Recent content by lmedin02

That is correct, however, I made a typo in my DE. It should be x''-4x'+5x=0. The idea is that you can find the characteristic equation from the DE, hence the roots, and then the general solution. So you may work backwards as well. Try it again.

No, that is a bit complicated. If you have the differential equation x''-4x'+x=0, how would you find the general solution? Just go through a few steps, then should have the solution to your problem as well. If not, I will give you another hint.

3 and 4 do not matter. Work backwards. If the solution in this case involves sines and cosines then we can conclude that the roots to the auxiliary equation are complex. Find the roots and then the polynomial. You will then have your differential equation and hence the values of r and k.

I have established existence and uniqueness of solutions to a nonlinear elliptic system of PDE's and would like to see how the solutions look like numerically. I have some programming background on MatLab and C++. I also understand basic ODE numerical schemes. But I am not so sure, if I need to...

Homework Statement Suppose f\in L^2(\mathbb{R}^2). Is f+c\in L^2(\mathbb{R}^2) where c is a constant? Homework Equations f\in L^2(\mathbb{R}^2) if ||f||_2<∞. The Attempt at a Solution I think the answer is no because ∫_{\mathbb{R}^2}{c^2}dx=∞. However, I am still unsure. Any guidance...

I am not sure what you mean by elemination failing. However, elimination give many rows of zero and hence infinitely many solutions for Bx=0. Consider doing elimination on C for a 2x2 matrix with the same columns and see what are your solutions. If you have learn the determinant, then the...

Bx=0 and Cx=0 are homogeneous system of equations. So there are only two posibilities for their solutions. 1. Either the solutions are trivial and unique or 2. Infinitely many solutions. Ask yourself if B is invertible? If it is, then multiply both sides of Bx=0 by its inverse to obtain only...

Got it. Thanks. Using Holder's inequality and noting that the size of \Omega is finite the results follows since f_k\rightarrow f in L^2(\Omega).

Assuming K and L are constants. How about dividing by (L-N) on both sides from dN/dt = k(L-N) instead of distributing the K? This equation is separable.

Homework Statement Let f_k\rightarrow f in L^2(\Omega) where |\Omega| is finite. If \int_{\Omega}{f_k(x)}dx=0 for all k=1,2,3,\ldots, then \int_{\Omega}{f(x)}dx=0. Homework Equations The Attempt at a Solution I started by playing around with Holder's inequality and constructing...

I am having a hard time making this conclusion. How about if the sequence is bounded?

Thank you all for your feedback.

This is what I thought. I have an excellent dissertation adviser. Well know in his field, but before I asked him of opinion I wanted to be more informed so I am seeking all inputs.

Does the institution where an individual receives their PhD degree in mathematics have a significant impact on their career? The question evolves from a merger among universities: If a university is under a merger with another well established university with a much much better reputation in...

Homework Statement I am considering the space \tilde{W}^{1,2}(\Omega) to be the class of functions in W^{1,2}(\Omega) satisfying the property that its average value on \Omega is 0. I would like to show that \tilde{W}^{1,2}(\Omega) is a closed subspace of W^{1,2}(\Omega). Homework...