Method Definition and 1000 Threads

Hi, I'm practicing some of the methods for solving LODE's for my exam tomorrow afternoon and am struggling to understand one of the steps, I'm hoping someone will be able to explain it for me :) So I have the equation $(x-1)y''-xy+y=0$ with x being a solution. Then: $y(x)=xv(t)$...

Ok, I'm going to be taking calc III next week, so I wanted to get a head-start by doing the MIT multivariable calculus opencourseware. While most of the material was easy, these proofs are really killing me. Here are two examples: Ex.1: Using vectors and dot product show the diagonals of a...

Hi everyone, I don't fully understand what is the regular method to state and solve problems in GR when no handy hints like spherical symmetry or homogeneity of time are assumed. If I find myself in arbitrary reference frame with coordinates x^0, x^1, x^2, x^3 the meaning of which is unknown...

This is a section from the Pan Air user's guide (Pan Air is a aerodynamic panel-method flow solver). I'm confused by the symmetry and anti-symmetry. The first one is easy enough: mirror about the XZ plane (Yimage = -Y, Ximage = X, Zimage = Z). The third one is no symmetry applied. Also easy...

Hey everybody, I thought I would share an algorithm for factoring that I designed a few years ago while working on a Z80 project. I noted the same thing Fermat must have: a^{2}-b^{2}=(a+b)(a-b) After a few moments of looking at it, I realized the translation of that simple expression: If I can...

By using frobenius method I find the roots of the indicial equation of a 4th order ODE to be 0, 1, 1, 2 Now, what is the form of the corresponding series solution of this equation with log terms?

Homework Statement Given f(x) = x^(2/3), find f'(x) using the Δ method. Homework Equations f'(x) = (f(x + Δx) – f(x))/(Δx) The Attempt at a Solution I understand the entire solution (that is attached along with the problem as a png file), except how to get [(x + Δx)^(4/3) + (x +...

So here I am trying to solve Rayleigh's differential equation using Rungen-Kutta 4th order analytic method. This is what the exercise gives me: X(0 to 40), Y1(0)=0.1, Y2(0)=0, H=0.1, μ=0.5 This is what I ve written and gives me this error: IMPLICIT REAL*8(A-K,O-Z) DIMENSION...

Homework Statement Use method of Frobenius to solve this equation: ##y''(x)-y'(x)=x## Homework Equations ------ The Attempt at a Solution Seek an answer of the form ##y=\sum _{n=0}^{\infty } a_n x^{n+r}## Plug into the equation to get... ##\sum _{n=0}^{\infty } a_{n+1} (n+r)...

I'm going to try my first chemistry experiment. http://www.chemteach.ac.nz/investigations/documents/chloride_mohr.pdf I bought 35g of potassium chromate and 5g of silver nitrate. 5g of silver nitrate is only enough for one test. What should I do with the silver afterwards? Is it...

I remember when I took Calculus B in college. I had never learned any math by reverse engineering before, but when I got to sequences and series, the only way for me to learn how to do it was to reverse engineer it. I had to look up the answer in the back of the textbook, and then work...

Homework Statement Find the voltage Vo using node voltage method specifically.Homework Equations The Attempt at a Solution I am able to get the correct answer when finding the equivalent impedance, then determining the current, and then finding the voltage at the first node V1 by subtrating...

Hey, I'm really struggling with this 'show that' question regarding the secant method, I just keep going in circles and I think I may be heading in completely in the wrong direction because I'm not getting anywhere. Homework Statement We're given that, if x* is the zero of f then (we...

In this experiment, we recorded a person saying "Aaaaaaa" on the mic as the analog source. And then the analog data was converted into digital data so that the programme in the PC could read it and then the digital data was converted into Analog again to reproduce the recorded voice. I attached...

Homework Statement Consider a potential function V(x) such that: $$ \begin{cases} V(x)\leq 0\text{ for }x\in[-x_0,x_0] \\ V(x)=0 \text{ for }x\not\in[-x_0,x_0] \end{cases} $$ Show, using the variational method that: (a) In the 1-dimensional case \lambda^2V(x) always possesses at...

Hi! Which is the better method for finding Fourier expansions of a function? The ordinary one (find a_0, b_n and a_n with separate integrals), or the one which uses complex numbers (just find c_n)?

Hi people, I need help to this problemSomeone has suggested that the device shown in the figure below be used to improve the maximum force F against the spring, which has a spring constant of k. This is accomplished by changing the temperature of the liquid-vapor mixture in the container. You...

Hello, I am trying to program a double pendulum via the 4th order Runge-Kutta method and I cannot seem to be getting the right output. At first I used the Euler-Cromer method, but now I am aiming to make it more accurate. Homework Statement I have the equations of motion: d(omega)/dt and...

Hi! Could you tell me the idea of using Jordan exchange for the Simplex Method?

Homework Statement Find the tension in the rope Homework Equations F=ma The Attempt at a Solution I was wondering whether I could use method of sections in this problem to divide the two systems so that I could find the tension in the rope. I have a strong feeling that I...

This is a problem from Tom Apostol's calculus book (the very first problem set in the introduction). It wants you to find $$\int_0^b (ax^m+c)\,dx$$ using Archimedes' method of exhaustion. I'm attaching a diagram and a pdf of my work for the problem since it's rather involved. I'm doing this...

Dear friends, can some one tell me the method to learn electrodynamics??(iam a postgraduate student). Thank you

Homework Statement There are 20 couples who attend a party where there is a raffle. 10 Winners are chosen in the raffle. What is the expected number of couples for which both members win. Homework Equations Assuming method of indicators is used to solve the problem, Ai={members of ith...

Dear Forum : I hung up with a integration http://ppt.cc/mIpV Can it be deduced to a simpler form? The distribution of σ(E) is http://ppt.cc/-5Z5 The estimation width of x is 10MeV , height is 200mb. The distribution of dE/dx is http://ppt.cc/vcVU Is there a way to do some simple...

Homework Statement A ball is dropped from rest from the top of a 6.10m building, falls straight down, collides inelastically with the ground and bounces back. The ball loses 10% of it's K.E every time it hits the ground. How many bounces can happen and the ball still reach a height of 2.44m...

This is a closed loop system. My teacher showed me that one of the methods to find the natural frequency of this system is by finding the frequency at phase -90 degrees. Why must it be -90 degrees? Please explain. From the phase graph, the frequency at -90 degrees is 32 [rad/s], so that's the...

I am wondering if this method is in use already somewhere, or if its possible to be used. For example, using the equation of gravitational potential energy a 100kg weight that freefalls 100 meters has 98,000 J of energy, which equals 24,000 watts after approx 4 seconds of freefall. Assuming I...

can someone explain me in detail or simply how Gauss-Jordan way of solving equations works? thanks.

Here is the question: I have posted a link there to this thread so the OP can see my work.

"Critiquing" separation of variables method for PDE. I am currently taking a course in PDE's and it has been very "applied" and not so much theory based. I can say its been separate this separate that separate this separate that… Enough! We are always "separating variables" and it always...

Homework Statement I want to find two linearly independent solutions of $$ x^{2}y''-2x^{2}y'+(4x-2)y=0. $$ The Attempt at a Solution The roots to the indicial polynomial are ##r_{1}=2## and ##r_{2}=-1##. I found one solution which was ##x^{2}## and I am having trouble finding the...

I have a problem on which I need to apply Euler's method - EXCEPT that I don't have one of the crucial components. Question and my thoughts below: **Question:** Consider the initial value problem $\frac{dy}{dt}=\alpha t^{\alpha - 1}, y(0)=0$, where $\alpha > 0$. The true solution is...

Homework Statement Homework Equations Pk = A*Xk - F τk = ((A*Xk - F)*(A*Xk - F))/(A*(A*Xk - F))*(A*Xk - F) Xk+1 = Xk - τk * (A*Xk - F) The Attempt at a Solution We are given a system of equations: AX=F, where A3x3= (2 1 0.95; 1 2...

Problem: I need to use the Monte Carlo method to generate the mean, variance and kurtosis of the standard normal distribution. It has to be coded in Matlab, so there are two parts to this question: 1) The theory 2) The code Any help on either is appreciated. My attempt: To find $E[X]$ for a...

Hi everybody, I am programming a new code for a problem. The problem is numerically solving the Simple Harmonic Motion using the Euler method. This approach is just an approximate solution and not a exact solution, however when I run the code successfully and plot my data, it comes up as an...

Though standard gravity is 9.80665 m/s2, it must vary from city to city, since the Earth is neither a perfect sphere nor of uniform composition. I'm looking for an experiment to accurately determine the value of g at my current location. The method needs to be precise enough to yield different...

In the above example, the method of sections is used to solve the truss. However, they do not consider the forces in other beams (the beams that are not being cut; e.g. AB, AH). Is this always the case with this method?

Ok so first I considered the entire structure (which is in equilbrium) and resolved to find out that HA = -4.8 kN, VA= -0.9 kN and VE=0.9 kN. (these answers were correct according to mark scheme) Then I considered each joint separately (in order to find the forces in each of the members). I...

Hello, I am stuck with this one. Your help/comments would be most appreciated. A charge "+Q" lies at a distance "d" above an infinitely large conducting plane. Applying the method of images, i found the right result that the total charge of the infinite plane is "-Q" and that the stored...

Homework Statement So, I've written a program that carries out Newton's method. The root of the equation which I am trying to find is approximately 13.1. This is fine and my program returns the correct value when my initial guess is around this value (up to about x = 50 as my initial guess)...

I am thinking about taking a finite element method course. I know what FEM is and how it solves boundary value problems and stuff but I'm wondering how widespread it is used... Is it a useful numerical technique? What industries/research use it? I am interested in research in continuum...

Greetings, If we have a function y=f(x), we can calculate the surface area traced by that function when rotating about the x-axis as 1: S=∫dx\,2πf(x), which makes perfect sense to me. I am told that, if we have x=x(t) and y=y(t), the equivalent expression is 2...

Homework Statement $$ \left(\frac{du}{dx}\right)^2 = au^2 + bu + c $$ Homework Equations The Attempt at a Solution What method is used to solve and ODE of this form

Homework Statement dv/dt = (v+1)/10v^2 Euler method delta t = .5, t =0 and v = 1, to find v(4) Homework Equations I'm using v = v(old) + (stepsize)(dv/dt) I'm just wondering if anyone can confirm my results. My teacher said that although this seems easy over half the homework will...

I want to compute the flux surfaces using FEM but i haven't found any good source to read. any help will be appreciated. Thank you

Homework Statement Differentiate the following with respect to x y = \frac{4}{x^{3}} + \frac{x^{3}}{4}The Attempt at a Solution So the problem here is really getting this into a form that is easy to differentiate and i'd just like to show what I'm doing before I go ahead and do the rest of...

I am trying to run a program with fortran. The program is about solving the Oscillator using Euler Method. I am trying to run this code and applying array arguments (as I want to extend it to 3 dimensions afterwards). When I try to compile, it comes up with an error "Unclassifiable statement at...

Consider the PDE xu_x + yu_y = 4u. Suppose that we want to find the solution that satisfies u=1 on the circle x^2 + y^2 = 1 using the method of characteristics. I have read that the boundary condition can be parameterized as x=\sigma, \qquad y=(1-\sigma^2)^{1/2}, \qquad u=1. My...

Hi all, I'm learning how to solve redox equations. I found the algebraic method to solve equations such as this one: Fe^{2+} + Cr_{2}O_{7}^{2-} +H^{+}\rightarrow Fe^{3+} + Cr^{3+} + H_{2}0 and i was able to solve it. What I don't see is how to use that algebraic method to solve an...

Hello, I was wondering, is there a preference for when to use either of these methods for solving statically indeterminate structures, or are both equally viable in all situations? Also, when using these how does one know where to ''cut'' the sections up to find the internal forces? Thank you