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    Very Easy Differential Question

    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...
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    Tuning Fork - Simple Harmonic Motion

    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...
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    2 dimensional PDE and a higher dimension problem.

    Homework Statement The 2d PDE Assume f\in S(\mathbb{R}^2) (Schwartz space) Then solve u_{xx}(x,y) + 2u_{yy}(x,y) + 3u_{x}(x,y) -4u(x,y) = f(x,y) ; (x,y) \in\mathbb{R}^2 u_{xxxx}(x,y) - u_{yy}(x,y) + 2u(x,y) = f(x,y) ; (x,y) \in\mathbb{R}^2 Homework Equations The relevant...
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    PDE math homework help

    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) ...
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    Inverting Consequences of Uniform Convergence

    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...
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    Mechanics which is lagrangian

    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...
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    Summation of a sequence by parts.

    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...
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    Sum of two square and complex quadratic

    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)...
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