Recent content by jwang34

ok...here's what I found So delta(ax)=[delta(x)]/|a|. Then could I do the following: Given delta(x/3+4)=[delta(x+12)]/|3|. Basically, I factored out the 1/3, and so a=1/3.

[b]1. Homework Statement \int x[delta(x)-delta(x/3+4)] dx Homework Equations so I'm supposed to use this principle: \int f(x)delta(x-xo)dx=f(xo) The Attempt at a Solution So it seems simple but I just want to make sure that I'm applying the above principle correctly. I...

Ok, thanks for the reply and I understand what you mean, but basically I'm supposed to show that as n increases, the graph does a better job of approximating the dirac delta function. Also, I just checked the equation again and d(t-t') has a period of 2pi, so P=2pi. So if I interpret your reply...

Homework Statement SO I'm given a dirac delta function, also known as a unit impulse function. d(t-t'_=(1/P) sum of e^[in(t-t')], for n from negative to positive infinity. I need to graph this. Homework Equations I understand that at t', there is a force made upon the system which...

Homework Statement I am given 9/[(s-1)(s-1)(s-4)] as part of a Laplace Transform. I'm supposed to decompose into partial fractions. Homework Equations So 9/[(s-1)(s-1)(s-4)]= D/(s-1)+E/(s-1)+F/(s-4) The Attempt at a Solution To simplify: 9= D(s-1)(s-4)+ E(s-1)(s-4)+ F(s-1)^2...

So I get dx/(rx(1-(x/K))=dt. Then I should use partial fractions to integrate?

So separation of variables in this case would be A(t)dt+B(x)dx=0. So I would have dx/rx=(1-x/K)dt. Then, I should integrate both sides? Is this the right track?

The logistic growth model is the following: dx/dt=rx(1-x/K), with r and K and as constants, and x is a function of t. I'm really not sure where to begin. First I tried separation of variables, but that didn't work out (and I don't even know if I was doing it right). Should I even be...

Yes, you are right. I think I understand it now. So I should set C1=(a+bi) and C2=(a-bi) and the complex matrices will be resolved. Thank you so much!

I'm not sure I totally understand. So you're saying I set C1=the conjugate of C2? Or should I do set C1=C2*conjugate(z)?

Homework Statement Given a general solution to a system of differential equations: Y(t)= C1(1;2i)e^(2it)+C2(1;-2i)e^(-2it) side note: i is sqrt of -1, and the (1;2i) is a 2 by 1 matrix. The idea is to simplify the solution such that the imaginary components go away. Homework...