Jackpot's Posts
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 Education › Re: Nairaland Mathematics Clinic by jackpot(f): 12:03pm On Oct 22, 2013 |
yeah. I got it clearly. Your solution is excellent, compact and you used a totally different approach from mine. Even though your solution looks short, you lifted some things like the formula for the scale factors(h1, h2, h3) and that of the unit vectors Tu, Tv, Tphi. I bet if you included the derivations of those formulas, your solution would have clocked more pages  welldone, DoubleDx. Your solution is cool. 1 Like |
| Education › Re: Nairaland Mathematics Clinic by jackpot(f): 12:06am On Oct 22, 2013 |
As a corollary to the above. Assume that x depends on one variable u, viz, x=x(u). Differentiating both sides w.r.t. X, we have 1= Xu* Ux therefore, Ux=1/(Xu). This is the same as writing du/dx= 1/ (dx/du), which is the normal relationship between the two, in single variable calculus. |
| Education › Re: Nairaland Mathematics Clinic by jackpot(f): 11:58pm On Oct 21, 2013 |
Laplacian: ...pls Maths Generals i'm so curious 2 knw d relation connectn d derivative Ux and inverse derivative Xu of a PDE...help pls!!!!!!Given that x,y,z depends on three variables, viz, x=x(u,v,w), y=y(u,v,w), z=z(u,v,w), we know that the three transformed equations u=u(x,y,z), v=v(x,y,z), w=w(x,y,z) is non-degenerate if the Jacobian of the transformation doesn't vanish. Now, consider the equation x=x(u,v,w). Differentiating both sides partially w.r.t. x, we have 1=Xu Ux+ Xv Vx+ Xw Wx so, the relationship is Xu*Ux=1-(Xv Vx + Xw Wx) |
| Education › Re: Nairaland Mathematics Clinic by jackpot(f): 11:30pm On Oct 21, 2013 |
Laplacian: ...@Math*Generals...any solution 2 Rhydex247's questns?....@Jackpot...ur solution is pretty...our differencies came essentially from our methods of obtainin Ux,Vx..etc...evri other thing are same...pretty or sexy? As for me, the solution is kinda sexy i must confess, I equally learnt one or two things from the way you began your solution. It is refreshing to note that even though my first step is 100% different from yours, our first partial derivatives (and ultimately), our result essentially remains the same. |
| Education › Re: Nairaland Mathematics Clinic by jackpot(f): 8:00pm On Oct 21, 2013 |
Laplacian: ....d sum of d digits of a 2-digit number is 12, find d number if d produt of its digits must be a maximum...The number too is 10x+y the problem is Maximize F(x,y)=xy subject to x+y=12 0<=x,y<10. You may use the Lagrange multiplier method to solve. carefully solving it yields x=6, y=6. Thus, the number is 66. |
| Education › Re: Nairaland Mathematics Clinic by jackpot(f): 7:50pm On Oct 21, 2013 |
Laplacian: ...d sum of d digits of a 2-digit number is nine...find d number if it must b a maximum...The number is 10x+y The problem is maximize F(x,y)= 10x+y subject to x+y=9 10>x,y > 0 integers you may use Lagrange multiplier method. solve and you'll get x=5 or 4, y=4 or 5. Thus, the number is 54 or 45. Sorry, I am quite busy. |
| Education › Re: Nairaland Mathematics Clinic by jackpot(f): 6:46pm On Oct 21, 2013 |
doubleDx: 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*feels so happy* Alright dear. I dey expect your solution ooo **rolls my mat on the floor of the thread and lies down on it, and with phone in my hand, refreshing the page**  |
| Education › Re: Nairaland Mathematics Clinic by jackpot(f): 7:40pm On Oct 20, 2013 |
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 |
| Education › Re: Nairaland Mathematics Clinic by jackpot(f): 7:03pm On Oct 20, 2013 |
Laplacian: hahahahhaahhahah!!!! abeg no kill me oooo...na 4pgs d bring plenty analysis like dis?...na 12pgs...ahhahhahahahahaehen, na now you come i don begin feel say you be James Bond.  1 Like |
| Education › Re: Nairaland Mathematics Clinic by jackpot(f): 6:37pm On Oct 20, 2013 |
Laplacian: there's one more score 2 settlehehehe. Score kwa? No be competition oooo you be my oga na. Oya, feel free. Temper justice with mercy though |
| Education › Re: Nairaland Mathematics Clinic by jackpot(f): 6:29pm On Oct 20, 2013 |
Laplacian: wit my 40leaves notebook, it barely took 4pgslol, 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 |
| Education › Re: Nairaland Mathematics Clinic by jackpot(f): 6:09pm On Oct 20, 2013 |
Laplacian: pls can u give a description?...my mobil phone cant read dateeya, 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. |
| Education › Re: Nairaland Mathematics Clinic by jackpot(f): 5:59pm On Oct 20, 2013 |
@benbuks, doubleDx, rhydex247, d citizen, Laplacian and other colleagues, your comments on the solution please |
| Education › Re: Nairaland Mathematics Clinic by jackpot(f): 5:49pm On Oct 20, 2013*. Modified: 10:46pm On Oct 22, 2013 |
Here comes the full solution in PDF format. already downloaded it? I need your reviews |
| Education › Re: Nairaland Mathematics Clinic by jackpot(f): 5:46pm On Oct 20, 2013 |
^ No, am just curious to know how many sheets/pages it took you, and not really you posting it. Is it up to 10? |
| Education › Re: Nairaland Mathematics Clinic by jackpot(f): 5:24pm On Oct 20, 2013 |
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,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 |
| Education › Re: Nairaland Mathematics Clinic by jackpot(f): 3:35pm On Oct 20, 2013 |
cconcept: still waiting for a general to respondna advanced program be that. I attended a workshop on the sister program SCILAB, but I must say, I don forget the thing sef. I'd advise you google MATLAB User Groups. |
| Education › Re: Nairaland Mathematics Clinic by jackpot(f): 3:32pm On Oct 20, 2013 |
benbuks: @jackport..shr d link 2 ur solution,or wot do u think..?acknowledged, Sir. Will do that soon. Let first see what Laplacian's have got! @Laplacian let's go there.  post your solution na, pls |
| Education › Re: Nairaland Mathematics Clinic by jackpot(f): 2:46pm On Oct 20, 2013 |
@Laplacian am happy. Post the solution, please. |
| Education › Re: Nairaland Mathematics Clinic by jackpot(f): 2:05pm On Oct 20, 2013 |
hod898: Its simple! Here it goes:na this yeye subject of the formula (quadratic equation in "t" solutioned)question you wan take use put confusion as you insinuated? SMH. 1 Like |
| Education › Re: Nairaland Mathematics Clinic by jackpot(f): 1:05pm On Oct 20, 2013*. Modified: 2:11pm On Oct 20, 2013 |
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? |
| Education › Re: Nairaland Mathematics Clinic by jackpot(f): 6:03am On Oct 20, 2013 |
d citizen:@d citizen Thank God that you fully recovered. While you were away, Sire, we your boys and girl couldn't resolve this. So we said make we wait for our only 5 STAR Math General to helep us scatter am. jackpot: [color=indigo]dear Math Generals, pls help me with this little problem.Expecting your answer, Sire! |
| Education › Re: Nairaland Mathematics Clinic by jackpot(f): 10:21pm On Oct 19, 2013 |
Alpha Maximus: ....haha!! Doubledx is a disappointment!!Alpha Maximus, if you desist from posting here, we will understand. To tell you the truth, you still have a very long way to catch up in Mathematics. We know you have every right to comment wherever you want, but you see, with what I've seen, your commenting here is risky and you run the risk of infecting the unsuspecting Jambites among us with your wrong solution-right answers. Its not actually mostly your fault since you only teach and believe whatever was shoved down your throat by whom you called teachers, coupled with the fact that you dont know that the solutions are actually wrong. I am saying this with lots of love. Cheers! |
| Education › Re: Nairaland Mathematics Clinic by jackpot(f): 10:50am On Oct 19, 2013 |
doubleDx: You manipulated the law of log and you are here trying to justify what you did? That your answer is correct doesn't mean your workings is!lols. You've gat jokes my guy Maximus na Charge and Bail na 2 and half-star maths general 1 Like |
| Education › Re: Nairaland Mathematics Clinic by jackpot(f): 10:44am On Oct 19, 2013 |
doubleDx: I started solving it a few days ago but did not finish. I will try to get it done and post it. Take careok, no probs. I'll be waiting. Where is our self-acclaimed "Only 5 STAR Maths General" d citizen ? He should come and post his solution ooo @benbuks bros, do something na. 4 STAR no be beans |
| Education › Re: Nairaland Mathematics Clinic by jackpot(f): 7:05pm On Oct 18, 2013 |
Alpha Maximus: Taking log of both sides, we have:  |
| Education › Re: Nairaland Mathematics Clinic by jackpot(f): 6:46pm On Oct 18, 2013 |
doubleDx: Lol, I see una!no ooo. No mind benbuks oooo. He is a praise-singer. :-D How can I test my baba. I have actually learnt a lot from you i no sabi that kweshun sef. My problem is how to get the first partial derivatives like Ux, Uy, Uz. I know the chain rule well, but what and what should I substitute as my Ux, Uy, Uxx and co? Teach me na, pls |
| Education › Re: Nairaland Mathematics Clinic by jackpot(f): 6:41pm On Oct 18, 2013 |
Laplacian: ...Hello Jackpot, i am more than glad 2 recieve dis correction from u, sometin i'd neva thought of...i should infer dat u're by no means an amature. 4 if u were, u wouldn't 've debugd dat intricate error...now, usin d same notation,Applying the chain rule and product rule on Fu to get Fuu, we will have Fuu=(Fx *Xu+Fy Yu+Fz*Zu)u =(Fx *Xu)u +(Fy *Yu)u +(Fz*Zu)u =Fx * Xuu +(Fxx Xu +Fxy Yu + Fxz Zu)+ Fy * Yuu+ (Fyx Xu +Fyy Yu + Fyz Zu)+ Fz * Zuu + (Fzx Xu+ Fzy Yu + Fzz Zu) so, you see, there are nine variables, not 3 as you suggested. The variables are Fx, Fy, Fz, Fxx, Fxy=Fyx, Fxz=Fzx, Fyy, Fyz=Fzy, Fzz. so its no longer 3 equations in 3 unknowns. Besides, how will you make Fv and Fu appear in the solution? Or, how will you sieve out Fxx, Fyy and Fzz and ignore Fx, Fy, Fz, Fxy and others? This reverse approach may likely hit a dead end. |
| Education › Re: Nairaland Mathematics Clinic by jackpot(f): 6:06pm On Oct 18, 2013 |
benbuks: Still waitin 2c solution 2 jackport's enigma.yeah, me too. Where is my DoubleDx, Richiez and our 5 Star General d citizen? I have been refreshing this page since for DoubleDx's expected solution. |
| Education › Re: Nairaland Mathematics Clinic by jackpot(f): 2:20pm On Oct 18, 2013 |
Laplacian: i use Fx to denot derivatv of F w.r.t.x....let q denot phi nowHi Laplacian. I may have to comment on the bolded. You see, even though it works like that in ODE(ordinary differential equation) where we say dy/dx=1/(dx/dy), it doesn't work like that in PDE(partial differential equation). As an example, consider the polar coordinate transformation equations: x=r cos T, y=r sin T, where we use T to denote theta. Now xT=-r sin T. But observe that tan T= y/x implies sec2 T *Tx= -y/(x2) implies Tx= -y/(x2) * cos2 T =-y/(x2) * (x/r)2 =-y/(r2) =-(sin T)/r so you see, xT=-r sin T Tx=-(sin T)/r clearly Tx is not equal to 1/(xT ). Thanks for attempting it though. I am happy someone actually wanted to put a smile on my face  |
| Education › Re: Nairaland Mathematics Clinic by jackpot(f): 8:58pm On Oct 16, 2013 |
doubleDx: I'm on it, maybe I'll post tomorrow! Where is our 5 Star General (d citizen); I was waiting for you to post first. You are the Boss, Sire! @Jackpot, are you a Mathematician/Mathematics Student or an Engineer/Engineering Student?***Happy Mood Activated!!!*** maths student |
| Education › Re: Nairaland Mathematics Clinic by jackpot(f): 2:42pm On Oct 15, 2013 |
d citizen:Hi d citizen, good to know you are a 5-STAR Maths general. Pls help me with the solution to this problem that I posted earlier jackpot: dear Maths generals, pls help me with this little problem.any clue to solving it will also be appreciated. thanks! |
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