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Could someone help me with this question? Because I'm stuck and have no idea how to solve it & it's due tomorrow :( Let S be the following subset of the vector space P_3 of all real polynomials p of degree at most 3: S={p∈ P_3 p(1)=0, p' (1)=0} where p' is the derivative of p...
2. ### Partial differential equation-delta Dirac& Heaviside function!

Well... that's the name of the math course I'm doing so yeah I think my p/f is wrong and my teacher way is right 1/s e^10s (s^2+4s+5) transform to and then you just look up the table =1/5 [(1/s -s+2/(s+2)^2+1 -2/(s+2)^2+1 ]e^-10s
3. ### Partial differential equation-delta Dirac& Heaviside function!

Well I know the Laplace you are talking about, I was using it for question 1. For an example 3/(s+3)^3 Y(t)= 3/2 t^2 e^-3t I usually do the algebra way but this question is too hairy so that's why I'm not sure if my working out is correct so if you could work your way and compare to my...
4. ### Partial differential equation-delta Dirac& Heaviside function!

Yes, I did. Sometime its hard to rearrange function for inverse lagrange. I managed to work out the solution for question 3. So could you or someone check my question 2 please!
5. ### Partial differential equation-delta Dirac& Heaviside function!

I got 2 questions to ask! I have finished one but not sure if it's correct so I need to double check with someone :) http://imageshack.us/a/img708/1324/83u8.png [Broken] Here is my worked solution, I took this picture with my S4 and I wrote is very neatly as I could! The reason I didn't type...
6. ### Vector calculus for ellipse in polar coordinates

sorry I type it all up on my phone and when I submit it it's so messy... so you are saying my integral y^4/4 must equal to fz which is z So the final answer is F=x^4/4 -3x^2y^2/2 +y^4/4 +z^2/2
7. ### Vector calculus for ellipse in polar coordinates

Can you please check this question for me because my answer is different to my friends and they say its wrong... Given the equation: G= (x^3 -3xy^2)I +(y^3-3x^2y)j +2k is conservative find the potential function for the fields that are conservative My answer f:grad f=F fx=x^3-3xy^2...
8. ### Vector calculus for ellipse in polar coordinates

Is this right? Can somebody double check this for me? It seem right to me... (x−1)²/9 + y²/8 = 1 8(x−1)² + 9y² = 72 8x² − 16x + 8 + 9y² = 72 9(x²+y²) − x² − 16x + 8 = 72 9(x²+y²) = x² + 16x + 64 9(x²+y²) = (x + 8)² 9r² = (r cosθ + 8)²3r = r cosθ + 88 + r cosθ = 3r a = 8, b = 3 c)R...
9. ### Vector calculus for ellipse in polar coordinates

o so the centre is (1,0) and the equation you show me I have already obtained But don't you move the 1 over? To just simply get x by it self? So it should be 4 and -3 (-4+1?)
10. ### Vector calculus for ellipse in polar coordinates

so for x it's 4 and -4 and for y its 2sqrt2 and -2sqrt 2 right? i did a sketch of it, by any chance you know how to do this question? =( Mod note: The image was way too large. Please scale the image down to about 900 x 600 pixels and edit this post to include it again, or add it in a new...
11. ### Vector calculus for ellipse in polar coordinates

Hello =] I'm having trouble with this question, can somebody please help me with it! I'll thanks/like your comment if help me =) ![Question][1] I know that for a ellipse the parametric is x=a sin t , b= b cos t t:0 to 2pi (?) for part a) I drew up the graph but not sure if it's...
12. ### Subspace theorem; differential equation for a subspace

Yea that what I understand as well when some people explain to me in the first place but when I explain to my friends they ask sin(0) is 0 so I don't know how to tell them. Further more explanations I was able to notice that sin(x) is by it self like a constant so yeah. The reason x^2 =0 cus of...
13. ### Subspace theorem; differential equation for a subspace

Well this is an assignment in uni & I guess the person asked is the one in my course as well for engineering. I got the answer and understand the problem Our lecture just teach us to test non-empty by sub in 0 to the equation so that exactly what the other person did as me so yeah. It end up...
14. ### Subspace theorem; differential equation for a subspace

OMG! thank you it's like crystal clear now! you are the life saver. THANK YOU LOTS! Have a nice day!
15. ### Subspace theorem; differential equation for a subspace

hm... Someone explain like that for me as well let y(1) and y(2) be the solution, if the set was a subspace then y(1)+y(2) be the solution but if we evaluate the left hand side Y(1)+y(2) the right hand side is 2*sin(x) <- that's the part where I do not understand why it's 2*sin(x) is it because...
16. ### Subspace theorem; differential equation for a subspace

LOL I'm confuse so much now... subspace theorem: 1/V≠∅. (V is non-empty.) 2/If p,q∈V, then p+q∈V. (V is closed under vector addition.) 3/If p,q∈V and α∈R, then αp∈V. (V is closed under scalar multiplication. from my working out i know that test 1 pass because it equal 0 since...
17. ### Subspace theorem; differential equation for a subspace

If y=0 mean its a linearly independent but y=sin(x) is a dependent equation. Is that what u mean @Mark44 ?
18. ### Subspace theorem; differential equation for a subspace

So uh it fail the first test as well so does addition right? It's a inhomogenous not homogeneous equation? I'm getting it now, this question is hard because it use differial equation instead of real number so yeah, really sorry! But after reading the question again make me thinking again: The...
19. ### Subspace theorem; differential equation for a subspace

Ok let me get it straight. So for the first test for being non-empty, it turn out to be 0 so the first test pass Y"+3y'+x^2.y=sinx 0+3(0)+x^2(0)=sin(0) Therefore =0 Is my working out so far so good? For second test, addition Let y1+y2 be the solution. If the set was a subspace then y1+y2...
20. ### Subspace theorem; differential equation for a subspace

It fail the first test for being non-empty ? Like if y1+ y2 was a subspace solution. Then in the left hand side we got 2sinx instead of sin x. Is that a good explain? Also how would you do addition for that equation? I saw an example in a textbook so I did it like that. Could you explain more...
21. ### Subspace theorem; differential equation for a subspace

I can't seem to work out this question because it's so weird The set F of all function from R to R is a vector space given the diffential equation f"(x)+3f'(x)+x^2 f(x) = sin(x) is a subspace of F? Justify your answer I know that we have to proof that it's non-empty 0. The zero vector has to...