Terms Definition and 1000 Threads

Hi, I wonder if anyone knows when (maybe always?) it is true that, where z=x+iy \text{ and } f : \mathbb{C} \to \mathbb{C} \text{ is expressed as } f=u+iv, \text{ that } f'(z)=\frac{\partial u}{\partial x}+i\frac{\partial v}{\partial x}? I'm pretty sure that this is true for f=exp. I...

Edward Nelson, a Princeton mathematician showed that quantum mechanics could be derived from the principle that elementary particles are subjected to a universal jiggling of an unspecified cause. As I understand the obstacle to use this mathematical model as a physical one, is that dynamics of...

Given an equation for a line y=7x/3, how can i define it in mathematica using x,y and theta. I am eventually going to have to find the intersection of this line to a circle with the equation Circle[{0,9},5] as a function of theta. I thought maybe if i use the rule tan(θ) = y/x then id get...

Homework Statement A ladder of length L and mass M leaning against a wall. Assuming the wall and the floor are frictionless, the ladder will slide down the wall and along the floor intl the left end closes contact with the wall. Before the ladder loses contact with the wall there is one degree...

"I have agreed to the Terms and Conditions..." Peng here. As I installed Adobe Flash update #15,203,203 and clicked the usual "blahb lah blah terms and crap, don't use Flash to create a nuclear weapon or biological warfare please or we'll sue you", I started wondering how often people ever...

Homework Statement Give an example of a sequence {an}, satisfying the following: {an} is monotonic 0<an<1 for all n and no two terms are the same lim(n→∞) an = 1/2 Homework Equations what is monotonic The Attempt at a Solution 1/(2√n) n/(2n-1) 1/2^n just been trying...

Homework Statement Find y" in terms of x and y: y^2 + 2y = 2x + 1 Homework Equations N/A The Attempt at a Solution I found the first derivative: y^2 + 2y = 2x + 1 2yy'+2y'=2 2y'.(y+1)=2 y'=2/2(y+1) y'=1/(y+1) But I'm having trouble moving on from there.

I appear to be getting two sides with the same unknown. Does it mean I'm screwed and can't solve it in terms of "r"? http://img716.imageshack.us/img716/4409/image2011121500032.jpg

Homework Statement given: Vn+1=Vn*cos(pi/2^(n+2)) Homework Equations Write a sequence Vn in terms of n The Attempt at a Solution we substitute n with n-1 and we get: V(n-1)+1= Vn-1*cos(pi/2^(n-1+2)) Vn=Vn-1*cos(pi/2^(n+1) Is this correct?

As part of my problem I need the following condition to hold: \frac{2^{n(H+\epsilon)}}{\epsilon}:=\delta^{-\theta} for some \epsilon, \delta and \theta all in (0,1). Now, I would like to rearrange the equation (solve for \epsilon[itex/] in terms of the rest of the parameters) so as to have the...

Hi. Can someone explain to me how to sort a Series so that the terms are in increasing powers of the exponent? For example the code: myseries = Normal[ Series[Sqrt[1 - w], {w, 0, 5}]] /. w -> 1/z produces 1-\frac{7}{256 z^5}-\frac{5}{128 z^4}-\frac{1}{16 z^3}-\frac{1}{8 z^2}-\frac{1}{2...

We just did atomic physics in class, and my teacher assumed everyone had already taken chemistry so she really skimmed through the material, and I have yet to take chemistry so I am beyond lost with this chapter. I read the chapter and it is so technically written that I don't comprehend it...

dear PF.. what is the Bernoulli equation in terms of energy per unit volume the equation include the 1) static pressure 2) hydrostatic pressure 3) dynamic pressure 4) stagnation pressure

Homework Statement \frac{\frac{2}{3}x(x^{2}+4)^{1/2}(x^{2}-9)^{-2/3}-x(x^{2}-9)^{1/3}(x^{2}+4)^{-1/2}}{x^{2}+4} The Attempt at a Solution \frac{x(x^{2}+4)^{-1/2}(x^{2}-9)^{-2/3}(\frac{2}{3}(x^{2}+4)-(x-9))}{x^{2}+4} Then: \frac{x(\frac{2}{3}(x^{2}+4)-(x-9))}{(x^{2}+4)^{3/2}(x^{2}-9)^{2/3}}...

This may seem obvious, but please define these for me, in as much details as possible. What does it mean to: "be at rest" "be still" "be stationary" "to be in motion" "to move" "to travel" Please do so without using one of the words in another one's definition (I.e. stationary means...

Homework Statement Let C be the line segment connecting the points (x1,y1) and (x2,y2). More over let the line integral over C of (x dy - y dx) = x1y2 - x2y1. Suppose the vertices of a polygon, listed in counter-clockwise order, are (x1y1), (x2y2), ... , (xnyn). Show that the area of the...

Homework Statement I can't figure out what my professor means in the last two lines: I'm trying to prove why the product of two analytic functions is analytic, and I think that I am going to need to use a similar construction. The Attempt at a Solution So far to prove the product...

Homework Statement A group G acts transitively on a non empty G-set S if, for all s1, s2 in S, there exists an element G in G such that g*s1 = s2. Characterize transitive G-set actions in terms of orbits. Prove your answer Homework Equations Transitive G-set Actions: for all s1, s2 in S...

Homework Statement Find the first 4 nonzero terms of: e^{t}cos(t) Homework Equations The Attempt at a Solution I am trying to multiply the terms of two known series for my answer, but I'm not sure how to do it efficiently. Should I list 4 terms of each series, then...

The concept of describing something in layman's terms has come into wide use in the English speaking world. To put something in layman's terms is to describe a complex or technical issue using words and terms that the average individual (someone without professional training in the subject area)...

A thought just struck me today after watching a lecture on the construction of the rational numbers. What is the definition of 'greater than (>)' and 'less than (<)' in the real number system. The only way I can think to describe it is to make some reference to the Euclidean distance between the...

Homework Statement How many terms of the series ∞ Ʃ (-1)n/(ln(n+1)) n=1 are needed in order to estimate the exact sum within .01 Homework Equations I know that I need to use the remainder estimate for the integral test where Rn=s-sn and that ∫ from (n+1) to ∞ of f(x)dx \leq Rn...

Homework Statement "A rod of mass 4.0 kg and length 1.5 m hangs from a hinge. The end of the rod is then given a 'kick' so that it is moving at a speed of 5 m/s. How high will the rod swing? Express you answer in terms of the angle the rod makes with the vertical.Homework Equations KE(rot) =...

Homework Statement The ground state wave function for a particle of mass m moving with energy E in a one-dimensional harmonic oscillator potential with classical frequency omega is: u(subscript 0) (x)= N(subscript 0) exp((-alpha^2)(x^2)/2) and alpha=sqrt (m *omega/h-bar) where...

Homework Statement I'm trying to simplify this polynomial ((s+1)/(2+s))/((s+1)+((s+1)/(s+2))(s+1)) It's more readable if you view it here: http://www.wolframalpha.com/input/?i=%28%28s%2B1%29%2F%282%2Bs%29%29%2F%28%28s%2B1%29%2B%28%28s%2B1%29%2F%28s%2B2%29%29%28s%2B1%29%29 It simplifies...

Homework Statement A particle moving in xy plane has velocity components in x and y directions Dx/dt = b1+c1t and dy/dt = b2+c2t A) integrate above equations to give displacement components x and y as functions of time B) write the velocity (v) of the particle at time t in terms of...

I'm relatively knew to fluid dynamics. I'm self teaching myself. Could someone explain what it means to say a function or vector is a source term? Are there any significant mathematical properties/uniqueness's? I'm working with vector matrices, so if you could explain in this context that...

If you have a polynomial like (1+x)^6 = x^6+6 x^5+15 x^4+20 x^3+15 x^2+6 x+1, What function would you use to pick only the last N terms? For instance, for N=3 pick x^6+6 x^5+15 x^4 I've being using sum of a binomial times something, but was wondering if there is anything more simple. Thanks!

THIS ISN'T WORKING AT ALL! I'm trying to define a matrix M in terms of a predefined matrix N by using the following for loop: For[a=1,a<=12,a++,M[[a,a]]=N[[1,a]]] So I just want the diagonal of M to be the first row of N. But this is not working at ALL. Does anyone see what I'm doing wrong?

Homework Statement Consider the following convergent series. Then complete parts a throw d below. sum[k=1,inf] 5/k^7 a. Find an upper bound for the remainder in terms of n Homework Equations Estimating Series with Positive Terms Let f be a continuous, positive, decreasing...

How can a system of non-linear differential equations be solved using Mathematica? More specifically, I understand the process that needs to be executed, but I don't understand how to make it work syntactically. The process as I understand it: Four expressions are given in four...

I'm looking for help to this problem. Here is my attempt: I being the identity matrix and B^(-1) being B to the negative 1st power. A (B B^(-1)) C D = B^(-1) I so A I C D = B^(-1) so A C D = B^(-1) Thank you for any help.

How do you go about solving implicit equations for y in terms of x that look like these? y2 + yx = 1 and y3 + yx = 1 or even more complicated implicit equations. I'm taking AP Calculus AB this year and am just curious how this is done. Here are the solutions from Wolframalpha...

Today my physics professor briefly skipped over this during a derivation: We started with 2 \sum F_{n}(x) = \sum G_{n}(x) , summed from n=0 to \infty which she then concluded 2F_{n}(x) = G_{n}(x) where F and G are functions of x, and different functions for different values of n...

Homework Statement The following series is a telescopic series. Find the exact sum of the series by performing a partial fraction decomposition and generalizing the formula for the nth partial sum Sn. Homework Equations The Attempt at a Solution 3n + 2 = A(n+1)(n+2) + B(n)(n+2) + C(n)(n+1)...

rewriting the fourth moment in terms of... Homework Statement X is a random variable with moments E[X], E[X^2], E[X^3]. Suppose var(X)= σ^2, and that skewness is given as, S=[E(X-μ)^3)]/(σ^3) Rewrite the right hand side of the expression(see below) in terms of μ, σ^2, S and μ4 Homework...

Homework Statement The Q asks to show that the time rate of change in mechanical energy for a damped, undriven oscillator is dE/dt=-bV^2.Homework Equations I assume you take the derivative of the total E eq, E=(1/2)mV^2 + (1/2)kx^2 but I'm unsure how to put the E eq into terms of t, like...

Hi, I need to split an expression into a list of terms, i.e. an expression like: a+b-c-d+... into: {a,b,-c,-d,...}. Can you help? Thanks in advance.

I feel that a lot of the misunderstaing in quantum physics arises from the misinterpretations of terms used by physicists. I think that the forum should have a page where all the quantum terms are explained in a precise technical manner to avoid confusion. I will state pop culture's...

Is there any definition of the zeroth law of termodynamics using the heat concept? And does the zeroth law imply that the only way 2 systems can transfer energy is if they're not in thermal equilibrium? If 1 system is transferring energy to another one, that means they're not in thermal...

1. Relevant problem integrate from 0 to infinity of r^2exp^(-r/a0)dr Homework Equations I'm also given; integral from 0 to infinity of x^nexp^-x dx = n! The Attempt at a Solution I'm just wondering if I can split up the exponential to make it look like this form. Eg; integrate from 0 to...

Homework Statement The matrix A = 1 1 1 1 -1 0 1 0 1 2 3 2 Express null space and row space of A in terms of their basis vectors. 2. The attempt at a solution I have found the null space to be: x3 [1 -2 1 0]^T + x4 [0 -1 0 1]^T. But my problem is how do i write the final answer correctly...

I am using smooth-particle hydrodymamics(SPH) method to model a deformable object. It is based on the procedure found in Markus Gross's point based animation book, the algorithm is attached in the image below. This algorithm uses Euler for numerical integration as seen in step 21 and 22, and...

Let's say I have an equation E=iE0cos(kz-wt)-jE0cos(kz-wt), how do I look at this and know, this is linearly polarized? or what if it changes and the kz is negative? or its a sin function with with (wt-kz-pi/4) in it. I just don't understand what this equation is supposed to be telling me and...

So I'm a second year Physics and Math major with the long term goal of a PhD in Theoretical Physics or maybe Math. I asked around at the start of this semester whether there was anything available for me in terms of research in the Physics department. I found a professor willing to take me on...

How should I go about starting the following two problems solve the following initial value problems x''-4x=0 ; x(0)=1, x'(0)=0 and x''-4x'+4x=0 ; x(0)=1, x'(0)=0 Should i use a general solution with the basis m^2-4=0 for problem one and m^2-4x+4=0 for the second?

Hi, this is not really a homework problem, but something that came up during my research, upon trying to integrate some empirical function. This function consists of many terms, but specifically, there is a term containing double exponential functions which is giving me some trouble. If...

Homework Statement "A passenger (mass m) initially at rest steps out of an airplane. Assume down is the positive x-axis and put the origin at the airplane. Assume the air resistance force is linear in the velocity so F(air)= -mbv. Find the distance D he has fallen when his velocity is...

Homework Statement Evaluate the sums: \sum^{n}_{i=1}ia^{i} Homework Equations The Attempt at a Solution I'm assuming that because there's no limit or anything, the professor wants an equation. I know \sum^{n}_{i=1}i is \frac{1}{2}n(n+1) and \sum^{n}_{i=1}a^{i} is \frac{a^{n+1} - 1}{a-1}-1...

Homework Statement Find the second derivative of 4x^2 + 3x - 9y^2. Answer in terms of y. Homework Equations All derivative formulas. The Attempt at a Solution [PLAIN]http://http://i52.tinypic.com/2w2ptex.jpg I can't get much further than this; the thing that gets me is how to put...