Terms Definition and 1000 Threads

I have set myself the task of teaching my Freshman in high school brother Calculus, and today while reviewing some topics I saw something I didn't see before. To start out, I let y = ln[x] => x = e^y Obviously, we know that y' = 1/x = e^-y So, I "discovered" that one can define the...

i want to use a 100 cm diameter piston witch will have 4000 kg of pressure on it. Questions -how thick does the piston have to be to hold that much weight if it is made of metal? -what material should i use to make a seal to the cylinder wall and should the cylinder wall be another material then...

I was reading some articles and discussions on the topic and got confused when I read that conventionally photons and all other massless particles aren't considered a form of matter. The Wiki article on matter begins with the statement that the term itself is poorly defined. I was thinking...

Homework Statement How many terms of the AP, 12, 16, 20, 24 . . . . . must be taken for the sum to equal 408? Solution For this series, a = 12, d = 4 and Sn = 408. its asking me to solve for n and gives me the answer to n as 12 at the end but when i try to calculate it myself i don't get 12...

Realised I probably posted this in the wrong forum before, should've been here.. I often see a function's differential expressed in terms of convenient partial derivatives eg dU=(dU/dT) dT + (dU/dV) dV And I've seen it written that "any system is uniquely specified by two parameters, such...

So, I know this stuff is probably very elementary for most of the people on this site, but I have never had physics before, and I just started physics I at college. The professor has asked us to learn a few basic physics terms and I am having a hard time finding clear definitions for some of...

Wikipedia says it deals with distinct objects and is differentiated from continuous math, which has objects that "vary smoothly." For a layman, can someone explain what this means? And is all math discrete or continuous? No other options?

Difference between 2 "Sum of n terms of geometric series" formulas Notation A) S_{n}= \sum_{k=0}^{n - 1} ar^{k} = ar^{0} + ar^{1} + ar^{2} +...+ ar^{n-1} = \frac{a(1-r^{n})}{1-r} Proof: S_{n}= ar^{0} + ar^{1} + ar^{2} +...+ ar^{n-1} - r*S_{n}= ar^{1} + ar^{2} + ar^{3} +...+ ar^{n}...

Homework Statement Four 3-vectors a, b, c, and d are related by the equation ax + by + cz = d; where x, y, and z are real parameters. Using a suitable combination of scalar and vector products, findd x, y, and z in terms of the vectors Homework Equations The Attempt at a...

Is there a general way of writing a complex valued function f(z)=u(x,y)+iv(x,y) in terms of z? For example, suppose that I know f(x,y)=(x/(x^2+y^2))-i*y/(x^2+y^2) How do I know that it is actually f(z)=1/z?

http://imgur.com/xe52P30 2. Vx= Vs(R1/R1+R2), V=IR 3. I combined the 1k Ω and 5k Ω resistors then used voltage division to find Vx. I used Vx to find Vo which I found to be (5/18)Vx. I don't know where I can do KCL or KVL to solve for Vx.

Find the sum upto n terms: 1.3.5+3.5.7+5.7.9....tn I solve it this way: tn=(2n-1)(2n+1)(2n+3) Now can I take summation on both sides? How? I mean when I add 2 on both sides the resultant is 0(2-2=0).Similarly the resultant summation will be zero? And if I take summation I get...

Suppose we have a curve, formed by a function f that maps real numbers to real numbers, such that f is everywhere smooth over a subset D of its domain. Let's suppose that, for all x in D, there is a vector space that contains all vectors tangent to the curve at that point, called the tangent...

Homework Statement Generate a random 10 x 10 symmetric matrix A (already done in MATLAB) . Express A in the formHomework Equations ## A = ## \displaystyle \sum_{j=1}^{10}λ_j(A)v_jv^T_j\ for some real vectors ##v_j, j = 1, 2, . . . , 10.## The Attempt at a Solution I'm pretty sure the...

Hi guys, I'm sure I'm being very stupid here but I'm reading through notes which contain various actions for fields, most of which are very similar, however there is some discrepancies with the way differential operators are shown acting on the fields and I can't for the life of me work out...

Hi everyone, I was reading the report about the Fukushima incident and I do not understand some concepts because of my limited understanding. Could you please help me? Combustible Gas Control. <----- can you explain this concept in simpler language The NRC regulations in 10 CFR 50.44...

So I've got to give a speech for a class soon with the informative topic of what is light. Light is just what we call the visible portion of the spectrum. How can i go about defining this to a group of college kids in a way they can understand? thanks

I've found the wave-packet picture quite useful as I work my way through the very basics of quantum mechanics. But I'm having trouble finding a wave-mechanical picture of operators. For example, at least in terms of a free particle, using the wave mechanics treatment (as opposed to the matrix...

Hi guys, So textbooks have it that: "Two Lagrangians differing by a total time-derivative of a function of the coordinates are equivalent". I have no idea what that means or how to use it; so I don't know which terms I can drop from Lagrangians, which is a bit of a problem. For example...

write the terms a1,a2,a3,a4 of the following sequence. an+1=0.4an+330, a0=550 everytime I get 550 for a1 a2 a3 and a4 is that correct or am I doing it wrong.

Homework Statement Show that the group velocity vg=dω/dk can be written as vg=v-λ*dv/dλ where v = phase velocity Homework Equations n=n(k)=c/v k=2∏/λ ω=2∏f=kv fλ=c The Attempt at a Solution dω/dk = d(kv)/dk= v+k(dv/dk)= v+ck(d(n^-1)/dk) =v-(ck/n^2)(dn/dk)...

Hello, I have a question regarding the expansion of the Kahler potential in visible sector fields C^{\alpha} : It is usually said that the Kahler potential can be expanded as follows: K = K_{hid}(\phi,\phi^*) + K_{\bar{\alpha} \beta}(\phi,\phi^*) C^{*\bar{\alpha}} C^{\beta} + \frac{1}{2}...

Homework Statement I'm curently designing a controller, I have calculated the desired controller in terms of phase lead and phase lag, however I'm designing the controller on labview FPGA, which can only cope with a PID controller, I'm just wondering if anyone could help me by pointing me in...

Homework Statement Expand f(x) = 1 - x2 on -1 < x < +1 in terms of Legendre polynomials. Homework Equations The Attempt at a Solution Unfortunately, I missed the class where this was explained and I have other classes during my professor's office hours. I have no idea how to begin this...

This is Dr. Stephen Marquadt. http://img404.imageshack.us/img404/1373/stephenmarquardt.jpg When he was a young child, his mother was horribly disfigured in a car crash. So he eventually took the route of becoming a reconstructive plastic surgeon. As a plastic surgeon, he had to work out...

Hi guys, I'm having troubles finding how to write the potential energy of a 1D pendulum down. In terms of displacement however. This should be easy and it is, but my professor had this nice "clean" solution whereas mine is really dreadfull, any help? :) edit: Ok nvm guys. I was thinking I went...

Find the resolving power of a microscope lens in terms of its diameter Homework Statement In this problem, we will find the ultimate resolving power of a microscope. First of all, in order to obtain a large magnification, we want an objective lens with a very short focal length. Second, in...

Homework Statement ((1/3)(y^3))+(1/y)=.5*ln((x^2)+1) Solve in terms of y Homework Equations The Attempt at a Solution I am in college differential equations, and i just can't solve in terms of y. y teacher wants that...i tried wolfram alpha, etc. How on Earth do you factor this...

(I hope this is the right subforum) I'm talking about the series 1, 1, -1, 1, -1, 1, -1... I thought about it for a long time but I have no idea. If that first term were gone it would just be (-1)^(n+1), but...it's there...

Hi, I'm struggling to understand this concept. I think the term probably comes from functional analysis and I don't know any of the terms in that field so I'm having trouble understanding the meaning of what a compact linear operator is. I posted this in linear algebra because I'm reading...

I feel like I should know this already, but I need to isolate y in the equation: x= 6y-y^2 I was thinking of using the quadratic formula, but that would keep the equation in terms of x. No matter how I seem to slice it, I can't figure out what to do... Which is kinda sad that I'm doing good on...

Problem: Derive a formula expressing the de Broglie wavelength (in Å) of an electron in terms of the potential difference V (in volts) through which it is accelerated. Solution (so far): The textbook's answer is the following, \lambda=12.27[V(\frac{eV}{2m_{0}c^{2}}+1)]^{-\frac{1}{2}} I'm...

Hi all, I derived the energy equation for compressible flow in terms of [SIZE="4"]pressure p from the governing equation in terms of [SIZE="4"]the total energy density e (using the perfect gas assumption and assuming constant viscosity), but I am not sure if I did it correctly. I post it...

Homework Statement I have developed an equations for calculating some pollutant concentration as a function of x and y. I'm trying to simplify the problem so that I can write the equation for wp as a function of x. All variables except x and wp are known. Homework Equations...

Homework Statement What are the cases in which constants of integration can and cannot absorb terms and operations and just be redefined as c. Homework Equations The Attempt at a Solution As long as I keep redefining my constant of integration I can say -c=k ac=k where...

Homework Statement Show that (\Delta A)^{2} = \langle \psi |A^{2}| \psi \rangle - \langle \psi |A| \psi \rangle ^{2}\\ \phantom{(\Delta A)^{2} }=\langle \psi | (A - \langle A \rangle )^{2} | \psi \rangle , where \Delta A is the uncertainty of an operator A and \langle A \rangle is the...

I am looking for a way to sum some numbers. I understand that if I want to sum pi, I can use the geometric series: \sum\limits_{i=0}^N p^{i} = \frac{1-p^{N+1}}{1-p} But can anyone help me with what to do when I need: \sum\limits_{i=0}^N p^{i} q^{ti} where t is just a constant...

Homework Statement Two blocks, each with weight ω, are held in place by a frictionless incline. In terms of ω and the angle θ of the incline, calculate the tension of the rope connecting the two blocks. Homework Equations ƩF=ma The Attempt at a Solution Since it is on a tilted...

Hello. I wish to prove this: $$\text{A function } f: X \to Y \text{ is continuous if and only if the inverse image of any closed set is closed.}$$ Proof: $(\implies)$ Let $V \subset Y$ be a closed se. By definition, $Y-V$ is an open set, and by the continuity of $f$ it follows that...

My questions are from lecture 9, MIT OCW SV Calculus, Jerison, 2009; At 27:50 he is deriving the linear approximation for the function e^(-3x)(1+x)^(-1/2)≈(1-3x)(1-1/2x)≈1-3x-1/2x+3/2x^2≈1-7/2x, for x near 0. In the last step he drops the x squared term since it is negligible(no questions so...

So I'm supposed to read Chapter 34 (Electric Current) in the next couple of days. I'm sure I'll have more questions about it but one question I have right now is what does the book mean by the term potential and potential difference. My teacher briefly explained it but I couldn't stay awake this...

I've been doing some self-study in Peskin and Schroeder and been struggling a bit in Part III. Right now, I am stuck on the last two terms in 16.6 (Lagrangian for Yang-Mills). Presumably these come from (-1/4) (F^{a}_{\mu\nu})^2, but I am getting stuck on getting the indices to work out...

This is not actually a homework question, but it seemed appropriate to put it here. In an old exam from 1921 I found the following problem. I never learned how to solve this type of thing and I haven't been able to figure it out, so: how does one solve this? Homework Statement Solve for...

1. Yes, I don't know this. =.= So how to you move sine to the y side? You can't say: arcsin(y) = sqrt(5x + 3), can you...? I don't know how to move the sin! Help! Thank you! :)

Hi there, I'm trying to comprehend Dirac Delta functions. Here's something to help me understand them; let's say I want to formulate Newton's second law F=MA (for point masses) in DDF form. Is this correct: F_i = \int [m_i\delta (x-x_i) a_i\delta (x-x_i)]dx Or is it this: F_i = [\int...

how do you "indicate transient terms" when y just equals 1 ? t is the dependent variable in this problem and I'm told to "indicate transient terms". Well, t=1 so is this a trick question or did I do something wrong?

Homework Statement I've still yet to learn Latex since I'm pretty good with words equation editor, so here's the question typed out in words. Homework Equations I really don't know what to do here. The Attempt at a Solution

Homework Statement Let A(x) = a0 + a1x + a2x2 + a3x3 + ... = Ʃanxn. Express E(x) = a0 + a2x2 + a4x4 + ... = Ʃa2nx2n. Do the same for O(x) = a1x + a3x3 + a5x5 + ... Homework Equations A(x) = a0 + a1x + a2x2 + a3x3 + ... = Ʃanxn The Attempt at a Solution So I tried using A(x2)...

I am embarrassed to be asking such an elementary question, but I want someone to explain the difference between amps, watts, and joules. I tried a dictionary, but it wasn't specific enough.

Dear Math Help Boards, I have a tricky problem that I hope one of you can help me with. (It's for a personal project, nothing to do with school.) I'm looking for a closed-form expression for the sum of the first through m-th terms of a combinatorial number. For those of you unfamiliar with...