Coefficients Definition and 753 Threads

I just don't get why the method of undetermined coefficients can't be applied to tan(x) and sec(x). What my book says is this- "Since the number of terms applied by differentiating tan(x) and sec(x) is infinity". What do they mean by that? Even the number of terms obtained by...

find a, b, c, and d, such the cubic $f(x)=ax^3+bx^2+cx+d$ satisfies the given conditions Relative maximum (3,3) Relative minimum (5,1) Inflection point (4,2) I approached this by using the f'(x)= a(3)(x^2)+b(2)(x)+c with the min and max and f''(x)=6x+2b for inflection pt to get $27a +6b + c...

While reviewing for my midterm I came across an old problem that asked me to find the expansion coefficient for n=1 given an expression for the superposition wavefunction. I also know the expressions for the individual eigenstates because it is simply considering a particle in a 1-D box. I am...

Homework Statement Work out the correct coefficient arrays for these equations: y(n)=y(n-1)+\frac{1}{5}(x(n)-x(n-5)) y(n) = 0.82y(n -1) + .28x(n) Homework Equations \sum a(r)y(n+1-r)=\sum b(k)y(n+1-k) where a(1) = 1  The Attempt at a Solution Ok for the second equation...

Homework Statement Let f(x) = x^{4}+ax^{3}+bx^{2}+cx+d be a polynomial with real coefficients and real zeroes. If |f(i)| = 1, (where i = \sqrt{-1}) then find a+b+c+d. Homework Equations The Attempt at a Solution f(i) = 1-b+d+ci-ai Taking modulus |f(i)|= |1-b+d+i(c-a)|...

Anyone know how would I simplify a cross product where the two vectors have coefficients? For example (x/(y^3))\bar{r} X (x/(y))\bar{L} Thanks!

Homework Statement Find coefficients A, B, and C. f'(x)= Af(x)+Bf(x+h)+Cf(x+2h)+O(h2) Using Taylor's Theorem. Note: O stands for Big O in asymptotic order notation. The Attempt at a Solution Here are the expansions: Bf(x+h)= Bf(x)+Bhf'(x)+(1/2)Bh2f"(x)+(1/6)Bh3f"'(x)...

Supposing $f$ is bounded and $A_n$ is given by 1-8, prove that $\sup_n|A_n|$ is finite. $$ f(\theta) = \sum_{n = -\infty}^{\infty}A_ne^{in\theta} $$ Since $f$ is bounded, $|f| < M = |z|\in\mathbb{C}$. Since it could be $\mathbb{C}$, $M$ would be the modulus correct? We know that the modulus of...

Homework Statement Expressing the binomial coefficients in terms of factorials and simplifying algebraically, show that (n over r) = (n-r+1)/r (n over r-1);Homework Equations The Attempt at a Solution I honestly don't even know how to come about this problem...I really need help in this...

Homework Statement Define (n k) = n!/k!(n-k)! for k=0,1,...,n. Part (b) Show that (n k) + (n k-1) = (n+1 k) for k=1,2,...n. Part (c) Prove the binomial theorem using mathematical induction and part (b). Homework Equations The Attempt at a Solution I'm wasn't able to...

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Folks, I am interested to know what the author is doing in the following ##\displaystyle B_{ij}=EL ij (L)^{(i+j-1)} \left[ \frac{(i-1)(j-1)}{i+j-3} -\frac{2(ij-1)}{i+j-2}+\frac{(i+1)(j+1)}{i+j-1}\right]## he states that this expression is not valid for ##B_{ij}## when ##i=1## and...

EDIT: I figured it out by looking at this link pages 65-66. Thanks for looking though! http://www.bfasta.net/assets/files/departments/science/ismith/Phys%20446/Phys%20446%20Information/HSU/Chapter%204%20Acceleration.pdf Homework Statement Recently I just did a physics lab for kinematics in...

Hiah, I've got a question concerning a t-pipe configuration and the corresponding friction coefficient values because there are two different friction coefficients stated in literature. Let's assume we have a simple t-pipe where the main passage is larger than the side branch. The friction...

I'm having trouble proving the following identity (I don't even know if it's true): $$\sum_{r=1}^k \binom{k}{r} \binom{n-k-1}{r-1}=\binom{n-1}{k-1}$$ $$\forall n,k \in \mathbb{N} : n>k$$ Thank you in advance for any help! Vincent

I have a quick question. The problem reads: Prove that there is no integer m such that 3x2+4x + m is a factor of 6x4+50 in Z[x]. Now, Z[x] is not a field. So, the division algorithm for polynomials does not guarantee us a quotient and remainder. When I tried dividing 6x4+50 by 3x2+4x +...

Homework Statement I found everything except step #5. Please tell me if I am correct Find a particular solution to (D - 1)(D^{2} + 4D - 12)y = cos(t) using the annihilator approach of the method of undetermined coefficients. Homework Equations 1) Find annihilator 2) Find A =...

I'm trying to estimate the heat transfer coefficient from the surface of a hot object moving through open air. After much searching, all I can find is coefficients for sundry fluids confined within the tubes of heat exchangers. I'm trying to calculate for a body at between 300-460K moving at...

Homework Statement I am working on this ahead of my fall class and don't actually want the answer... just pointers to help me understand something.. Thanks guys! :) I am really rusty with my general physics and calculus knowledge =( The original question asks me to prove that, for a...

Homework Statement http://gyazo.com/6c440aa92106f729639c91f6d59dcd89 The Attempt at a Solution My question is why is yp = At^3+Bt^2 +Ct. The reason I ask that is because is see t^2+2t so why wouldn't it be yp=At^2 +Bt +c?

I just want to know if I'm understanding this right. I haven't really seen homology/cohomology outside of Z-related coefficients before, so this still seems kind of weird. I also haven't actually learned sheaf theory, so this might just be totally wrong. So if I have a top space and a sheaf...

Hello! I have some examples of non-homogeneous ODEs to be solved by the undetermined coefficients method. Two from "Pauls math notes" page: y''+8y'+16y=e^{-4t}+(t^2+5)e^{-4t} The compsol. for this is: Y_{c}=C_{1}e^{-4t}+C_{2}te^{-4t} The first guess for a particular solution would be...

Homework Statement For any quadratic polynomial ax2+bx+c having zeros β and α Prove that β + α = -b/a and αβ = c/a. Homework Equations The Attempt at a Solution I have found a method myself to prove α+ β = -b/a. However, I could not prove αβ = c/a. It goes like this. If α and β are the...

I have a Mathematics C assignment, with one question being about static and dynamic friction. But I think it fits this forum. Anyway, we need to conduct experiments to show if there is a difference between static and dynamic friction or not with three different surfaces.The weight of the object...

[FONT=Tahoma]A polynomial $f(x)$ has Integer Coefficients such that $f(0)$ and $f(1)$ are both odd numbers. prove that $f(x) = 0$ has no Integer solution

Hello. I'm having some trouble balancing ionic equations.. Are we supposed to consider the coefficients of the reactants/products? I came across a contradiction in the examples given in my book : 1) Na + H(+1) → Na(+1) + H2 So in order to figure out the oxidation/reduction part, we...

[FONT=Times New Roman]Let a,b,c,d be real numbers. Sauppose that all the roots of the equation $z^4 + az^3 + bz^2 + cz + d = 0$ are complex numbers lying on the circle $\mid z\mid = 1$ in the complex plane. The sum of the reciprocals of the roots is necessarily: options a) a b) b c) -c d)...

Homework Statement Solve the following equation: (2x-y)dx+(4x+y-6)dy=0 Homework Equations Solve for M and N as a linear system of equations; and x_t = u + h y_t = v + k The Attempt at a Solution M = 2x-y=0 N = 4x+y-6=0 2x=y 4x+2x=6 6x=6 x=1 y=2 ∴ x_t=u+1 \\ dx=du...

Homework Statement I have some past exam questions that I am confused with Homework Equations a_{n} = \frac{1}{2\pi i} \oint_\gamma \frac{f(z)}{z-a}\, dz The Attempt at a Solution I'm not sure how to approach this, I'm completely lost and just attempted to solve a few: a) it says f(z)...

Homework Statement Find the first two non-zero terms in the Taylor expansion of \frac{x}{\sqrt{x^2-a^2}} where a is a real constantHomework Equations f(x)=f(x_0)+f^{\prime}(x_0)(x-x_0)+\frac{f^{\prime\prime}(x_0)}{2!}(x-x_0)^2+...+\frac{f^{(n)}(x_0)}{n!}(x-x_0)^n The Attempt at a Solution If...

let's say you are given the following matrix T: T11 T12 . . . T1n T21 T22 . . . T2n . . . . . . . ...

Hey, Every where I look I can only find books and pdf talking about the uniqueness and linear independence of the solutions but I haven't been able to find a procedure of finding the solutions to one of these ode's if you haven't been already given a particular solution. I've been trying...

Could someone provide me with a link or source which i can cite for the values of the hall coefficients of tungsten and silver. I have had no luck finding either of them that are proper sources. thanks

I was given a question and i am really unsure how to go about solving it. it appears to be solveable using the characteristic equation and whatnot, however i have my coeffecients in terms of the independent variable. so i am confused. the question initially asked to compute the wronskian, and it...

Hi all, I've been fiddling around with this problem for a while. I intuitively understand that the parallel propagator is the path integral of the connection. I would like to be able to show the converse (connection is derivative of parallel propagator) mathematically, and I am having a...

Let $f:\mathbb R\to\mathbb R$ be a continuous function of period $2\pi.$ Prove that if $\displaystyle\int_0^{2\pi}f(x)\cos(nx)\,dx=0$ for $n=0,1,\ldots$ and $\displaystyle\int_0^{2\pi}f(x)\sin(nx)\,dx=0$ for $n=1,2,\ldots,$ then $f(x)=0$ for all $x\in\mathbb R.$ I know this has to do with the...

Is there a way to use the Clebsch Gordon coefficients tables to find the coefficients of a three particle system? For example if there is a system of three spin 1/2 particles, how to find the Clebsch Coefficients for different spin states using tables?(say for the state, |s12=0, S=1/2 ms=1/2>)

I'm curious about the validity of various techniques from good old calculus in one real variable when dealing with complex coefficients. I know enough complex analysis to know that the rules change when dealing with complex variables, but I'm curious about the case when the variables are still...

do you have a idea about it?can you help me http://img17.imageshack.us/img17/1156/18176658.png

Compute the sine coefficients for f(x)=e^{-x^{2}} on the interval [0,2\pi]. Does this mean f(x+2\pi k)=f(x), k\in\mathbb{Z}? Can x\in[0,\infty)?

Homework Statement Prove that \sum\limits_{k=o}^l {n \choose k}{m \choose l-k} = {n+m \choose l} Hint: Apply binomial theorem to (1+x)^n * (1+x)^m Homework Equations The Attempt at a Solution Using the hint, I started by saying that (1+x)^n * (1+x)^m = (1+x)^(n+m) =...

Homework Statement If; a*x + b*y = c*x + d*y x ≠ y a,b,c,d ≥ 0 Prove that; a=c b=d 2. The attempt at a solution I've been fiddling with this equation and have been getting nowhere.

Homework Statement I need to generate coefficients of hermite polynomials up to order k. Recursion will be used. Homework Equations a[n+1][k] = 2a[n][k-1] - 2na[n-1][k] The Attempt at a Solution Its not pretty, but here is my code. #include <iostream> #include <iomanip>...

Homework Statement I wanted to solve a ode which has Brownian motion as a variable coefficient Homework Equations 2x2y'' + y' -ρy = 0 where x is the Brownian motion with respect to time ρ is a constant The Attempt at a Solution I have tried power series with no solution. Is there a...

I am designing a test rig for golf clubs at the university of nottinghamm, and due to a large spending spree, don't have much of my budget left. As a result of which, I was hoping to use a door closer as a spring damper system. Does anyone have any idea of rough values of the damping...

The expressions for the coefficients of a Fourier series are valid for all integers [0;n]. Though sometimes when I evaluate the Fourier series of an even function (composed only of cosines) I get an expression for the r'th coefficient, which has r in the demoninator. It could be for instance...

Homework Statement Show that the generating function A(x) = \sum_n a_n x^n of a_n = \sum_{k=0}^n {n+k \choose 2k} 2^{n-k} satisfies A(x) = \frac{1-2x}{4x^2-5x+1}Homework Equations The Attempt at a Solution A hint was given to "interchange the sums". After doing that, I don't see how to...

1. Homework Statement x^3 +px^2 + 56x + q = 0 I've attempted the first part but I have no idea what to do next. I know usually you'd have 3 new roots inn terms of alpha, beta and gamma but they're not given. 2. Homework Equations Given that the three roots are all positive and...

Homework Statement x^3 +px^2 + 56x + q = 0I've attempted the first part but I have no idea what to do next. I know usually you'd have 3 new roots inn terms of alpha, beta and gamma but they're not given. Homework Equations Given that the three roots are all positive and are the first free...

Hi, I've got an equation stating p=a(r-1). If p represents prime number and r is a positive integer, and a is a constant, what can we conclude for the constant a? Like a $\in${-1, 1, -p, p}? I suspect this has something to do with modular arithmetic...:confused: Thanks.