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Maths guru's ..... help needed

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Nick 50
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PostPosted: 11:01 - 15 Dec 2012    Post subject: Maths guru's ..... help needed Reply with quote
So i'm wondering if anyone can help with a problem i'm stuck with.

It's a Partial Differentiation problem and finding Stationary Points.

The problem:

https://i300.photobucket.com/albums/nn6/ElScampio/Maths_zps74166d91.jpg

As you can see, partially differentiating is no problem. I set both equations to 0.

The problems is now doing the maths where I have a singular value for either x or y which I can put back into the equations to solve for the other variable.
No matter which route I go down, I don't get anywhere near the answer.

Anyone any ideas?
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Tungtvann
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PostPosted: 11:13 - 15 Dec 2012    Post subject: Reply with quote
Yeah, gimme a sec. Just going to get a pencil and some paper...
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Nick 50
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PostPosted: 11:25 - 15 Dec 2012    Post subject: Reply with quote
Tungtvann wrote:
Yeah, gimme a sec. Just going to get a pencil and some paper...


Thanks and good luck........... you may need it. It has had quite a few people at Uni baffled. Laughing
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swampy
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PostPosted: 11:27 - 15 Dec 2012    Post subject: Reply with quote
Clearly the answer is potato hth.
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MCW
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PostPosted: 12:15 - 15 Dec 2012    Post subject: Reply with quote
Sorry to sound like my mother, but isn't the point of being set these questions for you to work out the answers, and thus learn something as you go?
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Im-a-Ridah
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PostPosted: 12:17 - 15 Dec 2012    Post subject: Reply with quote
Be interesting to see the results...

but computers FTW.
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hellkat
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PostPosted: 12:22 - 15 Dec 2012    Post subject: Reply with quote
MCW wrote:
Sorry to sound like my mother, but isn't the point of being set these questions for you to work out the answers, and thus learn something as you go?

But we're waiting for someone brainy to come along and tell us the answer AND how they achieved that answer.

I agree with swampy.
The answer is potato.

And my reason for that is that (everybody knows that) the back-to-front-6 is secret code for "This question looks complicated, but means nothing except for 'How much wood can a woodchuck chuck if a woodchuck could chuck wood?'"

... and of course the answer to that is ALWAYS "potato".
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MCW
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PostPosted: 12:24 - 15 Dec 2012    Post subject: Reply with quote
hellkat wrote:
But we're waiting for someone brainy to come along and tell us the answer AND how they achieved that answer.

I'll have a look at it later...
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Im-a-Ridah
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PostPosted: 12:28 - 15 Dec 2012    Post subject: Reply with quote
Have you tried...

https://www.google.com/search?q=partial+differentiation+stationary+points
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Nick 50
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PostPosted: 12:31 - 15 Dec 2012    Post subject: Reply with quote
MCW wrote:
Sorry to sound like my mother, but isn't the point of being set these questions for you to work out the answers, and thus learn something as you go?


I agree in theory.

This is of an revision sheet for exams I have in Jan. They do give answers to some of the questions. The idea of giving the answers is so you know you are doing it correctly and thus build up your confidence in what you are doing.
I'm only in the 1st year and the Maths part is vitally important for setting the underlying knowledge for the rest of the course. So I guess they do try and help so you understand as much as possible before we get hit with the complicated stuff in future years.

Im-a-Ridah wrote:
Have you tried...

https://www.google.com/search?q=partial+differentiation+stationary+points


I know the process for doing it and can happily do it for less complicated functions. This one though is seriously tough. Unfortunately no matter how much I try, my algebraic manipulation skills aren't good enough Crying or Very sad
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Im-a-Ridah
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PostPosted: 13:30 - 15 Dec 2012    Post subject: Reply with quote
Nick 50 wrote:
MCW wrote:
Sorry to sound like my mother, but isn't the point of being set these questions for you to work out the answers, and thus learn something as you go?


I agree in theory.

This is of an revision sheet for exams I have in Jan. They do give answers to some of the questions. The idea of giving the answers is so you know you are doing it correctly and thus build up your confidence in what you are doing.
I'm only in the 1st year and the Maths part is vitally important for setting the underlying knowledge for the rest of the course. So I guess they do try and help so you understand as much as possible before we get hit with the complicated stuff in future years.

Im-a-Ridah wrote:
Have you tried...

https://www.google.com/search?q=partial+differentiation+stationary+points


I know the process for doing it and can happily do it for less complicated functions. This one though is seriously tough. Unfortunately no matter how much I try, my algebraic manipulation skills aren't good enough Crying or Very sad


Are you studying maths?
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Skudd
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PostPosted: 13:36 - 15 Dec 2012    Post subject: Reply with quote
Just out of interest, what would you use this for and why. It used to cheese me off that when I was doing maths at school all those years ago, the tutors couldn't put things into real world situations, but since then I have come across load of things that the maths would have helped with, you have to remember though that I come from a time when we had to look up cos, tan, sin in a little book and no calculators were permitted.
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Pete.
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PostPosted: 13:39 - 15 Dec 2012    Post subject: Reply with quote
Quote:
Just out of interest, what would you use this for and why.


Helping out pretty maths students with a view to getting your nuts in?
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Nick 50
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PostPosted: 13:43 - 15 Dec 2012    Post subject: Reply with quote
Im-a-Ridah wrote:


Are you studying maths?


Thankfully not, i'm studying Mechanical Engineering.

Skudd wrote:
Just out of interest, what would you use this for and why. It used to cheese me off that when I was doing maths at school all those years ago, the tutors couldn't put things into real world situations, but since then I have come across load of things that the maths would have helped with, you have to remember though that I come from a time when we had to look up cos, tan, sin in a little book and no calculators were permitted.


Laughing I will try my best to explain in the limited knowledge I have.

Partial Differentiation is used when you have normally 2 independent variables in a a equation.

An analogy of sorts is Power of a bike engine. The Power depends on lots of differing things which can change independently of the others, e.g fuel mixture, revs used, temperature etc etc.

Partial differentiation allows you to analyse how Power output would change if you affected one of the input factors. It allows you to say "Well if I hold all the variables constant except for the fuel mixture, what would happen to the power output if I changed it?". Then you could hold fuel mixture constant and then change the revs and see how that will affect the Power etc etc.

Stationary Points allow you to identify when no change occurs. So if you anaylsed say changing the fuel mixture and differing the revs, is there any point on the power curve where there is no increase (a flat spot of sort)?

The link below explains it (probably better than I have) using hills:

https://www2.imperial.ac.uk/metric/metric_public/partial_differentiation/applications/stationary_points.html

In Engineering, many many things will have more than 1 thing changing. So Partial Differentiation is a "biggy" thing to understand.

Hope that makes some sense.
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Last edited by Nick 50 on 13:57 - 15 Dec 2012; edited 2 times in total
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noobRider
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PostPosted: 13:48 - 15 Dec 2012    Post subject: Reply with quote
Does this help?

Also Monkey Saddles ...

or this
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Lurkio
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PostPosted: 13:52 - 15 Dec 2012    Post subject: Reply with quote
Use the first equation to find y in terms of x. Plug this into the second. Rearrange to find a quartic. NB x^4 = (x^2)^2
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lihp
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PostPosted: 13:56 - 15 Dec 2012    Post subject: Reply with quote
Nick 50 wrote:


Thankfully not, i'm studying Mechanical Engineering.


Balls, I start my Mech Engineering in Feb, now I have that to look forward to Sad
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Nick 50
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PostPosted: 14:01 - 15 Dec 2012    Post subject: Reply with quote
noobRider wrote:
Does this help?

Also Monkey Saddles ...

or this


Thumbs Up

I fired it into Wolfram Alpha and it helps in show where the max,min and saddle points are on the plot.
Unfortunately it doesn't explain how they got the answer Crying or Very sad

Lurkio wrote:
Use the first equation to find y in terms of x. Plug this into the second. Rearrange to find a quartic. NB x^4 = (x^2)^2


Yep, I know the process of doing it and can do it with simpler functions. It's just this function is pretty tough and i've struggled getting from equation to 0, to getting to the stationary point co-ordinates.

PhilDawson8270 wrote:


Balls, I start my Mech Engineering in Feb, now I have that to look forward to Sad


Good choice.

What you level are you studying and where at?

There are few on here that have Engineering degrees or currently doing it, so if you have an issue, this is a good place to start.

But as you've guessed, Mech Engineering is very heavy in Maths.
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T0MMY
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PostPosted: 14:06 - 15 Dec 2012    Post subject: Reply with quote
Pete. wrote:

Helping out pretty maths students with a view to getting your nuts in?


Good luck with that Laughing
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lihp
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PostPosted: 14:17 - 15 Dec 2012    Post subject: Reply with quote
Nick 50 wrote:


Good choice.

What you level are you studying and where at?


Bachelors, though it's mechanical engineering design, but core modules will more than likely be similar, studying with open university as I still need to stay in full time work Sad I have been working in engineering for years, but maths will be a struggle initially!
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Lurkio
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PostPosted: 14:19 - 15 Dec 2012    Post subject: Reply with quote
3x^2 + 2xy - 4 = 0 gives y = (4 - 3x^2)/2x

Stop telling yourself this is difficult and just do it.
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Pete.
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PostPosted: 15:16 - 15 Dec 2012    Post subject: Reply with quote
T0MMY wrote:
Pete. wrote:

Helping out pretty maths students with a view to getting your nuts in?


Good luck with that Laughing


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

Smile
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Skudd
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PostPosted: 15:21 - 15 Dec 2012    Post subject: Reply with quote
Nick 50 wrote:
Im-a-Ridah wrote:


Are you studying maths?


Thankfully not, i'm studying Mechanical Engineering.

Skudd wrote:
Just out of interest, what would you use this for and why. It used to cheese me off that when I was doing maths at school all those years ago, the tutors couldn't put things into real world situations, but since then I have come across load of things that the maths would have helped with, you have to remember though that I come from a time when we had to look up cos, tan, sin in a little book and no calculators were permitted.


Laughing I will try my best to explain in the limited knowledge I have.

Partial Differentiation is used when you have normally 2 independent variables in a a equation.

An analogy of sorts is Power of a bike engine. The Power depends on lots of differing things which can change independently of the others, e.g fuel mixture, revs used, temperature etc etc.

Partial differentiation allows you to analyse how Power output would change if you affected one of the input factors. It allows you to say "Well if I hold all the variables constant except for the fuel mixture, what would happen to the power output if I changed it?". Then you could hold fuel mixture constant and then change the revs and see how that will affect the Power etc etc.

Stationary Points allow you to identify when no change occurs. So if you anaylsed say changing the fuel mixture and differing the revs, is there any point on the power curve where there is no increase (a flat spot of sort)?

The link below explains it (probably better than I have) using hills:

https://www2.imperial.ac.uk/metric/metric_public/partial_differentiation/applications/stationary_points.html

In Engineering, many many things will have more than 1 thing changing. So Partial Differentiation is a "biggy" thing to understand.

Hope that makes some sense.


Thumbs Up I get it.
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swampy
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PostPosted: 15:39 - 15 Dec 2012    Post subject: Reply with quote
hellkat wrote:
MCW wrote:
Sorry to sound like my mother, but isn't the point of being set these questions for you to work out the answers, and thus learn something as you go?

But we're waiting for someone brainy to come along and tell us the answer AND how they achieved that answer.

I agree with swampy.
The answer is potato.

And my reason for that is that (everybody knows that) the back-to-front-6 is secret code for "This question looks complicated, but means nothing except for 'How much wood can a woodchuck chuck if a woodchuck could chuck wood?'"

... and of course the answer to that is ALWAYS "potato".


Ahh yes, King Edwards theorem.... Very pertinent in this case...
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"Faster, faster, faster, until the thrill of speed overcomes the fear of death..." Hunter S Thompson
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T0MMY
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PostPosted: 16:00 - 15 Dec 2012    Post subject: Reply with quote
Pete. wrote:

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

Smile


https://www.thesundaytimes.co.uk/sto/multimedia/dynamic/00305/STR11WIN01_305195k.jpg

https://i1.ytimg.com/vi/p-16uZCXZfw/hqdefault.jpg

I stand corrected Laughing
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