# Thread: Ygolo's TypoC Math Tutoring Service

1. ## Ygolo's TypoC Math Tutoring Service

Why not something like this?

So if you don't believe this to be too pretentious or condescending, please bring me your math related frustrations.

I will try to clear things up for you, but there are no guarantees.

Things to note:
1. I will not do your homework for you
2. Service is provided as is
3. I may take my sweet time to respond
4. the focus will be on figuring out what math to use in particular situations, rather than plugging numbers into formulas or executing procedures just to get answers.

2. Originally Posted by ygolo
• the focus will be on figuring out what math to use in particular situations, rather than plugging numbers into formulas or executing procedures just to get answers.
so... you can't help me with my calc homework?

3. Oou. Can you also write about or link to explanations of what math can be about for those of us who never studied it at the post-secondary level? The theoretical part that seems fun but is waayyy beyond my reach as someone who stopped after grade 12 precalc? I just want to have a vision of what I can't do, really.

You are awesome btw.

4. Originally Posted by Haphazard
so... you can't help me with my calc homework?
I may be able to.

Like I said, I won't do your homework for you.

But if you are having conceptual difficulties, and just trouble getting past a sticking poiny, I'll help.

5. Okay, I'll keep this in mind. I may be taking calc 2 in the fall.

6. what's the integral of e^x^2 dx ?

I can't seem to do it, so I plugged it into wolfram and it gave me this.
I don't understand the erfi function.

7. Originally Posted by Usehername
Oou. Can you also write about or link to explanations of what math can be about for those of us who never studied it at the post-secondary level? The theoretical part that seems fun but is waayyy beyond my reach as someone who stopped after grade 12 precalc? I just want to have a vision of what I can't do, really.

You are awesome btw.
Alright.
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First and foremost, people often believe that math has little application to "real life." I'd like to provide a general framework for getting people to apply mathematics to many things they encounter every day.
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The central notion (at least for now) is the notion of a set. If you can create some sort of set, you can do mathematics on it.
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The main concept to apply mathematics is the idea of "state." I am not sure the best way to describe it, because it is a mix of the real world and conscious choices for what abstractions you will use.

For instance, a light switch can be thought of as having two states, "on" and "off."

You can abstract the states of an 8 slice pizza as having 0 left, 1 slice left, ...8 slices left.

Note that these are both abstractions. Light switches are not just on or off, the 8 slice pizza is not fully modeled by the number of slices left, etc.

In quantum mechanics, states (as state vectors) are central to understanding the wave-particle duality, and other such seeming contradictions (it is neither a wave nor a particle, but simply a state)
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Next we move on to "state variables." Each set of states will have one or more variables associated with them. For instance the set of states describing the position of a particle may have three variables, the x-position, the y-postion, and the z-position. You may decide to ascribe the set of states of a particle with 6 state variables, the x-position, the y-postion, and the z-position, the x-momentum, the y-momentum, and the z-momentum.

Note there are sets associeted with the state variables also, meaning you can do mathematics on them.

One og the main ways of describing the world in mathematical models are with "equations of state" (though inequalities are common too).

For instance, for the 6 state variables used for the particle, the square root of the sum of variances in position variables multiplied by the square root of the sum of variances of the position variables is greater than or equal to the Planck Constant divided by 4*pi. This is the famous uncertainty principle.
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That's a little taste. The types of mathematics that can be done fall into 2 main categories: analysis and algebra (according to me, some will say three, topology, analysis, and algebra, and others four real analysis, complex analysis, topology, and algebra).

Analysis is the study of particular sets, or particular types of sets to understand the natures of these sets--I include complex and real analysis in this, and also toplogy.

Algebra is the study of operations on sets. Operations are things like addition and multiplication.

Of course the two categories of mathematics work in concert. But the flavors and "feel" are quite different. To me, analysis is more difficult than algebra.

8. Originally Posted by A Schnitzel
what's the integral of e^x^2 dx ?

I can't seem to do it, so I plugged it into wolfram and it gave me this.
I don't understand the erfi function.
The definition of erfi is given here.

Still I think the use of the DawsonF is more intuitive. With this the integral is e^(x^2)*F(x)+C.

To see how you get this, do repeated integration by parts.

1. set u=e^(x^2), dv=dx, meaning du=2*x*e^(x^2) and v=x
You'll get: integral(e^(x^2)*dx)=integral(u*dv)=u*v-integral(v*du)=x*e^(x^2)-intergral(2*x^2*e^(x^2)*dx)

2. repeat integration by parts, set u=e^(x^2), dv=2*x^2*dx, meaning du=2*x*e^(x^2) and v=(2/3)*x^3
You'll get: x*e^(x^2)-(2/3)*x^3*e^(x^2)+integral((4/3)*x^4*e^(x^2)*dx)

keep repeating this process, and you'll get e^(x^2)*F(x). You can prove this is true through mathematical induction, but I believe the pattern is clear.

I though int{e^(x^2) ] was more usually evaluated by squaring it, converting variables via r^2=x^2+y^2,evaluating using complex variables, and then taking the square root. Something involving a square root of Pi. Int[-inf,inf]e^x^2; Int[-inf,inf]e^x^2*e^y^2=[r^2=x^2+y^2] Int[r=0,r=inf, theta=0 to 2Pi]e^r^2, evaluate in complex variables [gamma function connection maybe???] to get that 2Pi* other constant and then take a square root

So how much do you know about PDE's? Non-linear PDE's? Solution methods to PDE's other than SoV's [ie integral transforms, greens functions, numerical, method of characteristics]?

How much do you know about, say, fluid dynamics or continuum mechanics?

How much math and physics background do you have? I remember you posting in a theoretical physics thread, I should comment on that if I can find it again.

10. Originally Posted by ygolo
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Things to note:
1. I will not do your homework for you
2. Service is provided as is
3. I may take my sweet time to respond
4. the focus will be on figuring out what math to use in particular situations, rather than plugging numbers into formulas or executing procedures just to get answers.
You lost me here.

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