect to m. Then, you will have a system of two equations in two unknowns, so some algebra will lead you to the solutions.

[thegilseller]

Every time I skim the thread list, I read this thread as "Meth Problem".

I laugh each and every time.

[Nyson]

I havent done Calculus in so long wow