Favourite 4U Topic (1 Viewer)

What is your favourite 4U topic?


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porcupinetree

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They totally should ask one though.
Well, the last question in the 2014 HSC was probably the hardest integral they'll ask (at least for a while). Just a simple reverse quotient rule, really. Unfortunately I see little hope for your type of integrals making an appearance in a HSC exam :p
 

Paradoxica

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Well, the last question in the 2014 HSC was probably the hardest integral they'll ask (at least for a while). Just a simple reverse quotient rule, really. Unfortunately I see little hope for your type of integrals making an appearance in a HSC exam :p
C'mon, at least have the floor function integral.
 

leehuan

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The syllabus can only ever fit in so many things. Though conics is a dud imo.

I didn't even know that a name called the floor function existed until someone in my class brought it up to the teacher for a graphs question, let alone integration. At the same time the ceiling function was crammed.

Seriously though, whilst I'd love a Mathematics Extension 3, whilst it does not exist there's no reason to torture the current Extension 2 students further
 

Paradoxica

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The syllabus can only ever fit in so many things. Though conics is a dud imo.

I didn't even know that a name called the floor function existed until someone in my class brought it up to the teacher for a graphs question, let alone integration. At the same time the ceiling function was crammed.

Seriously though, whilst I'd love a Mathematics Extension 3, whilst it does not exist there's no reason to torture the current Extension 2 students further
It's a fine line between pleasure and pain... :p

Besides, floor functions are elementary, they aren't even uni level.
 

leehuan

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There's so many things I'd put in 4U after getting rid of conics LOL that was a good choice by the board with the new syllabus.
 

leehuan

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Basically yeah. But it's also pointless algebra, as opposed to mechanics.
 

Zen2613

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I voted for harder 3 unit. To all people who said integration, I despise you. Out of all the topics integration probably has the least amount of variety and is the most straightforward. It's like you enjoy math the most when it is the most familiar to you and easiest...
 

Ekman

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Cant decide between integration and harder 3u, can I vote twice?
 

Paradoxica

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I voted for harder 3 unit. To all people who said integration, I despise you. Out of all the topics integration probably has the least amount of variety and is the most straightforward. It's like you enjoy math the most when it is the most familiar to you and easiest...
Pnly the HSC integrals are straightforward. You should explore tge previous and current integration marathons.
 

glittergal96

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While I do agree with your point on proving things, we are also able to prove integrals that computers cannot. There are many elementary symbolic antiderigatives that humans can find but computers cannot, which overlaps with the point I agree with. There are also many definite integrals/improper integrals that we can do in closed elementary form but computers are still unable to evaluate them. honestly, as long as the problem can be done succinctly and elegantly instead of bashing it to death with a computer stick, it's pretty neat.
Sure, there definitely are a class of functions that have elementary symbolic primitives that we can find that certain software cannot.

When it comes to something like engineering though, this skill is completely moot, as we need a numerical output. And doing symbolic gymnastics to reach something that can be cobbled out of elementary functions is unnecessary, as we then need to evaluate these functions anyway, which is done using convergent series.

On the purer side, my indifference towards (especially indefinite) integration is just that the mathematics is not very deep at all. We are using our bag of tricks to solve first order single variable ODE's of the form f'=g. With some fancy tricks we might be able to get an elementary f, but for most g we cannot. But so what? We can still obtain pretty much all the properties of f without an elementary symbolic expression for it, indeed most special functions are usually DEFINED by some sort of differential equation and we can still study them and use them.

Definite integration can be somewhat nicer, as then we can exploit symmetries and such to tackle things that we can't antidifferentiate. It's kind of like finding clever ways to sum infinite series.

They can be pleasing to solve, and they certainly can be difficult, but in themselves they just aren't all that interesting or deep to me. (And the kind of difficulty that comes with some of them is not the kind that satisfies me, even if I do solve them.)
 

DatAtarLyfe

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I like harder 3u for the induction. Conics is sick coz i like parametrics in 3u. Graphs and integration is also really fun. Lol, i just love 4u XD
 

Paradoxica

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Sure, there definitely are a class of functions that have elementary symbolic primitives that we can find that certain software cannot.

When it comes to something like engineering though, this skill is completely moot, as we need a numerical output. And doing symbolic gymnastics to reach something that can be cobbled out of elementary functions is unnecessary, as we then need to evaluate these functions anyway, which is done using convergent series.

On the purer side, my indifference towards (especially indefinite) integration is just that the mathematics is not very deep at all. We are using our bag of tricks to solve first order single variable ODE's of the form f'=g. With some fancy tricks we might be able to get an elementary f, but for most g we cannot. But so what? We can still obtain pretty much all the properties of f without an elementary symbolic expression for it, indeed most special functions are usually DEFINED by some sort of differential equation and we can still study them and use them.

Definite integration can be somewhat nicer, as then we can exploit symmetries and such to tackle things that we can't antidifferentiate. It's kind of like finding clever ways to sum infinite series.

They can be pleasing to solve, and they certainly can be difficult, but in themselves they just aren't all that interesting or deep to me. (And the kind of difficulty that comes with some of them is not the kind that satisfies me, even if I do solve them.)
Isn't that also decrying olympiad problems? They only use elementary theorems and lemmas to achieve things that cannot be done by other means. For example, functional equations, and inequalities cannot be bashed using calculus, and aren't subject to most, if not all analysis techniques.
This is basically the same as your comment on "bag of tricks" applied in a similar manner.
 

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