How's School?

[Xevross]

Double antiderivatives. they are a real pain switching boundaries for me.

Easy problem here:

I've never done those before. Seems fairly simple except I've never been taught straight up integrating x terms with respect to y.

Polar coordinates are kinda cool.
(x,y)
In order to define every point in rectangular coordinates you need (-infinity,+infinity) for both the x and the y.   But with polar, you can define every point for r with just the positive numbers [0,+infinity), and for theta, just between [0, 2pi)  Seems like madness.

Done plenty of this though. I like polar coordinates, the graphs you get from them can be really cool

[the-pi-guy]

I've never done those before. Seems fairly simple except I've never been taught straight up integrating x terms with respect to y.

I know something you don't?  
I'll explain!
So basically first we learned about partial derivatives, a derivative with respect to another.  u = f(x,y,z).  The way we take the derivative in this case is by treating the other values as if they were a constant.  So if we had z = xy + y + x,  if we took the derivative with respect to y, we would treat x as a constant.  dz/dy = x+1, so we pretend that x is a constant.  d/dy (xy)=x is the same thing as d/dy (3y) = 3.   We also get the dz/dx = y+1.

The double integrals are generally used for volume, sometimes they are used for areas.  Basically it's kinda, but not exactly the opposite of that.  z= f(x,y), basically you take two integrals, one for y, and one for x.  And you keep the other variable as a constant.  
There are some cases, where the inside integral will have a function of the outer.  That case you plug in the function for the variable you are integrating. Sometimes you have to switch the outer and inner integrals and you also have to switch the bounds of the integral. I understand how to do this, but I keep having troubles getting the right answer.  

[Xevross]

I know something you don't?  
I'll explain!
So basically first we learned about partial derivatives, a derivative with respect to another.  u = f(x,y,z).  The way we take the derivative in this case is by treating the other values as if they were a constant.  So if we had z = xy + y + x,  if we took the derivative with respect to y, we would treat x as a constant.  dz/dy = x+1, so we pretend that x is a constant.  d/dy (xy)=x is the same thing as d/dy (3y) = 3.   We also get the dz/dx = y+1.

The double integrals are generally used for volume, sometimes they are used for areas.  Basically it's kinda, but not exactly the opposite of that.  z= f(x,y), basically you take two integrals, one for y, and one for x.  And you keep the other variable as a constant.  
There are some cases, where the inside integral will have a function of the outer.  That case you plug in the function for the variable you are integrating. Sometimes you have to switch the outer and inner integrals and you also have to switch the bounds of the integral. I understand how to do this, but I keep having troubles getting the right answer.  

Sounds pretty interesting! I'm sure I'll learn that at university

Why do you have to change the bounds?

[the-pi-guy]

Sounds pretty interesting! I'm sure I'll learn that at university

You definitely will.  

Why do you have to change the bounds?

Sometimes you have to switch the y and x functions.
Let's say you are to solve this integral

In it's current state it is unsolvable in elementary terms.  There's no nice way to solve it for an exact answer.  Some teachers might even tell you that it is completely unsolvable.  The only way to solve it, is using a series and that can get really messy and you'd have to add a lot of numbers to get some result.  
If you switch the bounds to being a dydx equation, it is actually really easy even to find an exact answer.  

[Xevross]

You definitely will.  
Sometimes you have to switch the y and x functions.
Let's say you are to solve this integral

In it's current state it is unsolvable in elementary terms.  There's no nice way to solve it for an exact answer.  Some teachers might even tell you that it is completely unsolvable.  The only way to solve it, is using a series and that can get really messy and you'd have to add a lot of numbers to get some result.  
If you switch the bounds to being a dydx equation, it is actually really easy even to find an exact answer.  

Hmm interesting. There is still a lot I have to learn

What school year are you in Pi / when were you born?

[the-pi-guy]

Hmm interesting. There is still a lot I have to learn

What school year are you in Pi / when were you born?

96

[Xevross]

96

After or before the school year started in 96?

[the-pi-guy]

After or before the school year started in 96?

Before.  I'm 20, in my sophomore year of university.  
But I was planning on taking the class my first semester, but didn't work out.

[Xevross]

Before.  I'm 20, in my sophomore year of university.  
But I was planning on taking the class my first semester, but didn't work out.

Ah okay so you're two school years ahead of me then. Explains why I don't know some things  

[the-pi-guy]

Ah okay so you're two school years ahead of me then. Explains why I don't know some things  

Nah.


It's more like one year ahead.  
You guys don't waste your time on silly stuff like English class.

[Legend]

Before.  I'm 20, in my sophomore year of university.  
But I was planning on taking the class my first semester, but didn't work out.

You've surpassed my college math.  

[Xevross]

Nah.


It's more like one year ahead.  
You guys don't waste your time on silly stuff like English class.

Haha yeah probably  

I did take further maths though which means I am one year ahead of most who take maths in the UK.

We do waste a lot of time though, our first year at school is basically just playing in sand boxes and shame like that. Also we do have an English class, we do Shakespeare and poems and stuff

[darkknightkryta]

It's been so long since I've integrated anything.  Oh well.  I'm taking a computer technology teaching course, since I'm technically not allowed to teach the computer engineeriing classes.  It's been good so far.  

[the-pi-guy]

You've surpassed my college math.  

If you say so!  
I have catching up to do in other departments though.  

Haha yeah probably  
I did take further maths though which means I am one year ahead of most who take maths in the UK.
We do waste a lot of time though, our first year at school is basically just playing in sand boxes and shame like that. Also we do have an English class, we do Shakespeare and poems and stuff

I just realized the dog I posted is on drugs....

I mean university though.  You guys don't waste any time in university.  At least not usually.  

[Mmm_fish_tacos]

Nah.


It's more like one year ahead.  
You guys don't waste your time on silly stuff like English class.

Must resist British joke