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[ZetaX]

Spehss_?
Please stop scaring me.

Spoiler: *eldritch noises* (click to show/hide)

Yes, this is actually maths. I actually need to condense half a book's worth of this stuff into a bachelor's thesis.

What kind of evil professor gives horribly technical stuff like stacks as a bachelor thesis' topic¿

[Arx]

Pseudoedit: Also what Ispil said. Markers tend to be anal about simplification at this level of calc.

My experience is the opposite. Once you get to calculus, it's all about the process, not about algebra. Usually if your answer is an unsimplified form, they'll accept it. The answer is only 1 point anyways.

For the more complicated calculus, fully agreed. For the more basic stuff with trivial simplification steps, I often find there's a mark for it.

[MagmaMcFry]

Spehss_?
Please stop scaring me.

Spoiler: *eldritch noises* (click to show/hide)

Yes, this is actually maths. I actually need to condense half a book's worth of this stuff into a bachelor's thesis.

What kind of evil professor gives horribly technical stuff like stacks as a bachelor thesis' topic¿

Technically it's sort of my own fault, I asked my Algebraic Geometry prof for a topic involving singularities and he started talking about reducing singularities on projective curves and also the Stable Reduction Theorem. The second part seemed pretty intuitive when he explained it, but apparently it was way more complicated in theory. We talked about it today and apparently he didn't actually expect me to do that theorem, but he didn't tell me because he wanted to see if I could actually pull it off (spoiler alert: I can't, I have way less than the necessary foundations). So that's nice, I can stop having nightmares about impenetrable textbooks and missing deadlines now.

[TheBiggerFish]

Ugh.  How do you even nest chain rule derivatives?  How do you even nest chain rule into other rules for that matter?
This is the last question on this worksheet:
(x²-2)⁴(3x+4)⁵
Heeeellllpppp.

[crazysheep]

You want the product rule for derivatives for that last one.

[Culise]

Ugh.  How do you even nest chain rule derivatives?  How do you even nest chain rule into other rules for that matter?
This is the last question on this worksheet:
(x²-2)⁴(3x+4)⁵
Heeeellllpppp.

Welp, let's start with the basics of a chain rule, using Leibnitz notation since it's easier to visualize here:

Code: [Select]

Dy   Dy   Du
-- = -- * --
Dx   Du   DxNow, to nest these together, you can just apply it to the bits inside:

Code: [Select]

Dy   Dy   Dv
-- = -- * --
Du   Dv   Du

Dy   ┌ Dy   Dv ┐   Du
-- = │ -- * -- │ * --
Dx   └ Dv   Du ┘   Dx
So, for example, if you did an equation y = e^5x2, you'd have:

u(x) = 5x²
y(u) = e^u (just substitute u in by using the above)

Dy/Du = e^u
Du/Dx = 10x
Dy/Dx = Dy/Du * Du/Dx = e^u * 10x = 10x * e^5x2

However, in this case, you're not really nesting the chain rule.  It's much easier to look at your function as the product of two functions multiplied together, where your two functions are (x²-2)⁴ and (3x+4)⁵.  So, I suppose the questions first are:
(a) Have you learned the product rule for derivatives, and
(b) Are you allowed to use it for this function, or are the instructions so very specific about the intended method you're supposed to use that you must use the chain rule? 

EDIT:
Oh, I think I might see what you're asking.  Are you just having trouble using the chain rule on each of these component functions?  It might help you out just to treat each one as its own problem.  Take the derivative of one of the component functions using the chain rule, then take the derivative of the other function using the chain rule, then plug each of those derivatives into the product rule to come out with your final answer. 

So, to elaborate, you've got your function f = g * h.  To find f' (feeling lazy, so now it's Lagrangian notation), find g' and h' by whatever means necessary (the chain rule, here, like the other problems on your worksheet), then use those in the product rule (g * h)' = g' * h + g * h'.  No special tricks, but feel free to point out where you're having trouble if there's an issue. 

EDIT 2: Glitched out on some of the notation.  Should be corrected now.  Also elaborated on the edit a bit. 

[TheBiggerFish]

That makes sense.  Thankye.

[bahihs]

Can I post some complex analysis stuff from this book?

Is there anyone here who knows complex analysis? I'm having a lot of trouble understanding the convergence of complex power series.

[ZetaX]

Spehss_?
Please stop scaring me.

Spoiler: *eldritch noises* (click to show/hide)

Yes, this is actually maths. I actually need to condense half a book's worth of this stuff into a bachelor's thesis.

What kind of evil professor gives horribly technical stuff like stacks as a bachelor thesis' topic¿

Technically it's sort of my own fault, I asked my Algebraic Geometry prof for a topic involving singularities and he started talking about reducing singularities on projective curves and also the Stable Reduction Theorem. The second part seemed pretty intuitive when he explained it, but apparently it was way more complicated in theory. We talked about it today and apparently he didn't actually expect me to do that theorem, but he didn't tell me because he wanted to see if I could actually pull it off (spoiler alert: I can't, I have way less than the necessary foundations). So that's nice, I can stop having nightmares about impenetrable textbooks and missing deadlines now.

Sounds a bit evil to do, but I can understand his motivations. Now that I think about it: I am really different in giving very hard (IMO and such) problems to students that are training for regional or national olympiads, because that was also mostly to see if they can solve them (some very few sometimes succeed). If I shall ever get to that point I might try that with my own students (PhD student close to the finish here).

My knowledge about stacks is pretty lacking (only knowing the basics), but I saw enough to know that this is far too technical for what I would like to work with.

Can I post some complex analysis stuff from this book?

Is there anyone here who knows complex analysis? I'm having a lot of trouble understanding the convergence of complex power series.

There are several as far as I know. Just carry on with the questions. Definitely not as hard as the stacks mentioned above ;-)

[bahihs]

@Zetax Regarding the stacks, I'll take your word for it

Let me start at the beginning then because there were a lot of things I had trouble with working through the book.

First, in the forward, the author mentions a geometric approach to calculus created by Newton. I was wondering where I might find a book that explores this (or do I have to read the Principia?)

[ZetaX]

First, in the forward, the author mentions a geometric approach to calculus created by Newton. I was wondering where I might find a book that explores this (or do I have to read the Principia?)

I have not heard of this before (it probably falls under "history of mathematics" more than under calculus; and I don't know much about such), but I can imagine it being related to the usual visualisations (derivatives as slopes of tangents, integrals as areas under a curve).

[Reelya]

https://en.wikipedia.org/wiki/History_of_calculus

Newton needed to develop calculus to compute his motion equations.

https://en.wikipedia.org/wiki/Method_of_Fluxions

[RoguelikeRazuka]

Spehss_?
Please stop scaring me.

Spoiler: *eldritch noises* (click to show/hide)

Yes, this is actually maths. I actually need to condense half a book's worth of this stuff into a bachelor's thesis.

What kind of math is it? Wanna get MORE like this.

Hey everybody what areas of mathematics should I get into first in order to gently approach group theory then? Now I'm trying my best to comprehend set theory and topology, and it kind of goes allright so far (even though I generally suck at math).

I also had some of calculus back in the day, but I feel there's no firm soil under my knowledge. Could some suggest a decent textbook on calculus? 

One more thing -- to the mathematicians of this forum -- how many hours a day do you guys dedicate to mathematics?

[bahihs]

Another question from my stat class:

(a) Suppose that your prior for µ is 2/3:1/3 mixture of N(0, 1) and N(1, 1), and that a single observation is made x ∼ N(µ, 1) and turns out to be equal to 2. What is the posterior probability that µ > 1?

First, I know that the prior is a mixture of normal distributions, so I am wondering if I can just add them (since a linear combination of normals is also normal)?

Second I know I have to use a Bayesian approach to calculate the posterior probability, however I am having trouble figuring out what to condition on. The observation that is given doesn't seem to make sense, since, we are talking about densities so that the probability of getting any particular value is 0.

Am I supposed to use the dirac function to circumvent this?

Any help would be much appreciated.

[Powder Miner]

THERMOCHEMISTRY EQUATION QUESTION (that I'm much too tired for):
If I have 90.0 g of 22.0 C water, how many g of 55.0 C water do I need to reach a total temperature of 37 degrees Celsius?
What is the structure of the equation I use for this?