Euler Definition and 414 Threads

How do i comput the euler phi function of a large interger? i know that if p is prime then phi(p)=p-1 and I've found a formula for computing non primes but i don't know how to implement in something like Matlab. Does anyone know how?

How do i comput the euler phi function of a large interger? i know that if p is prime then phi(p)=p-1 and I've found a formula for computing non primes but i don't know how to implement in something like Matlab. Does anyone know how?

Is it possible to prove Euler's identity (e^i*pi = -1) without simply taking it as a special case of Euler's formula (e^i*x = cos(x) + i sin(x))?

Hello, can anyone help with this question? Thank you. Let n even perfect number and q prime. Show that n/Φ(n)=2q/q-1. Φ(n) is the Euler function-totient (the number of positive integers less than or equal to n that are coprime to n) I have tried euler-euclid theorem but could not...

Homework Statement Check out problem 5.7 part a I want to express the exterior gravitational potential in terms of the Euler angles so that I might eventually use (dV/dB)B=B0 = 0 - the condition for equilibrium. I am therefore expecting the Lagrangian to be cyclic in terms of the other two...

Euler Method in Fortran - HELP! Using Euler method I want to calculate the equation below, deltat=0.3, 10 times. Problem: When n=1, Yn1(1) is calculated right. But, in the following steps it should assume that Yn(2)=Yn1(1) and the program is assuming Yn(2)=0, as well as Yn(3)=0,...and so on...

although is not valid in general (since an Euler product usually converges only when Re(s) >1) \frac{ d \zeta(1/2)}{\zeta (1/2)}= -\sum_{p} log(p)(1-p^{1/2}

I'm stumped on a HW question that I just can't seem to proceed on. Homework Statement An incompressible ( rho = constant ) flow in 2 dimensions [x = (x,z)], with F = (0,-g), satisfies Euler's equation. For this flow, the velocity is u = (u0,w(x)), where u0 is a constant, with w = 0 on x...

firstly, all d's i use will mean partial derivative 'do' because i don't have the font installed. sorry :( please help me with these.. u got to use euler theorem 1. if z= xf(y/x) + g(y/x), show that x2(d2z/dx2) + 2xy(d2z/dxdy) + y2(d2z/dy2) =0 2. if z= (xy)/(x-y), PT (d2z/dx2) + 2(d2z/dxdy)...

Hi all Im working on a systems dynamics problem which involves modelling a double pendulum, a chaotic system I have a non linear system of 4 1st order differential equations which I need to solve using numerical methods in MATLAB The methods are ode45, ode23s and euler method Ive...

Dear All, Suppose you have two versors x and y. You would like to calculate the 3 Euler angles between them. How would you do that? You know that x=Ry where R is the rotation matrix (see e..g Goldstein). Now the point is that I know both x and y and want to get phi, theta and psi (no...

The functions K maps to f(K) and C maps to U(C) are given as: F(K) = aK and U(C) = -C^2 +b here a and b are positive constants. the initial and teriminal conditions with the triminal time T = 1/a are K(0) = K_0 and K_T = K(1/a) here K_0 and K_T are positive constants. Write Euler...

Trying to implement QR decomposition using Givens rotations, I calculate G1 to zero n32 of original matrix A, then G2 to zero n31 of G1 * A, then G2 to zero n21 of G2 * G1 * A. Residual matrix, R = G3 * G2 * G1 * A comes upper triangular as expected, so I believe my code is correct. Looking...

Homework Statement integrate dy/dx = (1+e^y)(1+x) from x=0 using the improved euler method taking step sizes of 0.125. compare the numerical solution of y(0.5) with the exact value The Attempt at a Solution Firstly to find the exact value I use separation of variables and the initial...

can anybody please clearly explain me the difference between these two frames of reference with few examples. my exames are closing up. please help me.

I'm so confused on how to tackle this problem: 1. Truth tables are related to Euler circles. Arguments in the form of Euler circles can be translated into statements using the basic connectives and the negation as follows: Let p be “The object belongs to set A. “Let q be...

Hi, I don't know if this is the right forum to adress, but I will try nevertheless Im solving a simple two-dimensional differential equation: dx/dt = (-y,x) which will give a circle when integrating over time. Now, the problem is that the simple euler scheme seems to be a lot more...

In the general DE form, y"+y=0 and where the initial conditions are y(0)=2 and y'(0)=0, Euler realized that y(x)=e^ix+e^ix. How did he know that it's a cosine graph when there's no indication in the equation that any solution is possible? y= c1+c2=2 but y" gives 0.

Prove that if d divides n then phi(d) divides phi(n). Thanks

I'm trying to follow a professor's notes for finding Christoffel symbols for a two-sphere. He gives the following two equations: The Lagrangian for a two sphere:L = \left( \frac{d\theta}{ds} \right)^2 + sin^2\theta \left( \frac{d\phi}{ds} \right)^2 The Euler Lagrange equation: \frac{d}{ds}...

I have 15 equations with 15 unknowns describing a dynamic process. I would like to know how I can conbine solving non-linear equations together with ordinary differential equations (1st and 2nd order) simultaneously, without using ode45, but Euler's method.

Direction field Do anybody have a hint for drawing direction field of a non-autonomous differential equation? I mean do I have to calculate as many slopes of points as possible, then draw it? Also, Can I conclude that if we use Euler's Method to estimate a CONCAVE UP/ CONCAVE DOWN...

Simple question, I have used the euler expansion to estimate a variable that grows as a single exponential. adapt = Amax * exp(-tau*X); In excerpted form: for (i=1;i<npts; i++) { adapt[i] = adapt[i-1] + (Amax -adapt[i-1]) * dt / tau; } where dt is the step size and tau is...

Hi everyone :D This is my problem: Find conditions on \alpha and \beta in the Euler equation x^{2}y'' + \alphaxy' + \betay = 0 such that: a) All solutions approach zero as x \rightarrow 0 b) All solutions are bounded as x \rightarrow 0 c) All solutions approach zero as x \rightarrow\infty I...

Can someone explain "Euler" angles? From what I read, "Euler" rotations are composed out of matrices like * * 0 1 0 0 * * 0 * * 0 0 * * * * 0 0 0 1 0 * * 0 0 1 which is pretty distinctive in that they rotate around same axis twice, and makes sense for devices like this...

[SOLVED] Euler Lagrange Equation Hi there , I am missing a crucial point on the proof of Euler Lagrange equation , here is my question : \frac{\partial f}{\partial y}-\frac{d}{dx}\left(\frac{df}{dy^{'}}\right)=0 (Euler-Lagrange equation) If the function "f" doesn't depend on x explicitly...

Let's say you have some type of simplicial complex that is made only of 2 simplices. What happens if all those 2 simplices are adjacent to a single edge (creating a type of book shape), so that this complex can only be embedded in dimensions 3+? Would this complex have the same 2nd betti number...

i have an orientation of a 3d object in space given by theeta, si and phi i.e. angles which the objects makes with respect to three axis. Now i want to translate the problem such that i get an arbitrary axis rotation about which to some calculated degrees would produce same orientation...

Homework Statement Find the general solution of x^2y" - 2y = 0 Homework Equations The Attempt at a Solution Can anyone tell me how to find the general solution of the Euler Cauchy equation. How do we make it into one?? Thanks.

I have a number of objects (points) in a 3D space. I need to rotate this space using euler angles (or equivilent) and place it in another coordinate system. (ie i start with objects placed within the confines of a cylinder aligned with the z axis, and after rotation have a cylinder of objects at...

Hi people! Well i don't know if all here know about the Project Euler (http://www.projecteuler.net/) but i think it is very useful because for all of us here know how to program numerical algorithms fine is very important. "Project Euler is a series of challenging mathematical/computer...

I was wondering how I would go about proving this equation: \int_{1}^{\infty}\frac{u-[u]}{u^2}du=1-\gamma where \gamma is the Euler Constant, and [u] is the floor function

Is the Euler line in triangles USEFUL for anything in real life? This is the line which contains the concurrency points for the intersections of the triangle perpendicular bisectors, the medians, the altitudes, but not the angle bisectors. Interesting stuff, but are these points which occur on...

i was asked to calculate the integral: \int\frac{dx}{x+\sqrt{x^2-x+1}} by using euler substituition (i.e, finding a line which intersects sqrt(x^2-x+1) through one point and then the equation of the line will be y-y0=t(x-x0) where (x0,y0) is one point of intersection, and then substituing x for...

This may be a stupid question, but I do not understand why the Euler sum is infinite for zeta=1. Why is "1+1/2+1/3+1/4+... " infinite, but zeta=2 (1+1/4+1/9+...) not?

Hi everyone, I am trying to get an intuitive grasp of the Euler Relationship e^i(theta)=cos(theta)+i sin(theta) and also understand how to graph the exponential spiral, as demonstrated on this web page: http://www-math.mit.edu/daimp/ComplexExponential.html" Ok, first the neuron...

Hi i am reading about signal and systems course . What i want to prove is not a problem that i have to solve is something that the books take for granted and i want to prove it so i ll be able at exams to reprove so i won't have to remember it, (if u don't believe me i can give u the course's...

I went off on my own to study the Euler caracteristic + orentability caracterisation of closed surface and I must have gotten lost somewhere, because I do not find that the Klein bottle is homeomorphic to \mathbb{R}P^2\#\mathbb{R}P^2 as I should. I started with the result that for two surfaces...

(a) Let alpha (a) and beta (b) be given constant. show that t^r is a solution of the Euler equation t^2 d^2y/dt^2 + at dy/dt + by = 0 , t>0 if r^2 + (a-1)r + b = 0 (b) suppose that (a-t)^2 = 4b. Show that (ln t)t^(1-a)/2 is a second solution of Euler's equation. please help, i have no idea...

In "Dr. Euler's Fabulous Formula" by Paul Nahin, early in chapter 1 is discussed characteristic polynomials of a square matrix and the Cayley-Hamilton theorem, that any square matrix A satisfies its own characteristic equation. On page 21 it states p(lambda) = lambda^2 + a1*lambda + a2 = 0 and...

I've been trying to do some simulations using the Euler, improved Euler, and Runge-Kutta methods. My results for the improved Euler and Runge-Kutta are very close to my results with the plain old Euler method. If there is any improvement, it is negligible. This lack of improvement surprises...

Homework Statement For fun: show that B(a,b) = \int_0^1{x^{a-1}(1-x)^{b-1}\,dx} = \frac{\Gamma(a)\Gamma(b)}{\Gamma(a+b)} where a > 0 , b > 0 . Hint: start from the product \Gamma(a)\Gamma(b) and switch to polar coordinates. The radial integral is proportional to \Gamma(a+b).Homework...

"Euler" was pronounced with a long "u" sound Ok, Up until last week I thought "Euler" was pronounced with a long "u" sound (like Euclid). Since most of the famous names of science/math are names I have read, not heard, I was wondering if someone could give me the correct pronunciation of...

Hi How do I solve the equation x^7 \equiv 21 modulo 66 66 = 2.3.11 so try solving it mod 3 and mod 11 (mod 2 doesn't gives any new information). This tells us x is divisible mod 3, and x^7 = -1 mod 11. One solution to this is x = -1 mod 7. The smallest solution of these two congruences...

Hi I got two tasks which I have some trouble with. 1) A guy has 1770 dollars to shop food for. One bread costs 31 dollars and a jar of jam costs 21 dollars. How many loafs of bread and jar's of jam can the guy buy? I'm suppose to calculate it using Euler Algebra 31x + 21y...

Hi, I was wondering if Matlab was the sort of program I'd want to solve the Euler Equations (fluid dynamics). And if it is, I am sure this must be a very standard problem.. does anybody know of any tutorials for this sort of problem as I have never used matlab? :-p

The Euler Function \varphi (n) is defined as the number of natural numbers less than n that are relatively prime to n. That is, \varphi (n) = | \{ a \in \mathbb{N} | a < n and gcd (a, n) = 1 \} | I have been asked to show that if a number d divides a number n, then \varphi (d) divides...

I'm looking for a method to rotate a 3D vector, and place it at an arbitary 3D point (x,y,z) without changing the vectors magnitude. I have briefly investigated eulers angles (mainly through wikipedia links etc), but don't fully understand the process yet. As an example, given the vector ...

Can anyone describe what the effects of the Euler force are? If you're not familar with it, it is a fictitious force that arises from a rotating object undergoing a change in rotation speed. Can someone tell me what the effects of this fictitious force are?

In an anlaogy with the Euler product of the Riemann function we make: \prod_{p}(1+e^{-sp})=f(s) of course we have that: f(p1+p2+p3)=f(p1)f(p2)f(p3) f(x)=exp(-ax) if Goldbach Conjecture is true then p1+p2= even and p5+p6+p8=Odd for integer n>5? then this product should be equal to...