Math Is Fun Forum

harrorm

Member

Registered: 2016-06-27

Posts: 8

Reccurence problem - Need clear explanation

Hi,

I was watching the MIT video lectures and at the 25:17 mark, the instructor talks about residual. Can someone please give a clear explanation why he subtracted 1/2cn^3? I'm pretty bad at math, so I would really appreciate it if the explanations are clear as if I don't know anything!

Vid lecture: https://youtu.be/whjt_N9uYFI?t=25m17s

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Reccurence problem - Need clear explanation

Hi;

Why are you starting out with MIT videos if your math is shaky? Should you not have tried something easier?

The residual usually means the difference between the calculated value and the true value.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

harrorm

Member

Registered: 2016-06-27

Posts: 8

Re: Reccurence problem - Need clear explanation

Thanks for the reply! Well it's part of an online class I'm taking so no way to get around it. The part I'm confused about is that he set cn^3 to to 1/2cn^3 + n. So wouldn't subtracting 1/2cn^3 from itself be zero? Why would it be cn^3?

Last edited by harrorm (2016-06-28 01:55:40)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Reccurence problem - Need clear explanation

In algebra yes but this is not algebra. First of all I would think (1/2) c n^3 = c n^3, the 1 / 2 just gets absorbed into the constant c. Could be too that c n^3 = c n^3 + n because the n^3 is the dominant term and as n gets large the n^3 drowns out the n. But, are we talking about when n gets very large?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

harrorm

Member

Registered: 2016-06-27

Posts: 8

Re: Reccurence problem - Need clear explanation

n is defined as sufficiently large n. So he does this in the video: cn^3 - (1/2cn^3 - n) to get the final answer as <= cn^3.

Last edited by harrorm (2016-06-28 03:08:48)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Reccurence problem - Need clear explanation

That looks okay to me but I am hardly an expert.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Reccurence problem - Need clear explanation

---

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

harrorm

Member

Registered: 2016-06-27

Posts: 8

Re: Reccurence problem - Need clear explanation

I'm not asking if the step is correct. I'm asking for an explanation as to why subtracting (1/2cn^3 - n) from 1/2cn^3 + n results in cn^3. That's what I need help understanding, like why did he subtract that instead of anything else.

Last edited by harrorm (2016-06-28 09:35:07)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Reccurence problem - Need clear explanation

He does

cn^3 - ((1/2)cn^3-n) = ((1/2)cn^3 + n)

So

cn^3 = ((1/2)cn^3-n) + ((1/2)cn^3 + n)

What part of the vid do you see

subtracting (1/2cn^3 - n) from 1/2cn^3 + n results in cn^3

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

harrorm

Member

Registered: 2016-06-27

Posts: 8

Re: Reccurence problem - Need clear explanation

Well he originally had: ((1/2)cn^3 + n)
Then he said to rewrite that as: cn^3 and minus what he didn't want, so he ended up with: cn^3 - ((1/2)cn^3 - n).

= ((1/2)cn^3 + n)
= cn^3 - ((1/2)cn^3 - n)
<= cn^3

How did he get to the final line (<= cn^3). It seems like there are steps in between that I'm not understanding?

Last edited by harrorm (2016-06-30 13:47:03)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Reccurence problem - Need clear explanation

What steps?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Reccurence problem - Need clear explanation

It is just like saying  6-2 <6

---

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}