Recent content by Kamekui

Homework Statement Let f(x)=x, 0≤x≤p (a.) Compute the half-range sine series (b.) Use the series to show that 1-(1/3)+(1/5)+...=π/4 Homework Equations bn=(2/L)*int(from 0 to L) f(x)*sin(nπx/L) dx The Attempt at a Solution bn=(2/p)*int(from 0 to p) x*sin(nπx/p) dx Using...

Homework Statement (a.) Find an orthonormal basis of R^4 spanned by {1,1,1,1},{1,0,0,1}, and {0,1,0,1}. (b.) Use the inner product to express {2,2,2,2} as a linear combination of the basis vectors. Do not solve the equations. Homework Equations gram schmidt orthogonalization and...

Homework Statement Show the origin is the only critical point Homework Equations x'= -x-x3 y-= -y-y5 The Attempt at a Solution I'm not really sure how to go about this. I missed a few lectures due to a medical issue, and now were at the end of the semester and I can't get in touch with the...

Sorry if I seem confused but what blank spaces?

Homework Statement 1. Homework Statement [/b] Enumerate all possible Jordan forms for 3 x 3 systems where all the eigen-values have negative real parts. Do not use specific values. Instead, use possibilities like λ1; λ2; λ3, each with multiplicity 1, or λ (multiplicity 3). Homework...

Guys thank you for all the help! I was just sitting here and I finally saw the solution, I was just over thinking this problem big time. I determined the Jordan normal form for A, found the matrix exponential for it. The trivial solution for the matrix exponential displays asymptotically...

Ok, this is where I am getting confused with you in part (c): In circuit and spring problems, both constants are nonnegative. Assume that they are actually positive, and show that the eigenvalues have a negative real part, and conclude that the trivial solution is asymptotically stable. I...

Alright, I went back and worked out part (b) to this: det(A-λI)=λ2+aλ+b →λ=(1/2)*(-a±√(a2-4b)) Now, there are three possible cases: √(a2-4b)=0 √(a2-4b)>0 √(a2-4b)<0 Case 1: If √(a2-4b))=0 then trivially, λ= -a/2 By assumption, a ε ℝ and a>0 → -a/2<0 Case 2: If...

Ok, I went back and tried this: Let E4= \begin{bmatrix} 0\\ 1\\ 1\\ 0 \end{bmatrix} Then, (A+4I)E4=E3 \begin{bmatrix} 1 & -1 & -1 & -1\\ -1 & 1 & 1 & 1\\ 1 & -1 & -1 & -1\\ 1 & -1 & -1 & -1 \end{bmatrix}*\begin{bmatrix} 0 \\ 1 \\ 1 \\ 0...

Unfortunately, no. I directly copied and pasted the directions i here. The only thing that makes sense to me beyond the given directions is that 4b>a^2 so we would get a definite Real and Complex part.

Homework Statement Find the Jordan form and use it to find the matrix exponential. Homework Equations The Attempt at a Solution Let A =\begin{bmatrix} -3 &-1 &-1 &-1 \\ -1 & -3 & 1 & 1 \\ 1 & -1 & -5 & -1 \\ 1 & -1 & -1 & -5 \end{bmatrix}...

Homework Statement Consider the second order equation x''+ ax' + bx = 0: (a) Convert the equation to a 2 x 2 system. (b) Compute the eigenvalues. (c) In circuit and spring problems, both constants are nonnegative. Assume that they are actually positive, and show that the eigenvalues have...