Recent content by P-Jay1

Sorry that was mistake, but it's still wrong, I've tryed everything i can think of. n = NDSolve[{x''[t] + x[t] (x^2[t] - 1) + t == 0, x[0] == 1, x'[0] == 0}, x[t], t, {t, 0, 10}] above is what i got. Says duplicate variable t found, so it's still wrong. I'm not sure what to do, any...

On mathematica: Solve the differential equation d^2 x(t)/dt^2 + x(t)(x^2(t) − 1) + t = 0 numerically, subject to the initial conditions that x(0) = 1 and dx(0)/dt = 0. Use Plot to plot the solution for the domain t 2 [0, 10]. 2. Above is what I'm trying to do. Below is what I've...

1- A series electric circuit contains a resistance R, capacitance C and power source supplying a time-dependent electromotive force V (t). The charge q on the capacitor obeys R dq/dt + q/C = V (t) Assuming that initially, at time t = 0, there is no charge on the capacitor, and given that...

Thanks Ivy. How do I go about doing the second question?

Diagonalizing an N × N matrix H involves writing it as H = UDU† where D is a diagonal matrix, with diagonal elements equal to the eigenvalues of the matrix H, and U is a unitary matrix. We may write: D= (λ1 0 0 ... 0) (0 λ2 0 ... 0) (0 0 λ3... 0) (... ... ... ... λn)...

Using the standard inner product in ℂ^n how would I calculate the norm of: V= ( 1 , i ) , where this is a 1 x 2 matrix

On a P-V diagram, if the pressure stays constant and the volume increases, what happens to the temperature? Does it increase, decrease, or stay the same?

A = (a b c d) A = a (1 0 0 0) + b (0 1 0 0) + c (0 0 1 0) + d (0 0 0 1) Please excuse my lack of ability to lay this out correctly but each of these in brackets have 2 rows and 2 columns i.e 2 x 2. not 1 x4 a,b... Eℝ is a vector space over ℝ Is this...

So what does ker(T) stand for? I am still really clueless. So do I find an isomorphism from T[a,b;c,d] to (a,b,c,d)?

Prove that the space of 2×2 real matrices forms a vector space of dimension 4 over R. [12] Im unsure, anyone any idea?

Thankyou vela I see now! I've got one last question:What are the ranges of summation over k and l?

The above is a system of equations. I don't know how many it holds though. Is it 3? How do i show this?

(ABC)ij =Xk Xl AikBklClj where x is the sum of In the above equation which are the dummy indices and which are the free indices? I think i and j are free, and k and l are dummy. But I am not surre!

A is an M × N matrix, B is N × K and C is a K × L matrix. Consider matrix multiplication (AB)ij = Pk AikBkj . Using the formula, (AB)ij = Pk AikBkj, how would I calculate ((AB)C) and (A(BC))?

I just realized damn