Recent content by squelch

Homework Statement For each of the following, determine if the system is linear. If not, clearly state why not. (a) ##y''(t)+15y'(t)+sin(y(t)))=u(t)## (b) ##y''(t)-y'(t)+3y(t)=u'(t)+u(t)## (c) ##y'(t)=u(t)## and ##z'(t)=u(t)-z(t)-y(t)## Homework Equations None The Attempt at a Solution...

So I suppose my only recourse here is to go ask for clarification from the actual professor. Thanks for the sanity check.

I do not, precisely. I'm still not getting past the idea that the equation seems to describe a plane to me. It seems that if I pick any z, there would be infinitely many x and y that satisfy the equation, and that I wouldn't be able to pick out a particular direction.

Finding that is, I think, precisely my problem. I have a candidate relation: \hat x{A_x} + \hat y{A_y} + \hat z{A_z} = \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over A} But I'm not completely sure if I am using it correctly if I say: \hat x + \hat y2 - \hat z3 =...

Homework Statement A line is given by the equation ##x + 2y - 3z = 7##. Find any vector in the direction parallel to this line in the Cartesian coordinate system. Homework Equations I imagine that there are some fundamental relationships I am missing here that would make this more...

Homework Statement Count the number of surjective functions from {1,2,...,n} to {a,b,c,d}. Use a formula derived from the following four-set venn diagram: Homework Equations None provided. The Attempt at a Solution First, I divided the Venn diagram into sets A,B,C,D and tried to express...

That was exceedingly helpful, thank you.

That was an awful error of mine that I thought I had corrected via edit fast enough, but alas, I did not. Corrected: [ 26 choices for character 1] * [25 choices for character 2] * [25 choices for character 3] * [25 choices for character 4] * [25 choices for character 5] ... so 26*25^4 choices...

Okay, so I know that the total number of strings is 265. I consider a string where I'm selecting each character in turn to try to decide how many choices I get at each stage. If I want to construct a string where no two adjacent characters are the same, it seems that I could construct it in...

The problem statement: How many five-letter strings of capital letters have a letter repeated twice in a row? For example, include ABCCA and AAABC and ABBCC but not ABCAD. The attempt at a solution: First, let's break down how we would perform the selection of a string that meets the...

I'm just trying to derive a textbook definition, in case the derivation is required on an exam. At a point in the derivation, coming from the original equation, ##{e^{ax}}\cos (bx)[{C_1} + {C_2}] + i{e^{ax}}\sin (bx)[{C_1} - {C_2}]##. I combined the constants into a new ##C_1## and ##C_2##...

Homework Statement Suppose that the characteristic equation to a second order, linear, homogeneous differential equation with constant coefficients yielded two complex roots: \begin{array}{l} {\lambda _1} = a + bi\\ {\lambda _2} = a - bi \end{array} This would yield a general solution of: y =...

Homework Statement A particle is described by the wavefunction: \psi (x) = \{ \begin{array}{*{20}{c}} {A\cos (\frac{{2\pi x}}{L}){\quad\rm{for }} - \frac{L}{4} \le x \le \frac{L}{4}}\\ {0{\quad\rm{otherwise }}} \end{array} (a) Determine the normalization constant A (b) What is the probability...

If you're not in a formal class studying physics, there's a couple of books I might recommend for self study that's a bit less dense than University Physics (which does an excellent job of covering classical mechanics and electromagnetism; I'm less happy with its coverage of modern physics). If...

I'm having a lot of trouble unpacking your last statement : It seems like you're suggesting I say |U\rangle = \frac{1}{{\sqrt 2 }}|L\rangle + \frac{1}{{\sqrt 2 }}|R\rangle and |D\rangle = \frac{1}{{\sqrt 2 }}|L\rangle + \frac{1}{{\sqrt 2 }}|R\rangle and say: |\psi \rangle =...