Homework Statement
We have f(x,y) = \frac{xy}{x^2+y^2}
Show that the first partial derivative w.r.t. x and w.r.t y exist
Homework Equations
f(x+dx,y)-f(x,y) = a(dx) + o(dx) where a is some number and o(dx)(not o multiplied by dx rather a 'function', if so to say, o of dx) is such that...
I don't know why the Latex failed but anyway it is quite a complicated equation with a damping effect and the part without the damping. My question was how can you get to the ODE in the first and keep going and second how does the damping come in.
That much I know about the tuning fork. My point is the ODE of the harmonic oscillator. In fact we have the ODE
m\frac{d^2x}{dt^2} + b\frac{dx}{dt} + kx = F cos(wt)
Which leads eventually (with damping to)
x = Ae^-^\gamma ^t cos(w_1 t + \theta) + \frac{Fsin(wt+ \theta _0)m}{[(w^2_0 - w^2)^2...
This topic has proved itself to be a hard one in, in terms of looking it up online. I'm interested in simple harmonic motion, in specific that of a tuning fork vibrating between two electromagnetic devices, a microphone ad a detector.
My main interest in it is to write a lab report about an...
If you are up to level with engineering math course then you should be able to tackle this. In the end engineers do have to take partial differential equations. If you know all basic calculus and are comfortable with the complex plane (Not as in need to know full complex analysis, just a mild...
The sequence an converges therefore it is bounded. So every an<M where M is some number. So the sum becomes less that (M-L) ...n-N+1 times over n and from there go on.
But I don't get it. Graphically that is. The integral on R of higher dimensions is analogue to summation of R. Now if f = sinx /x the summation (if x belongs to N) is finite but |sinx/x| is not finite. Doesn't the same apply for the integral? Let x belong to R of higher dimensions. Wouldn't the...
No I'm not missing anything in the solution. That's the problem. If the constraints on the extremities of x were there it would be a piece of cake. And if we had them then there would be no need for f to be belong to C or PS. Even in the question it tells us to solve the PDE using fourier series.
Homework Statement
We are given f \epsilon C(T) [set of continuous and 2pi periodic functions] and PS(T) [set of piecewise smooth and 2pi periodic functions]
SOlve the BVP
ut(x,t) = uxx(x,t) ; (x,t) belongs to R x (0,inf)
u(x,0) = f(x) ...
Hi. Now you probably know that if a function fk(x) converges uniformly to f(x) then we are allowed to certain actions such as
limn-> \inf \int f (of k) dx = \int f dx
In other words we are allowed to exchange limit and integral. Now say we have any sequnce valued function fk(x) . And we...
The hamiltonian is a constant if no dissipative forces are present. That's how you can build a phase space for idealistic examples, by looking at the hamiltonian.
The Susskind lectures are really good. Is this the same for all stanford (or any other university for that matter) courses?
First off, thanks for replying.
Bringing up the subject of calculus of variations. I'm not sure which one(L or I) but I think I[L] is a functional...right!? May I ask what exactly is a functional. Because they said that a functional is a function from the space of functions to R....by space of...
Hi. There is just this one thing in mechanics which is lagrangian that I just simply can't grasp physically. I'm taking a mechanics course I simply do not understand what the lagrangian is. There is calculus of variations (at least a tiny but of it) a bit of geodesics and the least action...
I hope can someone clarify this for me.
I have a sequence f(of n) which is like this:
fn(x) = 0-- if--x<\frac{1}{n+1}
is = sin^2(x/pi)--if--\frac{1}{n+1}<=x<=\frac{ 1}{n}
is = 0--if--\frac{1}{n}<x
(the - are for spaces because I don't know how to do it. Nothing is negative)
Then...
The auxiliary equation is x = \frac{-b \frac{+}{-} \sqrt{4ac - b^2}}{2a} where ax^2+bx+c=0. That's what I know it as anyways. Anyways, even the teacher said you can't do it that way. But if you can find a way, then I'd be more than happy.
You're right, I'm not saying a can't be real, but we...
Actually, break i into its polar form which is i^2^n = e^i^n^(^p^i^) . Now expand using Euler's identity and you are left only with cos\ n(pi) = (-1)^n From there it is a geometric series.
I actually have two questions, both are in the complex plane.
Homework Statement
Q1: Express 962 as a sum of two squares (Hint: 962 = (13)(74)
Q2. Given z,a belong to C (complex). Find a such that the roots of the equation z^2 + az + 1 = 0 have equal absolute values (or modulus)...