Method Definition and 1000 Threads

Hello! An assignment for my computational modeling course is to demonstrate the use of the Standard Euler method for modeling a simple harmonic oscillator; in this case, a mass attached to the end of a spring. I have the two coupled first-order differential equations satisfying hookes law...

The question is... So of course I rearrange my ellipse formula to get y=\pm\sqrt{1-\frac{{x}^{2}}{4}} Then I calculate my radius as x-(-2)=r \implies x+2=r I know the formula for finding volume with the Shell Method is V=\int_{a}^{b}2\pi x\cdot f(x) \,dx To make it easier I decide to just...

Homework Statement Let u = ∂f/∂x and v = ∂f/∂y. Use Lagrange's method to set up the equations necessary for finding the maxium of u^2 + v^2. Homework EquationsThe Attempt at a Solution I know how to minimize and maximize a function that's a subject to another one. I'm not quite sure what the...

Homework Statement Which of them is an example of polymorphism? public Class D extends B { public void f() { this.g(); // 1 } public void g() { super.g(); // 2 }} Homework Equations Polymorphism: The ability of an object to refer to objects of other types. The ability of a method to...

Hi, I have a somewhat strange request (hence did not knew which section to use for this post). I have no formal training in sciences (have a degree in philosophy, and no matter how much my peers disagreed with my opinion, that is not a science:), but I fell in love with science while studying...

I've been reviewing my knowledge on the technique of variation of parameters to solve differential equations and have a couple of queries that I'd like to clear up (particularly for 2nd order inhomogeneous ODEs), if possible. The first is that, given the complementary solution...

hello all dear please help me can solve this Example By Simulation With matlab

Homework Statement I am writing a simple program in Mathcad for Newton's Method. The function is x^3-5*x^2+3*x+4. The root is between 0 and 3, and we want a tolerance of 0.00001. My code is the exact same as a program I made in Matlab that works, but since I am new to Mathcad, I am getting an...

Homework Statement Homework Equations V=IR The Attempt at a Solution I believe my a1 and a2 are correct. But my b1 is definitely wrong. Even if I carry out the above subtraction for the v1 part (which gives you b1) I will not have somethign as simple as R2 + R3 on the numerator [/B]...

Homework Statement Evaluate the following integral using a change of variables: \int\frac{dx}{\sqrt{1-\sin^4{x}}} Homework Equations If f(x)=g(u(x))u'(x) and \int g(x)dx = G(x) +C then \int f(x)dx = G(u(x))+C The Attempt at a Solution It seems helpful to first simplify a little to obtain...

Homework Statement For the portal frame geometry and factored loading shown in the figure below, calculate the shear force, axial load and bending moment diagrams using the Portal Frame Method. You may use the principle of superposition for gravity and lateral load effects. Note: • all...

Homework Statement Not really for homework, but it is a script I am working on. It involves utilizing the Bisection Method for solving equations in one variable. However, I cannot seem to get it to work properly. It seems to enter the while loop and become stuck their. When I execute it by...

I'm using the method of characteristics to solve a pde of the from ## au_{x}+bu_{y}=c## where ## a=\frac{dx}{d \tau} , b= a=\frac{dy}{d \tau}, c=a=\frac{du}{d \tau}## where initial data is parameterised by ##s## and initial curve given by ##x( \tau)=x_{0}(s)##, ##y( \tau)=y_{0}(s)## and ##u(...

Good day, guys ! I am working on a project regarding the transfer matrix method used in quantum tunneling by means of a MATLAB program --- Cantor set fractal potentials. I am trying to represent some things here (as seen in the document below) : - the eigenvalues for the energy - the...

What I learned from a book, B-spline is constructed by knowing some control points. However, below video showing that a B-spline is not constructed by a control point instead of fitpoints and tangent weight (handle). Anyone know what is the name of the theory of it in a book and how to solve...

Hello! I have some queries regarding Vortex Lattice Method. I want to design an airfoil using Vortex Lattice Method. For that, I need to find out the equation of airfoil first. So how exactly am I going to do that? Please refer the following link...

I have a question regarding the legality and generality of the following method for simplifying a vector expression. The specific expression that arose my question is ##\left[\left(\vec{P}\cdot\hat{r}\right)\left(\hat{r}\times\vec{M}\right) +...

Hi, I'm looking at the Jacobian condition which is ## J= a \frac{dy_{0}}{ds}-b\frac{dx_0}{ds}## where the pde takes the form ##c= a\frac{\partial u}{\partial x} + b \frac{\partial u}{\partial y} ##, where ##a=\frac{\partial x}{\partial \tau } ##, ##b=\frac{\partial y}{\partial \tau }##...

NOTE: I know the solution, but I challenge it. Specifically, I feel that the generally accepted solution to this problem is not intuitive. I have shown the accepted solution, and below that I have shown what I feel seems more intuitive (from a geometric standpoint)...

Homework Statement Hey, first time poster here, I'm current writing up a lab report I just wanted to check my method is correct. I'm doing alpha particle spectroscopy using a cloud chamber setup. Most published reports seem to vary pressure (so the mass thickness varies). Our chamber let us...

Hi, I am trying to solve the following ODE for my maths project: ## y'' = \frac{\alpha}{2}y^3 - \frac{3}{2}y^2 + y - \frac{3}{x} y'## under the following boundary conditions: ## y'(0) = 0 ## ## y(x) \rightarrow y \_ \equiv 0\ \text{as}\ x \rightarrow \infty ## As a first step, I converted...

Homework Statement Consider a one-dimentional particle in a box with infinite potential walls at x=0 and x=L. Employ the variational method with the trial wave function ΨT(x) = sin(ax+b) and variational parameters a,b>0 to estimate the ground state energy by minimising the expression E_{T}=...

How to find the Initial guess for Newton method with high accuracy ?? Is there a way rather than using mean value theorem [which is used to test whether there is a solution on a closed interval to the equation] ?

Dear All, I am trying to understanding Cardano's method to solve the cubic equation. Please first see the reference text that is attached (Alan F. Beardon, Algebra and Geometry). My rough understanding is that we make 2 substitutions (## P1(z - a/3)## and ##P(z - b/z) ## ) to...

I saw this method of calculating: $$I = \int_{0}^{1} \log^2(1-x)\log^2(x) dx$$ http://math.stackexchange.com/questions/959701/evaluate-int1-0-log21-x-log2x-dx Can you take a look at M.N.C.E.'s method? I don't understand a few things. Somehow he makes the relation...

when we calculate the neutron flux in finite medium using sn method for steady state neutron transport equation, it gives us some numbers up to 1. I am sure its not the real flux, can someone explain how we can calculte the real flux using sn method.

I will even take book recommendations, though I have read Polya's "how to solve it," and Vellemans similarly titled "How to Prove it." I think I am looking more for how to organize my thoughts, and much of this overlaps with "how to study," which, I am still trying to learn how to do. My...

Homework Statement I'm going to list two questions as they offer the same problem with more choices, hopefully it will help realize the method (?) used (A) An electron, confined in the two dimensional region 0<x<L and 0<y<L with infinite potential walls, is subject to the potential...

What is the easiest method for adding and subtracting rational numbers

In C#, byte[] tail={...} short reader = BitConverter.ToInt16(tail, 4); which is to convert 2 bytes 4 and 5 to a short value. I'd like to do this in C++ So I do char tail[]={...} short reader=toInt16(tail,4); ... short toInt16(char*tail,int index) { int n=index; int m=n+1; string...

Hello, i'm willling to solve partial differential equation of the form: dy/dt = d2y/dx2 + 2/x * dy/dx - 4y where d here means partial derivation of course. boundary conditions are: dy/dx(0,t) = 0, y(1,t) = 1, t>0 initial condition is: y(x,0) = 0; (x,y) is position and t is time. and...

Homework Statement Find ix and Valpha [/B] Homework Equations KCL KVL The Attempt at a Solution [/B]How do I determine the number of KCL and KVL equations? In this problem I am solving, there are 6 unknowns so I need 6 equations. I can write 4 independent KCL equations, 1 KVL at loop 1(to...

Hi I was hoping someone could clear something up for me, I've been set an virtual load (unit load method) question at University, that part of the question I can do however its the calculating the force on the members part that I am struggling with. The question asks for all the forces in the...

Homework Statement Use Euler's method with h=0.1 to find approximate values of the solution of the initial-value problem y'+3y=7e^(4x), y(0)=2 at x=0, 0.1, 0.2, 0.3, ..., 1.0. Homework Equations f(x, y)=7e^(4x)-3y x0=0, y0=2 The Attempt at a Solution y(0.1)=y1=y0+f(0, 2)(0.1)=2+(0,1)f(0...

Homework Statement Consider a mass sliding down a frictionless curve in the shape of a quarter circle of radius 2.00 m as in the diagram. Assume it starts from rest. Use Euler’s method to approximate both the time it takes to reach the bottom of the curve and its speed at the bottom. Hint...

is there a general formula/algorithm to parameterize an equation? for example if i have a function f(x,y)=0 then can i always change it to the form x(t),y(t)? or if i had g(x,y,z)=0 then can i change it to something like x(u,v),y(u,v),z(u,v) i know of examples, like if i have x^2+y^2=1 then...

Homework Statement Write a program to simulate motion of simple harmonic oscillator. Initial conditions: Let ω = 1, x(t=0) = 1, v(t=0) = 0. Integrate over 30 seconds in intervals of 0.05s. Homework Equations δ2x / δt2 = -ω2x As set of 2 coupled ODE's; x' = v, v' = -w2x The...

Dear All, I am trying to understanding Cardano's method to solve the cubic equation. The reference text is attached (Alan F. Beardon, Algebra and Geometry). My rough understanding is that we make 2 substitutions (## P1(z - a/3) and P(z - b/z) ## ) to simplify the cubic equation...

Homework Statement Integreate: ##T = ∫ \frac{dy}{V_ab (y)} = \frac{2}{v}∫[1 + \frac{\alpha^2 y}{L} + 2\alpha \sqrt\frac{y}{L} cos(\phi(y))]^\frac{-1}{2} dy## where ## \phi (y) = \frac{\pi}{6} + sin^-1(\frac{\alpha\sqrt{y}}{2\sqrt{L}}) ## The limits are between 0 and L Homework EquationsThe...

Is there any method for deduce Schrödinger equation from quantization of action??

It is common that we replace \int u(x)v'(x)dx by \int udv where both u and v are continuous functions of x. My question is, must we ensure that u can be written as a function of v before applying this? The above substitution method is involved in the proof of integration by parts but I cannot...

Hi, I am trying to plot a function subjected to a nonlinear wave equation. One of the method I found for solving the nonlinear schrodinger equation is the split step Fourier method. However I noticed that this method only works for a specific form of PDE where the equation has an analytic...

Homework Statement dx/dt= -x2-2x(1+t+t2) x(1)=2 estimate x(1.2) with h=0.2 Homework Equations Implicit Euler: I was taught that we must solve for yk+1 using Newton's method: This doesn't seem like it will work because Newton's method assumes a function of only one variable. According to...

Hi, Can somebody tell me if my kinetic energy (T) and potential energy of spring (V) for this system in matrix form is correct or wrong, m1= 2, k1 =5, m2 = m2, k2 = k2 T = 1/2 (2* q1'^2+ m2* q2'^2) so in matrix form it was 1/2(q'^T) (2 0 *( q')...

Hi everyone, I'm having a bit of difficulty choosing an admissible function for a fixed-fixed nonuniform bar. I chose the function φ(x) = 1 - cos(2πx/L). But when solving for the the stiffness and mass coefficients: kij = ∫EA(x)φiφjdx mij = ∫ρ(x)φiφjdx, I am not sure where I should have...

We have been covering the annhilation and creation operators in class. You can use the annihilation operator to find the groundstate wavefunction, and then use the hamiltonian in terms of annhiliation and creation operators to find the energy eigen value of that state. (or you could put the...

Homework Statement I'm asked to solve the Hermite Differential Equation y''(x) - 2 x y'(x) + \lambda y(x) = 0 using the Frobenius method 2. Homework Equations I am to assume the solution is in the form y(x) = \sum a_n x^{n+r} where r are the roots of the indicial equation that in this...

Hi. In class, the professor has tried to derive the equation by using the principle of least-action. (But not yet completed. Maybe next class...) However I heard this method is used by Hilbert, who had derived the equation 5 days before Einstein derived it. Then, what method did Einstein use...

Homework Statement The Newton iteration formula is based on a Taylor series expansion of the function f(x) around an estimate of the root xn, truncated after the linear term. You are asked to derive a more accurate iteration scheme as follows: Start from the Taylor series expansion of f(x)...

Homework Statement I have been asked to show a graphical, more accurate method to calculate power used when running up a flight of stairs. The method I have used previously is measuring the height of the stairs, recording my weight in Newtons, timing how long it takes to run from the bottom to...