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...
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...
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...
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...
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)...