Non-linear Definition and 318 Threads

Hi, let's suppose we are given N statistically independent samples x_1,\ldots,x_n from a certain distribution f_X(x;\theta) depending on a parameter \theta. We are also given an estimator for \theta defined as follows: \hat{\theta}}(N) = \min\{ x_i \\ : \\ i=1..N \} How am I supposed to...

"Non-linear Lines". How to Avoid Lying, without Confusing. Hi, everyone: I will be teaching an intro course in Linear Algebra this Spring. Problem I am having is that the definition of linear does not apply to lines that do not go through the origin: Let...

Hi, I'm new to this forum. It looks like an amazing source of information and people here seem to be helpful and knowledgeable. Briefly, I'm an undergrad student currently studying Mechanical Engineering at Concordia University, Montreal, Canada. The first equation seems a bit tricky...

Is there a strict connection between non-locality and non-linearity? Is it true that non-local systems must have non-linear equations? Are non-linear equations the consequence of non-locality?

Firstly, this is a great forum! Maybe this is more of a mechanical engineering question, but ... Can someone help give me some examples of non-linear levers? I want to be able to stretch a rubber band with factored-increasing force. Like a reversed camber on a compound bow. I hope I...

Homework Statement We are given the real sequence x_n+1 = (x_n)^2 - 100 + sin(n), some x_0 Prove that if the sequence is bounded with positive numbers, then necessarily 10 <= x_n <= 11 for all n>=0. Homework Equations The Attempt at a Solution I tried induction and...

We have a force which changes according to what point you're at, e.g: f=(4x²,3z-2y,2z), we need to calculate the work done by this force from point (0,0,0) to (2,1,3) on different curves I don't want an answer I just want an explanation for how this is done, this is what I understand so far...

The equation of motion of a rocket with mass depletion during ascent and subject to drag forces can be written as M(t) dV/dt = A - M(t)g - BV^2 (Eq. 1) with initial condition V(t=0) = 0 (V is velocity and t is time) Let us assume a linear mass depletion according to...

Homework Statement Im taking a dynamics course and I am using The strogatz book Non-linear Dynamics and Chaos I need to solve a problem that is similar to problem 6.1.14 Basically it consist in the following You have a saddle node at (Ts,Zs) which is (1,1). Consider curves passing through...

Question: (t-1)^4+5=3 I know the answer to the question states that there are no solution, but I would like to understand the intuition behind this. If I had this in a test I would waste ages trying to work out why I couldn't solve it. Any advice would be heaps appreciated. Thanks...

Hello, I have numerically solved the system below: dalpha/dx = -beta/(c_1) dbeta/dx = -(c_2)*beta/(c_1)+(c_3)*gamma*dgamma/dx dgamma/dx = (c_4)*[alpha^(c_5)]/c_2 where c_1, c_2, etc. are specified constants. If one plots beta as a function of x, there's a peak. I would like to use...

Tensor densities are normally defined in terms of coordinate transformations. Could they also be defined as functions of p tangent vectors and q cotangent vectors, just as tensors are defined, except relaxing the condition of linearity? Can anyone suggest a good, basic introduction to...

I have a third order, non-linear, homogeneous, constant coefficient ODE that I need to solve but have no idea how to do it. To make matters worse, one of the boundary conditions are indefinite. Here's the equation, y''' + y*y'' - y'^2 + 1 = 0 and the BC's y(0) = 0 y'(0) = 0 y'(\infty) =...

Homework Statement Solve the given differential equation by using the substitution u=y' y''+(y')2+1=0 The Attempt at a Solution If I got to this last integral correctly, I don't know how to solve it. I'm thinking I didn't get to that step correctly.. But I can't find my mistake..

Homework Statement I'm trying to solve the equations: \ddot{\phi} + 2\left(\frac{\cos \theta}{\sin \theta}\right) \dot{\theta}\dot{\phi} =0 and \ddot{\theta} - \sin \theta \cos \theta \dot{\phi^2} =0 for \theta(\lambda), \phi(\lambda) where the dots represent differentiation w.r.t...

Homework Statement (x+y)dx-(x-y)dy=0 Homework Equations The Attempt at a Solution The solution is c=arctan^-1(y/x)-(1/2)*ln(x^2+y^2) but I don't know how to get the answer. If someone could explain how to solve the above DE, that would be great.

Non-linear Differential Equation - Pulling my Hair ! Hi, What seems like a simple problem could be going abit better. Any ideas would be sincerely appreciated. (y'')^2 -xy'' + y' = 0 The squared term is causing me grief ! If I set say v = y' , that still leaves me with the squared term...

Homework Statement dx/dt = x - y + (x^2) - xy dy/dt = -y + (x^2) - Determine the critical points for the equation, - Determine the linearized system for each critical point and discuss whether it can be used to approximate the behaviour of the non-linear system. What is the type and...

Here is an image of the first order linear differential equation and my attempt to solve it. It ends in an integral that can not be solved. http://img831.imageshack.us/img831/9937/math1.gif And here is an image of the first order non-linear differential equation and my attempt to solve...

Hello; I do not have any experience in solving non-linear recurrence relations, so I was just wondering how one solves them. For example, consider the sequence: 1, 2, 6, 15, 31, 56 In general, F_{n+1} = F_{n} + n^{2} Do I still substitute F_{n} = k^{n}? Thanks.

Homework Statement y' = ( y - 1 )^2 +0.01 y(0)=1 (trying out latex) y' = (y-2)^{2} + 0.01; y(0)=1 Homework Equations Separation of variables, Right? The Attempt at a Solution The solution is is y(x)=1+0.1 Tan (0.1x) How did they get this? I did separation of variables...

Hi, I have a differential equation of the form d2 x ---------------- = g/z * x(t) dt2 Here g and z are constants. So, this is a 2nd order ODE which has a closed form solution. In fact, i know the solution for x in terms of cosh and sinh functions. In the above differential...

Homework Statement See figure. Homework Equations The Attempt at a Solution I tried KVL (see figure), but still got stuck with only 1 equation and two unknowns. Any ideas/tips on what I should try next?

Homework Statement See figure Homework Equations The Attempt at a Solution Again, see figure I tried something and it looked promising but the answer doesn't work out. Any ideas?

Hi, I just had my ordinary differential equation final exam today (summer class), the exam was fine. We had a bonus question though, it was a nonlinear second order differential equation, we didn't learn anything about those except for one existence and uniqueness theorem. I am curious if I got...

Cheers I am currently studying non-linearity properties of hydrodynamic waves from a purely mathematical stance. At the moment, I am concerned with radiation, modulational instability described by korteweg-De Vries equation (fifth order) and Spatial Instabilities and chaos in a high order...

Homework Statement It will be great if someone could show me some options: I need to prove the following: A particle of mass m is attracted toward a fixed point O (the origin) with a force proportional to its instantaneous distance from O raised to a positive integer power, i.e...

How to solve two nonlinear ODEs with boundary conditions? Here is the Q:

Homework Statement Determine the equation of the following points: (12. 270) (14, 300) (16, 330) (18. 380) Homework Equations The Attempt at a Solution I realized right away that this is not a linear set of points, so it wouldn't work out to just find the slope between two...

Im trying to check my answers to a problem, and in the past I've used a 3d grapher to graph functions like f(x,y) = whatever. but now i need to find a tangent plane to a surface at a point. the surface is: x2y+y2z-z2x=1but i don't know how to go about graphing something expressed that...

I've been trying to think of a really good experiment in which the data gathered would be non-linear. The only ideas I've managed to come up with were either way to simple and boring, or way to hard for me to set up and measure accurately. Some examples of experiments include splash radius of a...

Hi everyone, Homework Statement I've been having a bit of trouble with my mathematics coursework. We have to model an aeroplane that has just landed with two equations. One prior to braking, one after. I've used a model with a quadratic drag approximation; and I'm not certain if my result...

I was thinking about the non-linear Navier-Stokes equation this morning and was briefly browsing a text on the subject. I'm aware that one popular approach to dealing with turbulence is to take averages and look at correlators (which, in turn, can be related to field theory.) Now, one thing...

Homework Statement Find the general solution of y'=\sqrt{2x-y} Homework Equations -- The Attempt at a Solution I've tried approaching this equation through several methods, but I can't separate the variables, I can't make it fit the pattern for linear, I can't make it fit the...

Hi everyone. This is not a homework problem. I am very familiar with the case of linear(direction) friction. F_{friction}=\mu F_{normal} ...(1) However my question is closer to something like this: \tau_{friction}=\beta F_{normal} ...(2) Where \tau_{friction} is a torque Imagine if a...

Hello, I was wondering if anyone could shed some light upon solving this: s(x)'' = (a b s(x)) / ||s(x)||^3 Where s is a n dimensional vector, || || is operation finding the magnitude and a and b are constants. Is this solveable or will I have to use alternative numerical methods?

Out of boredom* I derived some simplified equations to describe the dynamics of a pneumatic gun. These equations are extremely simplified, but they should provide some insight into the system that my numerical models can't. This system had one non-linear equation that could be rewritten as the...

I was just thinking about this the other day... Given any 'blackbox' circuit, for which the values of the thevenin voltage and thevenin resistance are known. And given that a non-linear device is placed across the terminals of the circuit. What relation would one use to find the current...

Homework Statement If a delicate istrument havng a mas of 5 kg is placed on a springof length L so tha its base just touches the undeformed spring and then inadvertly released from the position, determine the maximum deflection xm of the spring assuming (a) linear spring constant k=3000N/m...

Hello, having a lot of trouble with a dodgy question one of my lecturers has set us before teaching us how to do it, none of my course can seem to work out what to do. The question is: dy/dx=(x(y+3)+(y+3)2)/x2 where y(1)=4, and x>0 I tried a substitution of z=y/x to eventually give...

Can someone please give me a hint to solve \frac{d^2x}{dt^2} = \frac{1}{x^2} It is not a homework problem, but something for fun. It looks simple but is the solution simple? thanks

Googling this has only given me fairly detailed scientific papers and wikipedia (unusually) doesn't come up. Does anybody have a cheap and cheerful definition? Deducing these terms literally is not risk-free, but I suppose it involves a Gaussian probability distribution N(mu,sigma) where mu and...

Homework Statement This problem shows up in Anton's Elementary Linear Algebra in the first chapter. It's one of the last problems, so I don't think that it is crucial for me to 'solve' it. But I would like to clear up some conceptual questions I have. First here is the problem...

Homework Statement \frac{dy}{dx}+2xy^{2}=0 I am stuck on this. I realize that this is a non-linear exact equation, but I just cannot wrap my mind around any type of method to attack this one. TIA for any help

Hello, Could anyone help explain why \partial/\partialx[K(x,u)\partialu/\partialu] is not a linear operator?

I've run across a PDE that (since I've failed to take a PDE class!) I'm finding some difficulty in solving. Does anyone have any suggestions? It's on a function R(r,t), with functions a(r,t) and b(r,t) and a constant k. If it's easier to solve with a and b not having t-dependence (just being...

I am new to non-linear PDEs. So I tried to solve it, but I stuck in the beginning. U^2_xU_t - 1 = 0 U(x, 0) = x

I am not able to find the general integral of the following non-linear 2nd order equation: y^2 y'' + a y^3 - b = 0 in which: y = f(x) 0 < a <= 1, is a constant b > 0 , is a constant.

Hi Consider a set of n non-linear equations and I have m unknowns and n<m, so I don't have enough equations to solve the problem. All the unknowns are parametrized by say t A possible solution to this that I considered was to take the derivative w.r.t. t and obtain another set of n...

I am currently using a pulse generator with a reasonably fast rise-time (something like 1 ns) for some experiments. It works well as long as I am using e.g. 50 Ohm loads but the problem is that it can't source much current, meaning it doesn't work well for lower impedances. Now, my problem is...