Higher order Definition and 97 Threads

Hello I have a mathematical dilemma. How can the following transfer function be simplified: \frac{s^{2}+1}{s+1} in order to be able to have a 1st order nominator, maximum, compared to the denominator. But what if there is s^2(/<1...∞>) ? Is this possible? I know that the following...

Basically I'm writing my MSc dissertation right now, and I've been doing a lot on primes I've written all my code in MATLAB, but my supervisor told me today that MATLAB is crap for higher order arithmetic and the primes only go up to something like 10 digits long. SO I'm kinda screwed...

Many a times, in papers written on experimental work, there are statements like "there are no first order changes in time, but only those of the second order". What do such statements mean?

Homework Statement My teacher likes to teach us the D-notation methods for higher order DE's. I am having a hard time with this one and I can't seem to find the formula for the general solution Find a fundamental set of the equation (D-1)^{2}(D^{2}-6D+13)^{3}y = 0 Homework...

Dear all, Sorry to post this question in this section again. I am currently looking into few static analyse algorithms. I noticed that they are analysing with different order moments or cumulants to analyse the data. I guess it is because these algorithms are focus on different aspect of...

Homework Statement Evaluate the ratio of the power contained within a circle of radius W(z) in the transverse plane to the total power in the Hermite-Gaussian beams of order (1,0) Homework Equations P=\intIdA The Attempt at a Solution I have determined the ratio for the Gaussian...

Any books discussing the formula of d^2Z and d^3Z? Are they liked that? Anyone saw them before? Z(x, y)\\\\dZ=Z_xdx+Z_ydy\\d^2Z=Z_{xx}(dx)^2+2Z_{xy}dxdy+Z_{yy}(dy)^2+Z_xd^2x+Z_yd^2y\\d^3Z=Z_{xxx}(dx)^3+3Z{xxy}(dx...

Hi, I'm not exactly sure how to solve the following non-homogeneous ODE by variation of parameters. Solve the given non-homogeneous ODE by the variation of parameters: x^2y" + xy' -1/4y = 3/x + 3x Can someone please point me in the right direction? Help will be much appreciated...

Homework Statement In control engineering, I want to have a mathematical model of a physical system as a set of input, output and state variables related by higher order differential equations. 2. Relevant concepts As we all know that, in control engineering, we can solve linear-system...

The question asks the student to use Taylor's formula to calculate the exact values of higher derivatives f '[0], f '' [0], f ''' [0], ... , f^6'[0] of the function f[x] defined by the power series x/2 + x^2/12 + x^3/240 +x^4/10080 + ... +((k x^k)/(2 k)!) + ... My first...

How does higher order derivatives affect the graph? Mostly just the 3rd, 4th or 5th derivatives. I believe I have found the 3rd one but I'm not sure about it or the others.

For the life of me I cannot figure out how to factor higher order equations so that I can find the poles and zeros, my professor will not show how to do it and expects everyone to already know how, but i have forgotten and cannot find anywhere on the web to show a one and done method, please...

Homework Statement Let p be an arbitrary polynomial p(x) = anxn + an-1xn-1 + ... + a1x + a0, an cannot equal 0. a) Find (dn/dxn)[p(x)] b)What is (dk/dxk)[p(x)] for k>n Homework Equations The Attempt at a Solution Im actually not really sure what to do for this question...

Homework Statement Find the 73rd derivative of f(x) = sin(2x) + 3 (Hint: Take the first five derivatives to find a pattern) Homework Equations dy/dx The Attempt at a Solution I took the first five derivatives to find the pattern: dy/dx = 2cos2x d2y/dx2 = -4sin2x d3y/dx3 =...

Hi everybody, I have a question: We know that the geometrical representation of 1st order derivative is the slope of a function. Then what is the geometrical representation of derivatives having order more than 1? I mean what does it actually represent in a function? Please some body clear my...

I am using smooth-particle hydrodymamics(SPH) method to model a deformable object. It is based on the procedure found in Markus Gross's point based animation book, the algorithm is attached in the image below. This algorithm uses Euler for numerical integration as seen in step 21 and 22, and...

I was wondering if there are any topics for calculus based or advanced high school math project that I can devote my whole semester to at school.

Homework Statement The function F is defined by F (r, θ) = f (x(r, θ), y(r, θ)), where f is twice continuously differentiable and x(r, θ) = r cos θ, y(r, θ) = r sin θ. Use the chain rule to find d2F/dθ2Homework Equations The Attempt at a Solution I know that dF/dθ = (df/dx)(dx/dθ) +...

Homework Statement x^4 + 4x^3 - x^2 + 16x - 12 I know that with some higher order polynomials you can substitute say x^4 as a = x^2 thereby making it easier to break the thing apart and find its factors. I know I am looking for 4 roots, but my little substitution method doesn't really work...

It is common lore to write lagrangians in field theories in the form L(t)=\int d^{3}x\mathcal{L}(\phi_{a},\partial_{\mu}\phi_{a}). Nonetheless, is there any particular reason for doing that? Why do we neglect higher order derivatives? Does it mess around with Lorentz invariance or something...

Hi, As per Clariut's theorem, if the derivatives of a function up to the high order are continuous at (a,b), then we can apply mixed derivatives. I am looking at http://en.wikipedia.org/wiki/Symmetry_of_second_derivatives and I cannot understand in the example for non-symmetry, why the...

Consider the partial dierential equation, (y4-x2)uxx - 2xyuxy - y2uyy = 1. We will make the substitution x = s2 - t2 and y = s - t, to simplify (a) Solve for s and t as functions of x and y the farthest point i got to was x = s^2 - t^2 = (s+t)(s-t) = y(s+t) y = s - t s+t = x/y i...

Homework Statement Verify that the differential operator defined by L[y] = y(n) + p1(t)y(n−1) +· · ·+ pn(t)y is a linear differential operator. That is, show that L[c1y1+ c2 y2] = c1L[y1] + c2L[y2], where y1 and y2 are n times differentiable functions and c1 and c2 are arbitrary...

Homework Statement Given the following differential equation t^3y''' - t^2y'' + 2ty' - 2y = 0; t > 0 Find a solution that satisfies differential equation and the initial conditions y(1) = 3; y'(1) = 2; y''(1) = 1 Homework Equations The Attempt at a Solution I tried plugging in...

hi. i was able to prove the trapezoidal rule and simpsons rule. (basically i used matrices to determine the coefficients m and b for mx+b when proving the trapezoidal rule and a,b,c for ax^2+bx+c such that the points coincide, then i integrated the approximating polynomial) the amount of...

Hi I am asking, if I am trying to make inference using Bayes rule based on a prior probability that is a random variable by itself; is it sufficient to use the expected value of such probability or there are other details. Thanks in advance.

Hi, all, Let's assume a random variable's variance is zero as sample size tends to infinity somehow, can I say that its higher order central moments are also zero as the sample size tends to infinity? Thks a lot

Hello Forum, I am not clear on what higher order statistics actually mean. I know that if a process is Gaussian, it is fully described by its mean and variance. The higher order statistics are zero or redundant...IF the process is not Gaussian, then the HOS are useful... 1) How do we...

I'm having some trouble getting my head around the concept of multiple solutions of differential equations of higher order, that is the general solution to a linear homogeneous equation is a linear combination of constants and solutions like y(1)C1 + y(2)C2 +y(n)C(n) where N is the order of the...

Homework Statement Given that x, x2 and 1/x are solutions of the homogeneous equation corresponding to: x^3y''' + x^2y''-2xy'+2y=2x^4 x>0 determine a particular solution. Homework Equations The Attempt at a Solution I'm trying to solve this problem using three...

Hello. I need finite difference expression of sixth order derivative in h^2. I derived it using Mathematica 6 but when I use the expression there appear a problem. Solution is wrong. I check everythin and realized that only i m not sure about that expression. I ll be appreciated if you help...

I want to write a function that takes other functions as inputs. Specifically I want to define a function F that takes input 't' (time) and 2 distribution functions, D1 and D2, as inputs (each distribution function itself a function of 't'). For a simple example, if function F is the product...

what is quotient rule for higher order derivatives ? i mean the one analogous to http://en.wikipedia.org/wiki/Leibniz_rule_%28generalized_product_rule%29" .

Hi Friends, Could anyone answer my question please I am not good in math: Why we do Higher order derivatives..? What its physical meaning ...? we keep on finding the derivatives till we get function zero...why...? Lets say my equation is Y= x3 + 3x2 + 3x + 2 Thanks Rsvsk

Homework Statement Solve the following initial value problem: 2007y(4)-18y(3)+178y(1) = 0 with initial conditions y(0)=y(1)(0)=y(2)(0)=y(3)(0)Homework Equations Differential equations.. The Attempt at a Solution From the equation I get r(2007r3 - 18r2 +178) = 0 Well first I can't seem...

Homework Statement Use the method of variation of parameters to determine the general solution of the given differential equation: y^(4) + 2y'' + y = sin(t) Homework Equations characteristic equation is factored down to (r^2 + 1)^2, so r = +/- i. this gives the general solution to be...

Hi guys, please see attachment Basically, could somebody please explain to me how I find {\varphi}_u_u, I really don't understand how it's come about. Apparantly I need to use the chain rule again and the product rule but I don't understand how to, if somebody could show me explicitly how to...

Homework Statement a) s^2*t''+st*t'=s b) y(dx/dy)^2=x^2+1 c) 17y''''-t^6*y"-4.2y^5=3cost(t) Homework Equations The Attempt at a Solution For part a I thought about doing a reduction of order but I can't because I have the variable s present. Not sure what my other options are...

I haven't done this in ages, and I'm having trouble recalling how to factor a higher order polynomial. I almost always do this graphically, but for this case I'm interested in an algebraic solution. Specifically, I'm looking at ax + x^3 - x^5 = 0 (with a = an integer >0.) Clearly 0 is one...

hi... can anyone could help me by explaining about higher order tensor and it's calculation rules ? or perhaps u could give me a link to a website where i could find complete information about it. thanks...:rolleyes:

I need to know how to evaluate higher order poles. I have the answer for the integral of this function [tex]\frac{(1 + x^2)}{(1 + x^4)}[\tex] from integrals.wolfram.com, but think it can be done using residues. I believe it involves taking a derivative and then multiplying by the pole...

hi guys! okz this is a question from Higher Order Differential Equations. We are solving it from General Method to find y_{p}. y_{p}=\frac{secax}{D^{2}+a^{2}} I solve it and reaches this point: y_{p}=\frac{1}{D+a\iota} e^{a\iota x} \int secax.e^{-a\iota x} dx Please tell me some...

Let E, F be Banach spaces, and let L(E;F) denote the space of linear, bounded maps between E and F. My goal is to understand better higher order derivatives. Let's take E=\mathbb{R}^2, F=\mathbb{R}. Consider a function f:U\subset\mathbb{R}^2\rightarrow\mathbb{R}, where U is an open subset of...

Higher Order Homogenous ODE (Euler-Cauchy) *sigh* I am (yet again) stuck on a problem.. I would greatly appreciate any help! x^3y''' - 3x^2y'' + (6-x^2)xy' - (6-x^2)y = 0 \inline y_1 = x is a solution to the equation above y'(0) = 3 y''(0) = 9 y'''(0) = 18 I'm not quite sure...

Hello, I have two questions about this problem: (D^4 + 5D^2 + 4)y = 0 y(0) = 10 y'(0) = 10 y''(0) = 6 y'''(0) = 8 \lambda^4 - 5\lambda^2 + 4 = 0 (\lambda^2 + 4) (\lambda^2 + 1) Until here I am fairly sure that I didn't mess it up.. But I'm not sure if I have the roots...

Higher Order Homogeneous ODE (IVP) [Solved] I am having problems with this IVP: y'''' + y' = 0 y(0) = 5 y'(0) = 2 y''(0) = 4 What I have done so far is: \lambda^3 + \lambda = 0 \lambda(\lambda^2 + 1) = 0 So one roots is \lambda = 0 (though.. can there be a root that...

Hello Everyone, I'm doing some questions on higher derivatives, and they should be easy but I am worried that my answers are not quite right. There just seems to be something 'off' about them. Anyway here are the questions and my answers. 1) Find the first and second derivatives of y=...