Application Definition and 945 Threads

Solve $\begin{aligned} & {{u}_{tt}}={{u}_{xx}},\text{ }x>0,\text{ }t>0 \\ & u(0,t)=0,\text{ }t>0 \\ & u(x,0)=x{{e}^{-{{x}^{2}}}},\text{ }0<x<\infty \\ & {{u}_{t}}(x,0)=0. \end{aligned} $ The condition $u(0,t)$ is new to me, since I usually apply the method when only having $u(x,0)$...

Homework Statement Okay so I'm supposed to find the least squares solution of a set of equations, which I can do, but it adds that I must use QR decomposition. I don't really know how to apply QR decomposition to this problem. Problem: Find the least squares solution of x_1 + x_2 = 4...

Hey all. I sure hope somebody can assist with this! I am a hobby beer brewer and am writing my own heat control algorithms. Part of the process involves heating water to a desired temperature setpoint. I'm using an electric water heater element (5500W) inside the water vessel (~5-10 gal)...

Homework Statement Given: f is an entire function, Re f(z) ≤ n for all z. Show f is constant. Homework Equations The Attempt at a Solution So I thought I'd use Liouville's Theorem which states that, if f(z) is entire and there is a constant m such that |f(z)| ≤ m for all z...

Hello. I am trying to learn how to apply my knowledge of torque to a real life problem but I'm not quite sure how. I have attached a picture describing what I am trying to do. I would be very appreciative if anyone would take the time to take a look at what I have done and see if my view of...

Hi. In my homework I've encountered a discrete probability distribution of this form: f(k,\lambda)=N \frac{\lambda^k}{k!} k is the variable, and \lambda is a parameter. I'm curious what is this distribution - what's its name and where can it be applied. I will be grateful for, for...

Hi there, I am currently a secondary school student in the south east of England, and I wish to become a Physicist or Astro-Physicist somewhere along the line in my wonderous future... *hint of sarcasm for wonderous* Anyway, I think for my Physics exams at GCSE level I would acquire a B, and...

I have spent many hours today trying to determine at what distances certain substances will condense in protoplanetary disks around stars or temperatures different to that of our sun. I have come to the conclusion that the Inverse-Square Law is key to determining this. However, I am unsure as...

Homework Statement http://www.scribd.com/doc/82645310 In Figure 3-31, the lines AB and CD are the center lines of two conduits 1 ft. and 2 ft. in diameter respectively. Determine the maximum value of z so that the two may pass without interference. Conduit CD must pass under AB...

I was given an assignment in my Fluid Mechanics Module with the title: Application of the Navier-Stokes Equations in Tribology Applications Yet the lecture has given no starting point and we haven't yet done anything to do with Navier-Stokes Can anyone help me on where to start?

Why are derivatives of inverse functions important? My students are giving me questions like: When would using the theorem be useful? Can't you just find the inverse function and take its derivative? I'm sure many of you know the type of question: "Who cares?" My answers are that the theorem...

Hey all, I've been wondering about a few questions that seem to turn up a lot in math competitions—namely, what are the last 2 nonzero digits of some number x!. I've seen it a lot, and I'm wondering how one would go about solving that? I believe that one can use some modulus techniques to...

f is analytic on an open set U, z_0\in U, and f'(z_0)\neq 0. Show that \frac{2\pi i}{f'(z_0)}=\int_C\frac{1}{f(z)-f(z_0)}dz where $C$ is some circle center at $z_0$. S0 ,f(z)-f(z_0) = a_1(z-z_0)+a_2(z-z_0)^2+\cdots with a_1=f'(z_0)\neq 0. But why can f(z)-f(z_0) be expanded this way?

Hello, I am a sophomore physics and mathematics double major, and I plan to attend graduate school for physics with a concentration in biophysics, or just biophysics. However, this is subject to change, as I find a lot of areas of physics interesting. I was recently accepted to two REU...

Do Wien's displacement law hold true even for bodies with emissivity not equal to 1, that is, non-black bodies?

I apologize for the rather vague title. It's space-limited and I'm not sure how to concisely state what I want to know. Basically, I understand that the solutions to quadratic equations (and if I remember correctly cubic equations) often had surveying problems land surveying. However, quartic...

A "simple" application of dirac delta "shift theorem"...help Homework Statement show that for a, b, c, d positive: δ(a/b-c/d) = bdδ(ad-bc) Homework Equations ∫f(x)δ(x-a)dx = f(a) The Attempt at a Solution Ok so I start with ∫δ(a/b-c/d)f(x)dx But I am not sure how to apply the shift...

Homework Statement My teacher put us into groups and we each selected a wall of the rectangular room. He attached some sort of machine to the wall that spins in a circle with a laser on it, creating a laser point revolving around the walls. Our task is to create a function for the...

I'm just wondering if anyone has any advice on writing personal statements. Is there anything I should absolutely say or anything I should absolutely not say? What should the focus be? Should it go something like: why I like math, what kind of math I like, any relevant experiences with math I...

Suppose I have a non-linear load in my home (A half wave rectifier supplied DC load, say). Since it will consume current from the source only during +ve cycle of the Voltage, the current will be half-wave too. The current isn't sinusoidal. We can mathematically say that Distored Current =...

Homework Statement I need to show that the first equation becomes the last. First sub in for r1 and r2 and then use the binomial theorem to expand to first order in d. Then use the assumption that d<<r1 and r2. To show it reduces to the last eqn **In the first eqn it is NOT r3 is should be r2...

From Acoustics, Resonance, Energy, Power, Intensity and The Doppler Effect Homework Statement An old-fashioned hearing trumpet has the shape of a flared funnel, with a diameter of 8 cm at its wide end and a diameter of 0.7 cm at its narrow end. Suppose that all of the sound energy that...

Homework Statement A generated AC voltage has a value given by V = 4cos2θ. You will need to use the identity cos^2⁡θ = 1/2(1+cos2θ) Homework Equations a) Find the mean value of the voltage over a full cycle (0 ≤ θ ≤ 2π) using integral calculus b) Find the r.m.s. value of the...

Hi, I've had something that's been bothering me for a while and I've been researching it, but I just want to clear something up. I understand that the exclusion principle dictates that fermionic particles with half-integer spin have an anti-symmetrical wavefunction under exchange, and...

Hi all, I want to resonantly charge a capacitor, i.e. using a coil and diode combination instead of a resistor, in a very short period, which means a high current at high frequency. The problem is the coil. I read that at high frequency AC you get to deal with the skin effect, and also the...

I'm completing my transfer application to Towson University. The "essay prompt" is the following: I'd like to highlight the fact that I spent about six years teaching English in China. I learned a lot about the culture, I can speak (and read a bit) of Mandarin, I studied kung fu... Lots of...

Homework Statement a jar containing an iron block was floating on water in a bigger container. the block was taken out and put into water. as a result, the level of water in the container will (a)rise (b)fall (c)remains the same (d)rise or fall depending on the mass of block The Attempt...

Hi, Currently my wife and I are stuck in a two body problem with a separation of about 1500 miles. I have been looking for postdocs in her area (not many but a few more within a few hundred miles). My question is whether it is at all appropriate to mention the living situation and how getting...

Plz i want to know the practical applications of schrodinger's equation ??

Application of Gauss' law -- some doubts Homework Statement Revered Members, I have attached images of applications of Gauss' law namely 1) Electric field due to an infinitely long charged wire and 2) Electric field due to an infinite charged plane sheet. In both cases Gaussian surface is...

Homework Statement http://img593.imageshack.us/img593/5713/skjermbilde20111204kl11.png The Attempt at a Solution I thought it seemed appropriate to use divergence theorem here: I have, div F = 0 + 1 + x = 1+x I let that 0≤z≤c. If, x/a + y/b = 1then y=b(1-x/a) x/a +z/c = 1 then...

Hello, I'm intending to apply for an REU internship at Caltech for next summer, and I have a question that somebody American might be able to help me with. The application is an online application which asks for your name, address, programming languages etc. It seems like the application is...

I am applying to grad schools now, and I have a question on what I should be putting in the space that asks for GPA. I transferred from a community college, and some of my community college classes go back 11 years. The GPA I'm graduating with from my 4 year university only takes into...

Homework Statement I'm trying to include rigid body rotation in a problem I'm working on but can't seem to figure it out. Two shafts oriented vertically are connected by a thin cross member of length R. Holding one shaft stationary and applying a constant tangential load F to the other...

Quick one If I have an electric motor with a gear box (what ever ratio) and I want to install an electric holding brake will my holding power be greater if the brake is installed on the output shaft of the gearbox or the shaft of the driving motor to the gearbox ? my educated guess is that...

Homework Statement Find an equation of the line passing through the point (1, 4) such that the area of the triangle formed by this line and the positive coordinate axes is as small as possible. Homework Equations The Attempt at a Solution No idea where to start this one please...

Homework Statement We have to give the total charge, dipol and quadrupol moments of a charge constellation, but I seem to be falling at the first hurdle. Q = \frac{1}{4\pi \epsilon_{0}} \int_{vol} \rho(\vec{r}) d^{3}\vec{r} whereby the charge density of the group of particles is...

Help with graduate ChemE application! I really want to apply to MIT for the ChemE Phd program and apparently they look at your class rank quite a bit...I might not have a very good class rank, let alone be the top student! What are my chances going to be if I spend about 2.5 doing research and...

m using SciDAVis on a Athlon based system running Debian Linux. I am try to produce some graph of functions. The math part is working fine. However, when I try to change the axis labels, a blue box forms around the axis label and remains there. When I export the plot, the blue box is still...

This might be the wrong forum for this question, anyway here it is: I'm using SciDAVis on a Athlon based system running Debian Linux. I am try to produce some graph of functions. The math part is working fine. However, when I try to change the axis labels, a blue box forms around the axis...

Homework Statement I have a circular plate made of some metal and it is shaped like the equation [SIZE="2"]x^2 + y^2 \leqslant 1 The temperature at any given point in this plate is given by the function [SIZE="2"]T(x,y) = x^2 -x+2y^2 I'm supposed to find the hottest and the coldest...

Homework Statement Two ships, A and B are sailing along straight routes with constant velocities. At 10 o clock morning, ship B is 8 nautical miles from A and its bearing from A is 315°. At 10.15 in the morning, ship B is 6 nautical miles from A and its bearing from A is 320°. Find the...

Hi. Which language is used in creating windows OS and it's application?

Homework Statement In a steam engine the pressure and volume of steam satisfy the equation PV1.4=k, where k is a constant. Calculate the work done by the engine (in ft/lbs) during a cycle when the steam starts at a pressure of 100 lb/in2 and a volume of 400in3 and expands to a volume of...

Homework Statement A turn in the road with a radius of 30m is banked at an angle of 40 degrees. If \mu=.75, what is the minimum and max speed a 1200 kg car can travel without sliding off the turn. Homework Equations F=ma, Mv^2/R, Fw = mg The Attempt at a Solution Alright, so...

Polynomial Function. Homework Statement f:ℝ→ℝ x→x^2+x+2 Homework Equations Prove that: f(ℝ)=[7/4,+∞[ The Attempt at a Solution Well I don't know how answer this, so can someone give me a clue on how to start it off?

Homework Statement A leaky 6lb bucket is lifted from the ground to a height of 30ft at a constant speed with a rope that weighs .5lb/ft. Initially, the bucket contains 60lbs of water, but the water leaks out at a constant rate and finishes draining just as the bucket reaches the 30ft level...

So I am wanting to start applying for PhDs for entry in Sept/Oct 2012, I graduated from Uni last year so I don't really have any guidance on this! I do have a good idea of what I want to apply to do, and have a list of places I would like to apply (saving this for another thread haha :) )...

Homework Statement A cylindrical shell of radius 7.00 cm and length 240 cm has its charge uniformly distributed on its curved surface. The magnitude of the electric field at a point 19.0 cm ra- dially outward from its axis (measured from the midpoint of the shell) is 36.0 kN/C. Use approximate...

Homework Statement A ship moving at 8 mi per hour, Sails W for 2 hours, then turns N 30 E. A search light, placed at the starting point, follows the ship. Find how fast the light is rotating, (a) 3 hours after the start; (b) just after the turn. Homework Equations The Attempt at...