Coefficients Definition and 753 Threads

Is possible classify the quadric equation Axx + Bxy + Cyx + Dyy + Ex + Fy + G = 0 how straight, hyperbola, circle, ellipse, parabola, etc, in the same way that is did in the phase plan: https://upload.wikimedia.org/wikipedia/commons/3/35/Phase_plane_nodes.svg...

Homework Statement (f) At t = 0, a particle of mass m trapped in an infinite square well of width L is in a superposition of the first excited state and the fifth excited state, ψs(x, 0) = A (3φ1(x) − 2iφ5(x)) , where the φn(x) are correctly-normalized energy eigenstates with energies En. Which...

Homework Statement y'' + y =3*sin(2t) +t*cos(2t) Okay, so I have found the complimentary solution, and the first partial solution as listed in my work below. My problem is the work on the second partial solution. I have got all the derivatives plugged into the differential equation, my...

Hey! :o We have the initial value problem $$u'(t)=Au(t) \ \ , \ \ 0 \leq t \leq T \\ u(0)=u^0 \\ u \in \mathbb{R}^m$$ A is a $m \times m$ matrix The eigenvalues of $A$ are $\lambda_j$ and the corresponding eigenvectors are $\phi^{(j)}$. The general solution of initial value problem is...

Assuming the 2s and 2p wavefunctions are normalized, determine the coefficients in the hybrid orbital: Ψ(sp3) = aΨ(2s) + aΨ(2px) + aΨ(2py) + aΨ(2pz) (the other 3 hybrids have – signs for some of the coefficients. [SIZE=16px]I have no clue where to start. I know this is a tetrahedral hybrid...

Homework Statement Usually in any question will the magnitude of the couple(friction) be given or is it possible to find the couple from the co efficient of friction between the rotating object and the axis ? Homework EquationsThe Attempt at a Solution

Homework Statement Show that the binomial coefficients ## \binom {-1}{n}=(-1)^n## Homework Equations ##\binom{n}{k}=\frac{n!}{(n-k)!k!} \\ ## The Attempt at a Solution ##-1!=(-1)\cdot 1! \\ -1!=-1 \\ -2!=(-1)^2 \cdot 2! \\ -n!=(-1)^n \cdot n!\\ \mbox{for n=0} \\...

rude man submitted a new PF Insights post Misconceiving Mutual Inductance Coefficients Continue reading the Original PF Insights Post.

Homework Statement ##\sum\limits_{r=0}^n\frac{1}{^nC_r}=a##. Then find the value of $$\sum\sum\limits_{0\le i<j\le n}(\frac{i}{^nC_i}+\frac{j}{^nC_j})$$ Homework Equations I have used two equations which I derived myself. This is the first one. The second one is: 3. The Attempt at a...

Note that the general solution to $y'' - y = 0$ is $y_h = C_1e^t + C_2e^{-t}$ In the following, use the Method of Undetermined Coefficients to find a particular solution. a)$y'' - y = t^2$ So here is what I have so far $y_p = At^2 + Bt + C$ $(y_p)'' = 2A$ Ive got $A = -1, B = 0 , C = 0$ so...

On one hand, in reading Georgi's book in group theory, I comprehend the invariant tensor as a special "tensor", which is unchanged under the action of any generators. On the other hand, CG decomposition is to decompose the product of two irreps into different irreps. Now it is claimed that...

Homework Statement http://puu.sh/gGhdb.jpg Solution:[/B] http://puu.sh/gGh3E.jpg Homework EquationsThe Attempt at a Solution How did they get that solution for the Fourier coefficient? When I evaluate the integral I can only seem to get it to: (1/-jk2π)[2*exp(-jkπt)-exp(-jk2πt)-1]

Homework Statement Find the roots of z^4+4=0 and use that to factor the expression into quadratic factors with real coefficients. Homework Equations DeMoivre's formula. The Attempt at a Solution I have been able to identify they are \pm 1 \pm i but i have no idea how to factor the...

Homework Statement Find the Fourier Coefficients for the triangular wave equation shown in this picture: Homework Equations ##f(t)= a_0 + \sum_{n=1}^\infty a_{n}cos(n{\omega}t) + \sum_{n=1}^\infty b_{n}sin(n{\omega}t)## ##a_0 = \frac{1}{\tau}\int_{-\tau/2}^{\tau/2} f(t) \, dt## ## \omega =...

Hi all, I have an apparently simple equation. I copy here its Mathematica code: Sum[(p/(1 - p))^s*(q/(1 - q))^s*Binomial[n, s]*(Binomial[m - 1, s]*(p*q*(m + n) + (2*m - 1)*(-p - q + 1))), {s, 0, n}] == Sum[(p/(1 - p))^s*(q/(1 - q))^s*Binomial[n, s]*((-(-p - q + 1))*Binomial[m - 2, s] +...

So a p-adic expansion of a rational number was presented to me as an analogue of a Laurent-series expansion and defined as: $$\sum\limits_{n=-{\infty}}^{\infty}a_np^n$$ Can you find the coefficients for these the same way you would for a Laurent series? I've not gotten to that part of this...

I have a problem that works out to this s, but with a coefficient, what do I do with it from this point?

Homework Statement The state of an electron is, |Psi> =a|l =2, m=0> ⊗ |up> + Psi =a|l =2, m=1> ⊗ |down>, a and b are constants with |a|2 + |b|2 = 1 choose a and b such that |Psi> is an eigenstate of the following operators: L2, S2, J2 and Jz. The attempt at a solution I am really not sure...

Homework Statement Given f = a0 + sum(ancos(nx) + bnsin(nx)) and f' = a0' + sum(an'cos(nx) + bn'sin(nx)) The sums are over all positive integers up to n. show that a0' = 0, an' = nbn, bn' = -nan Then prove a similar formula for the coefficients of f(k) using induction. Homework EquationsThe...

Hi all, I have a quick question. I was taught this, but wasn't explained to at all why it is the case. So let's say I have a differential equation with constant coefficients i.e. y'' - 4y' + 4y = e^2x And the general solution to its associated homogeneous equation is Ae^2x + Bxe^2x [A &...

Edit: I forgot to add the picture, and I'm having trouble adding it from Tapatalk. I'll add it soon. I'm trying to understand the derivation in my textbook of the wave function for a potential step. The derivation reaches the step shown in the attached photo, which I am fine with. However, the...

If a function f'(u) has Fourier coefficients anμ and bnμ, by integration one can make new coefficients Anμ ,Bnμ which include constants of integration. My question how can I verify that : Anμcos nτ + Bnμ sin nτ= -i/2 ((Bnμ) -Anμi) einτ- (Bnμ-iAnμ) e-inτ I assume this is the complex form of...

Let $ax^2+bx+c$ be a quadratic polynomial with complex coefficients such that $a$ and $b$ are non-zero. Prove that the roots of this quadratic polynomial lie in the region $|x|\le\left|\dfrac{b}{a}\right|+\left|\dfrac{c}{b}\right|$.

I'm using Pascal's (n choose k) method for calculating the coefficients of the terms of a binomial expansion. However, if the exponent is a negative integer, how can one use this method, seeing as factorials for negative integers are undefined. For example, how could one determine the...

So, I'm currently writing a mathematical analysis of a bullet with a muzzle velocity of 790 m/s. I have found that the standard equation for drag force... Fd = 1/2 * ρ * v2 * Cd * A does not work because the drag coefficient for a bullet (.295) does not account for supersonic speeds. What I...

Homework Statement If the method of undetermined coefficients is used to find a particular solution yp (t) to the differential equation y'''-y'=te^(-t)+2cos(t) should have the form: ?Homework EquationsThe Attempt at a Solution LHS r^3-r=0 roots= 0, 1 y_c(t)=c_1e^tRHS te^(-t)+2cos(t)...

Homework Statement y''-y=t-4e^(-t)Homework Equations method of undetermined coefficients The Attempt at a Solution solving for characteristic equation first y''-y=0 r^2-1=0 c_1e^(-t)+c_2e^(t) RHS particular solution t-4e^(-t) y_p(t)= At+B+Ce^(-t) y_pt'(t)=A-Ce^(-t) y_p''(t)=Ce^(-t)...

Homework Statement What are the expansion coefficients of a wavepacket \Psi (x) = \sqrt{\frac{2}{L}}sin \frac{\pi x}{L} in the basis Ψn(x) of a particle in a periodic box of size L? Homework Equations \Psi (r,t) = {\sum_{n}^{}} a_{n}(t) \Psi _{n}(r) The Attempt at a Solution \left \langle...

Homework Statement Solve the following: [/B] y'' = c2 / (x2 + c1*x) * y c1, c2 are constants, x is variableHomework Equations As above The Attempt at a Solution I have used the method of Frobenius and regular power series and obtained an infinite series on top of an infinite series, which is...

Hi, I've recently been given a series of questions on heat transfer to do and have done most of them with general ease, but this one question I've been stuck on for ages and i can't seem to figure out: "A double pipe heat exchanger is made up from a length of 25mm i.d. steel pipe of 2.5mm...

Hi, friends! Let ##f:[a,b]\to\mathbb{C}## be an http://librarum.org/book/10022/173 periodic function and let its derivative be Lebesgue square-integrable ##f'\in L^2[a,b]##. I have read a proof (p. 413 here) by Kolmogorov and Fomin of the fact that its Fourier series uniformly converges to a...

Hello guys, I need help solving this problem. Find the particular solution using method of undetermined coefficients: X'=AX + F(t) A= [4 ,1/3] <-- 1st row [9 , 6] <-- 2nd row F(t) = [-e^t,e^t] The complementary function is Xc=c1[1,3]e^(3t) + c2[1,9]e^(7t) Any help would be...

For the question attached in the file, how exactly does one go about finding a solution? Problem 28 says that if n does not equal m, then ## \int_{-1} ^{1} {P_n}{P_m} = 0 ## With that statement, I've tried treating this as a Taylor series (centred at 0, arbitrarily) and then trying to find a...

Hi there, I know that when I am to guess a solution to to a polynomial for g(t) that I guess Ax^n + Bx^n-1... when the highest power of the polynomial is n but what is my guess supposed to be if the power of n is negative? ex. y'' + 4y' + 4y = t^-2*e^(-2t) so far my guess is, A*e^(-2t)(B*?...)

1. A magazine reports that a new type of plastic ski is even more water repellent and that, on a gentle 203-m slope in the Alps, a skier reduced his time from 61 to 42 s with the new skis. Assuming a 3.0 degree slope, compute the coefficient of kinetic friction for each case. I am having...

Homework Statement A block of weight 20 N (m = 2 kg) sits on an plane inclined at 37°. g = 10 m/s2 (for simplicity). a) Calculate the value of the weight components. b) Calculate the acceleration assuming no friction. c) Calculate the acceleration assuming μk = 0.125. d) What value of μk is...

Homework Statement Find the general solution by finding the homogeneous solution and a particular solution. y'' + 4y' = x Homework EquationsThe Attempt at a Solution First, I found the corresponding solution to the homogeneous differential equation: y'' + 4y' = 0 r^{2} + 4r = 0 r_1 = 0...

Homework Statement Two bicycle tires are set rolling with the same initial speed of 3.30m/s along a long, straight road, and the distance each travels before its speed is reduced by half is measured. One tire is inflated to a pressure of 40 psi and goes a distance of 17.3m ; the other is at 105...

Consider the following generic equilibrium: aM + bN ⇌ cO + dP An equilibrium constant, K, can be defined as: $$K = \frac{[O]^c [P]^d}{[M]^a [N]^b}$$ But couldn't we also define another equilibrium constant similarly with coefficients that are in the same ratio as our original equation? For...

Homework Statement y'' + 9y = 3sin(3x) + 3 + e^{3x} Homework EquationsThe Attempt at a Solution This is my first post here so let me know if I've done anything wrong, I've been looking at questions here for a long time though ^^. So the problem asks me to solve for one particular solution...

For a simple equilibrium or non-equilibrium chemical reaction, while I understand that the ratio of the coefficients of each reactant/product is mathematically equal to the molar ratio, I am not quite sure whether or not it is equal to the ratio of concentrations of each component in the...

Hello, I am in an introductory undergraduate course on ODEs, currently on the method of variation of constants to solve nonhomogenous equations. I am noticing that with many of these problems, when solving for constants after plugging in my guessed values for y I end up with enormous...

When talking about ordinary (real) linear differential equations with constant coefficients the idea is that we are dealing with the vector space of real functions over the field of real numbers. But when we allow the coefficients of a linear differential equation to be functions are we dealing...

Homework Statement An object consists of 3 connected masses as seen in the figure. None of the surfaces have friction except the surface on m1 which has the coefficients μs=0.4 y μk=0.3. What is the acceleration of each one of the masses? It looks like the following image but m1 is the table...

My task is to find Linear homogeneous D.E. with constant coefficients which has solutions: $$\\\varphi 1(x)=x^2,\varphi 2(x)=e^{-3x},\varphi 3(x)=cos(5x)$$ Any idea?

Hi, I have an ordinary least squares setup y = Ac where A is an NxM (N>>M) matrix, c the unknown coefficients and y the measurements. Now WEIGHTED least squares allows to weight the MEASUREMENTS if, for example, some measurements are more important or contain a lower variance. However...

I have around 550 asymmetrical sigmoid curves fitted to a function with 4 varying coefficients. Each of these curves represent strength as a function of time and temperature for a different compound. Each compound is made up of varying substances at varying concentrations. Overall, I have 550...

I'm doing a practice problem I found online, and I get a solution, but I think it should have a sine term in it. I looked up the solution, and most sites say to use variation of parameters, but is it possible to use the method of undetermined coefficients? The problem is as follows: y'' + 4y...

Hello, Does anyone know the value of the coefficients of friction between the following surfaces? (I've searched all over internet and literature but cannot find them :( ) 1) Aluminium on concrete. 2) Steel on concrete. 3) Iron on concrete. Thanks a lot!

Dear Fellows, If we fit our data to a quadratic equation then What is meant by standard error for linear and quaratic coefficients ? I know that standard error is the standard deviation from the Sampling data. But for individual coefficients what is its interpretation ? Best Wishes Masood