Laplacian:
first i need to point out 2 u dat in PDE one can take d differental of an eqn b4 proceedin 2 d limt witout fear of error...it is rigorous & not an assumption...wit our former notation; now x=uvsinq, y=uvcosq, z=0.5(u^2-v^2), like b4,
Fx=Fu*Ux+Fv*Vx+Fq*Qx...to get Ux, Vx, and Qx we take d differential of d transformation equations; first we take Log of x=uvsinq,
Logx=logu+logv+logsinq, let d denot delta, so dat
1/x*dx=1/u*du+1/v*dv+1/sinq*cosq*dq, divide thru by dx and proceed 2 d limt;
1/x=1/u*Ux+1/v*Vx+cotq*Qx, similarly for y=uvcosq,
logy=logu+logv+logcosq,
1/y*dy=1/u*du+1/v*dv-1/cosq*sinq*dq, divide thru by dx but this time partial derivativ of y w.r.t.x is zero since x and y are independent variables;
0=1/u*Ux+1/v*Vx-tanq*Qx...again for z=0.5(u^2-v^2),
dz=udu-vdv, dividin by dx;
0=uUx-vVx...from d 3 eqns above solve 4 Ux, Vx and Qx...in d eqns above, divide, respectively, by dy and dz to obtain Uy, Vy, Qy and Uz, Vz, Qz...substitute and differentiat Fx,Fy,Fz respectively...u 'll obtain ur answer as i 've done here after simplification...

well, the only lil' harmless mistake is the bolded, cos you swapped the definitions of x and y. apart from that, your method is correct so far.

Why not, for fun-sake, complete the solution? I really want to know whether the solution will be shorter

jackpot: well, the only lil' harmless mistake is the bolded, cos you swapped the definitions of x and y. apart from that, your method is correct so far.

Why not, for fun-sake, complete the solution? I really want to know whether the solution will be shorter

u certainly dont xpect me 2 do all dat computatin here...like i told u b4, d solutn is right here wit me...just follow d recipe...u can as well describ ur own method if u dont mind...

^



No, am just curious to know how many sheets/pages it took you, and not really you posting it.

Is it up to 10?

Here comes the full solution in PDF format.


already downloaded it? I need your reviews

jackpot: ^



No, am just curious to know how many sheets/pages it took you, and not really you posting it.

Is it up to 10?

wit my 40leaves notebook, it barely took 4pgs

jackpot: Here comes the full solution in PDF format.


@Readers, pls download it. I need your reviews

pls can u give a description?...my mobil phone cant read dat

1. Show that V=IR^2 is not a vector space over IR with respect to operation (a,b)+(c,d)=(a+c,b+d) and k(a,b)=(ka,kb).

2. Show that the vectors u=(1,2,3), v=(0,1,2) and w=(0,0,1) span R^3.
Hmmm. All is well.

Laplacian:
pls can u give a description?...my mobil phone cant read dat

eeya, your phone doesnt have PDF reader? You can still view it via a PC.

Description?
I obtained Ux, Uxx, Vx, Vxx, Qx, Qxx, Uy, Uyy, Vy, Vyy, Qy, Qyy, Uz, Uzz, Vz, Vzz, Qz, Qzz.

Next, I obtained the expressions for Fxx, Fyy and Fzz which I added and simplified. Later, I equated everything to zero.

jackpot: eeya, your phone doesnt have PDF reader? You can still view it via a PC.

Description?
I obtained Ux, Uxx, Vx, Vxx, Qx, Qxx, Uy, Uyy, Vy, Vyy, Qy, Qyy, Uz, Uzz, Vz, Vzz, Qz, Qzz.

Next, I obtained the expressions for Fxx, Fyy and Fzz which I added and simplified. Later, I equated everything to zero.

there's one more score 2 settle

Laplacian:
wit my 40leaves notebook, it barely took 4pgs

lol, I bet you that solving for Ux, Vx and Qx simultaneously from what you posted earlier will take more than a page.

Next, you will still apply your same approach to obtain Uy, Vy and Qy and it will take up to the same number of pages.

Next, you still do same for Uz, Vz and Qz. This will equally take its own page.

At least, 3 pages don go oooooo

And that is just for first partial derivatives ooo.

We neva consider how much pages the second partial derivatives (Uxx, Vxx, Qxx, Uyy, Vyy, Qyy, Uzz, Vzz, Qzz) will take. For each, you will apply quotient rule which takes, at least, 4 lines for each.

You will still obtain chain rules formula for Fxx, Fyy and Fzz.

Then, add and come simplify.(at this point, you will basically do the same thing I did, same fixed step. My own addition and simplification is 3 pages.)

All that in 4 pages! Bro, come on! Small salt dey am

Laplacian:
there's one more score 2 settle

hehehe. Score kwa? No be competition oooo
you be my oga na.

Oya, feel free. Temper justice with mercy though

jackpot: hehehe. Score kwa? No be competition oooo
you be my oga na.

Oya, feel free. Temper justice with mercy though

na learn i want learn ooo..no vex..since
Ux#1/Xu, which relation d connect Ux and Xu

jackpot:
lol, I bet you that solving for Ux, Vx and Qx simultaneously from what you posted earlier will take more than a page.

Next, you will still apply your same approach to obtain Uy, Vy and Qy and it will take up to the same number of pages.

Next, you still do same for Uz, Vz and Qz. This will equally take its own page.

At least, 3 pages don go oooooo

And that is just for first partial derivatives ooo.

We neva consider how much pages the second partial derivatives (Uxx, Vxx, Qxx, Uyy, Vyy, Qyy, Uzz, Vzz, Qzz) will take. For each, you will apply quotient rule which takes, at least, 4 lines for each.

You will still obtain chain rules formula for Fxx, Fyy and Fzz.

Then, add and come simplify.(at this point, you will basically do the same thing I did, same fixed step. My own addition and simplification is 3 pages.)

All that in 4 pages! Bro, come on! Small salt dey am

hahahahhaahhahah!!!! abeg no kill me oooo...na 4pgs d bring plenty analysis like dis?...na 12pgs...ahhahhahahahaha

Laplacian:
hahahahhaahhahah!!!! abeg no kill me oooo...na 4pgs d bring plenty analysis like dis?...na 12pgs...ahhahhahahahaha

ehen, na now you come

i don begin feel say you be James Bond.

...pls Maths Generals i'm so curious 2 knw d relation connectn d derivative Ux and inverse derivative Xu of a PDE...help pls!!!!!!

i will investigate later. I sense it may have to do with the Jacobian of the transformation.

Other generals, pls help Laplacian if you are chanced

I can't view the pdf file @ jackpot. Buh nevertheless i will see what i can do to that. Laplacian,d citizen, doubledx,jackpot,benbuks,alphamux nd oda maths general make una help me solve my questn.

jackpot: @benbuks, doubleDx, rhydex247, d citizen, Laplacian and other colleagues, your comments on the solution please

,ok, i av dowloaded it,i will try and get a pc 2 view it better..maybe 2maro..

rhydex 247: 1. Show that V=IR^2 is not a vector space over IR with respect to operation (a,b)+(c,d)=(a+c,b+d) and k(a,b)=(ka,kb).

2. Show that the vectors u=(1,2,3), v=(0,1,2) and w=(0,0,1) span R^3.
Hmmm. All is well.

let u, v and w be elements of S, the span of R^3, then there exist x, y and z € R such that
xU+yV+zW=Q, for some Q€S, so
Q=x(1,2,3)+y(0,1,2)+z(0,0,1)=
(x, 2x+y, 3x+2y+x) hence S is contained in R^3. Now suppose
u, v and w are in R^3, then we show that there exist x, y and z for every vector
(p, q, r) for which u, v and w combine linearly...let
xU+yV+zW=(p,q,r) then
x(1,2,3)+y(0,1,2)+z(0,0,1)=(p,q,r) or
(x, 2x+y, 3x+2y+z)=(p,q,r) so that
x=p
2x+y=q
3x+2y+z=r, hence for any choosen vector (p,q,r) we can find x=p,
y=q-2p and z=r+p-2q for which the vectors u, v and w are combined linearly, so R^3 is contained in S...hence
SpanR^3=(u,v,w)....all is well

@ laplacian,

Relationship bt Ux and xu derivative can be obtained by jacobian method. I know dat the problem posed by jackpot involved jacobian method. That is why i am yet to provide a detailed solution to the problem. I am even planning to go to ikeja library if i am on night shit to get input from engineering math to deal with the problem. Jackpot, u are welcomed on board and i are very happy dat we are having a sound female mathematician in the house. Jackpot, u must be possessed with 7 golden spirits of math, lol. Math goes beyond the physical realm becos it is a tool dat help us to understand the physical and abstract world. It is a driving force behind civilisation. It is practically impossible to imagine civilization dat is worth sacrifices and dreams without a sound intellectual framework in math. Jackpot, once again, u are welcome on board. To laplacian, i salute ur math ingenuity and astuteness. The five star general

.

Dekins88: chai bros, can't just believe all these are from you. You disappointed me big time, you are one of the nairalanders i really respect for being humble, can't you just abandon that mediocre, he is not ready to learn,
Imagine him requesting for your CGPA just because someone else corrected you, na too know they kill some folks sha.

Sorry bros, I wasn't myself; I have never insulted anyone on this forum b4. Anyway, I'm sorry for acting that way; the guy wasn't polite. My comment about demoting him was only a joke & he took it far! He is a good Mathematician anyway, I respect that....Let's all squash the issue & thanks for your comment!

jackpot: Ok, fellow STARRED generals.

As regards to my question, I got the Cartesian-Paraboloidal transformation equations and I knew that Laplace equation have its equivalent in other curvilinear coordinates(like Spherical, Polar, Cylindrical coordinates, etc). So, I decided to obtain the equivalent of the Laplace's equation in Paraboloidal coordinates. I did and I posted it here. So, I have actually attempted that question, and I got the answer.

I posted the question here for a purpose. Not that I wanted to test us. No, not that. I wanted to see how others will solve it.

Reason?

My solution was a 10-paged CRACKER. Are you kidding me? Should that be the only way? Isn't there another shorter method? So, thats why I posted it.

Now, I can share the solution, but I must say, I got it typed in PDF format.

So, fellow generals benbuks, DoubleDx, d citizen, Richiez, etc. decide. Can one upload PDF here, and should I?

It's crazy really, I'm still on it....will post mine today or tomorrow! Sorry to y'all for what happened between Alpha & I! 1luv

Alpha Maximus: Alright I'm gonna post a question and no matter how simple it appears just try to solve it! I'm not joking here. As far as it isn't x+1=2, that counts right?
Question: As they say, beggars can't be choosers. A beggar is able to make one cigarette out of every six cigarette butts he finds. After a day of perusing and ransacking public ashtrays, he finds a total of 72 cigarette butts. How many cigarettes can the beggar make and smoke from the butts he found?
P.S: even if you think this is still a joke, at least you know the solution won't take time, chacha!!

.....12 bro

Alpha Maximus: .....seriously, are you guyz kidding me(no offence intended before you guyz blast your sirens again!!) My good man Cashio already attempted the question!! So no-one else is gonna try out this simple thing? *slowly azontos away in disappointment*

none

Hmm.

Alpha Maximus: Thanks for answering!!! You got it WRONG!!!!!!! Another considerate mathematician paid attention to my post!!! Attempt appreciated......I need 4 more attempts/answerrs/criticisms before I post the solution!!!

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