Recent content by Mattbringssoda

I think I have it now; u" = 0 means that u MUST beinn linear. u' = some constant, and go from there. Thanks SO much for your help...

Well, the G" equals a Dirac function with its jump at xBar, So below xBar: G" = 0, Meaning G' = a constant , Meaning G is generally some form of Cx, where C is a constant...?

Hmm, well that's the area I thought would be of form xc for x < x_bar (PS Thank you for your responses thus far..)

Well, we're only doing a very surface introduction to Greens functions in class, and were using them to construct inverse matrices in which to numerically solve boundary value problems and to look at the stability of those methods. The only other Greens function we encountered was for one that...

Homework Statement [/B] Determine the Green's functions for the two-point boundary value problem u''(x) = f(x) on 0 < x < 1 with a Neumann boundary condition at x = 0 and a Dirichlet condition at x = 1, i.e, find the function G(x; x) solving u''(x) = delta(x - xbar) (the Dirac delta...

Homework Statement [/B] Show that every trajectory, except r = 0, is asymptotically orbitally stable Homework Equations [/B] I have a hint that: I should think of two initially close trajectories (say a(0) = |x(0) - y(0)| sufficiently small and see how the difference evolves over time (the...

Homework Statement [/B] Give examples of fixed points of vector fields and maps that are stable in the linear approximation but are nonlinearly unstable Homework EquationsThe Attempt at a Solution [/B] I was able to find an example in a vector field that, when the Jacobian is found and the...

I'm turning in my assignment now. You've been an incredible help. Thanks!

Oh, I see. I forgot about that... So, now, I think I figured out part a, thanks to you, and it seems to work on paper. And I THINK I have figured out part b, setting it up along the lines of: And then solving for the Σ_orthog and using the orthogonal U and U* from the left side to work...

Thanks! I think I'm starting to see a glimmer... But, when you say P=UE11U∗, I'm not sure how the typical UEV* became UEU*, in other words, why does V* = U*?? Really - thanks again!

Homework Statement Let q ∈ C^m have 2-norm of q =1. Then P = qq∗ is a projection matrix. (a) The matrix P has a singular value decomposition with U = [q|Q⊥] for some appropriate matrix Q⊥. What are the singular values of P? (b) Find an SVD of the projection matrix I − P = I − qq∗ . In...

Thanks for all your help, all. The posts through #6 clued me in as to how to actually show the sines do indeed disappear, and now I understand WHY, instead of just taking it as gospel that it does. The work shown above helped me confirm my understanding (and the work I turned in) was correct...

Thank you two so much for your insight! I was making a silly error when integrating the absolute value. I'm still getting a little stuck (very stuck) on b: "Show that the complex Fourier Series can be rearranged into a cosine series" So, for part A: Represent /x/ with a complex Fourier...

Homework Statement a. Represent f(x)=|x| in -2<x<2 with a complex Fourier series b. Show that the complex Fourier Series can be rearranged into a cosine series c. Take the derivative of that cosine series. What function does the resulting series represent? [/B]Homework Equations...

Thank you two very much; it all stemmed down to a simple oversight that I wasn't catching from the (z^2 + 1) term. Thanks again!