What is Integration: Definition and 1000 Discussions
System integration is defined in engineering as the process of bringing together the component sub-systems into one system (an aggregation of subsystems cooperating so that the system is able to deliver the overarching functionality) and ensuring that the subsystems function together as a system, and in information technology as the process of linking together different computing systems and software applications physically or functionally, to act as a coordinated whole.
The system integrator integrates discrete systems utilizing a variety of techniques such as computer networking, enterprise application integration, business process management or manual programming.System integration involves integrating existing, often disparate systems in such a way "that focuses on increasing value to the customer" (e.g., improved product quality and performance) while at the same time providing value to the company (e.g., reducing operational costs and improving response time). In the modern world connected by Internet, the role of system integration engineers is important: more and more systems are designed to connect, both within the system under construction and to systems that are already deployed.
In this solution, in the last 3rd line, I get the first part (-e^-1 - e^-1), however, after the '-' symbol, the person writes (1/b * e^1/b - e^1/b) and takes the limit as b->0. However, shouldn't this give him (inf. * e^inf - e^inf)?
Thanks
(His answer is correct, by the way)
Hi, I had a quick question about something from Section 3 of Srednicki's QFT book. In it, he's discussing the solution to the Klein-Gordon equation for classical real scalar fields. He gives the general solution as:
$$\int_{-\infty}^{+\infty} \frac{d^3 k}{f(k)}...
I would like to ask you why the author does not use absolute value of y instead of y?
Source: Mathematical Methods in the Physical Sciences by Mary L. Boas
Thank you.
Homework Statement
I am trying to show that ## \int \delta (x-a) \delta (x-c) dx = \delta (-a-c) ## via integeration by parts, but instead I am getting ##\delta (c-a) ## (or ##\delta (a-c)## depending how I go...).
Can someone please help me out where I've gone wrong: struggling to spot it...
Hello, I am having trouble with solving the problem below
The problem
Find all primitive functions to ## f(x) = \frac{1}{\sqrt{a+x^2}} ##.
(Translated to English)
The attempt
I am starting with substituting ## t= \sqrt{a+x^2} \Rightarrow x = \sqrt{t^2 - a} ## in $$ \int \frac{1}{\sqrt{a+x^2}}...
Homework Statement
I have
##\int dx \int dy \delta (x^{2}+y^{2}-E) ## [1]
I have only seen expressions integrating over ##\delta## where the ##x## or the ##y## appear seperately as well as in the delta function and so you can just replace e.g ##y^2 = - x^{2} +E## then integrate over ##\int...
Homework Statement
Integrate by changing to polar coordinates:
## \int_{0}^6 \int_{0}^\sqrt{36-x^2} tan^{-1} \left( \frac y x \right) \, dy \, dx ##
Homework Equations
## x = r \cos \left( \theta \right) ##
## y = r \sin \left( \theta \right) ##
The Attempt at a Solution
So this is a...
∫ ln(e^{Φ^2}+1)dΦ
I am a high school math student, so my calculus knowledge is that of high school. I tried to solve this problem, but nothing I have learned seemed to work so far, substitution didn't work, integration by parts didn't work. I presume this problem is beyond high school level...
Consider the integral ##\displaystyle \int_{-\infty}^\infty \frac{e^{-|x|}}{1+x^2}dx ##. I should be able to use contour integration to solve it because it vanishes faster than ## \frac 1 x ## in the limit ## x \to \infty ## in the upper half plane. It has two poles at i and -i. If I use a...
OK, I admit: this will be the most idiotic question I have ever asked (maybe: there could be more)
So, I am aware of the differential calculus (derivatives) and the integral calculus (integrals).
And separate from that, there is the first fundamental theorem (FFT) of the calculus which relates...
1. The problem statement
Solve the following problems assuming air density is proportional to respective pressure at each height: What is the normal pressure at the atmosphere at the summit of a. Mt. McKinley, 6168m above sea level and b. Mt. Everest, 8850m above sea level c. At what elevation...
Homework Statement
turning on the engine of a motorboat (v0=0),
K = constant force due to the engine
drag force of the water D = -cv
find v(t)=?
Homework Equations
integration
f=ma, a=dv/dt
The Attempt at a Solution
[/B]
D+K = MA
K-cv = MA
(A=dv/dt)
K-cv=Mdv/dt
Mdv=dt(K-cv)
?
i want to do...
Homework Statement
[/B]
##C_\rho## is a semicircle of radius ##\rho## in the upper-half plane.
What is
$$\lim_{\rho\rightarrow 0} \int_{C_{\rho}} \frac{e^{iaz}-e^{ibz}}{z^2} \,dz$$Homework Equations
If ##C## is a closed loop and ##z_1, z_2 ... z_n## are the singular points inside ##C##...
Here's a graph and its triple integral. How are the limits of integration for the outer integral [-2,2]? I have no idea how this was found.
Any help would be appreciated!
Hello, I'm currently taking calc 1 as an undergraduate student, and my professor just showed us a new? way of solving Integration By Parts.
This is the example he gave"
Is there a name for this technique that substitutes d(___) instead of dx?
Thank you,
Homework Statement
##∫45.1/3x^2 (4-2x)^3dx##[/B]Homework EquationsThe Attempt at a Solution
##45/3∫x^2(4-2x)^3dx = let u = x^2 du= 2x, dv= (4-2x)^3 v=(2-x)/-4 ##
using intergration by parts is this right[/B]
If a brick is pulled across the floor by a rope thruogh a pulley, 1 meter above the ground - and work = W, where W = 10N , (in Newton).Show that the horizontal component of W, which is pulling the brick has the size
\frac{10x}{\sqrt{1+x^2}} (*)
Use this to calculate the amount of work needed...
I was thinking if the known methods of integration are enough to integrate any given function. In differentiation, we've evaluated the derivatives of all the basic functions by first principles and then we have the chain rule and product rule to differentiate any possible combination (product or...
Homework Statement
Using Taylor series, Find a polynomial p(x) of minimal degree that will approximate F(x) throughout the given interval with an error of magnitude less than 10-4
F(x) = ∫0x sin(t^2)dt
Homework Equations
Rn = f(n+1)(z)|x-a|(n+1)/(n+1)![/B]
The Attempt at a Solution
I am...
Problem
F denotes a forward Fourier transform, the variables I'm transforming between are x and k
- See attachment
Relevant equations
So first of all I note I am given a result for a forward Fourier transform and need to use it for the inverse one.
The result I am given to use, written out...
Hi.. I am stuck up with a double integration where one of the integration limit is infinity. I know quadpack (qagi) can handle integration over infinite intervals. But how to make it work for the double integration. Or if there is any other routine that can handle both double integration and...
1. Homework Statement
I'm trying to integrate this, the only variable is y the others(x,w) are all constants.
Homework Equations
The ways of integrating that I am familiar with are substitution, trigonometric substitution, by parts & partial fraction decomposition.
The Attempt at a Solution...
Homework Statement
Using contour methods, evaluate the following integrals. In any case in which you wish to argue that some portion of a closed contour gives a negligible contribution, you should explain why that is so.
Integral[E^I(k+delta*I)x^2 dx from negative Infinity to Infinity]
as...
Consider the following integration:
$$\int \frac{d^{4}k}{(2\pi)^{4}}\ \frac{1}{(k^{2}+m^{2})^{\alpha}}=\frac{1}{(4\pi)^{d/2}} \frac{\Gamma\left(\alpha-\frac{d}{2}\right)}{\Gamma(\alpha)}\frac{1}{(m^{2})^{\alpha-d/2}}.$$
---
How does the dependence on ##d## arise in this integral?
Can someone...
This question deals specifically with complex analysis.
Let C be the unit circle in the complex plane (|z| = 1). If you calculate the contour integral of (1/z)dz over C using Cauchy's Integral Formula, you get 2*pi*i. If you calculate it using the path z(t)=e^(it), t in [0,2pi], you also...
Homework Statement
The maximum torque on a lever is 1.5 x 10^6 Newtons. How many people of weight 750N can stand evenly spaced on this lever, which has a length of 20 meters?
Homework Equations
T=FR
Weight=mg
W=Fd
X = Number of people
The Attempt at a Solution
I have set 1.5x10^6 N =...
Homework Statement
Find the general solution to the differential equation:
Homework Equations
Separation of variables for solving 1st order separable differential equation.
The Attempt at a Solution
Using separation of variables, I can write:
My questions are:
1) Am I correct to...
Homework Statement
I have three integrals, from 0 to 1
∫ -4x5 ex3-x4dt
∫ 3x4ex3-x4dt
∫ 2tex3-x4dtHomework Equations
Looks like they are not integrable, as ex3-x4 is not,
I tried by part, let say u =
The Attempt at a Solution
This is from a physics textbook, a chapter on rocket launch velocities, but really the question is how to integrate the first equation to get to the next.
The way I was approaching it was like this:
From
## V \frac{d\gamma}{dt}=-g \cos \gamma##
Integrating from ##t=0## to some ##t##...
I have ## \int_{t = 0}^{t = 1} \frac{1}{x} \frac{dx}{dt} dt = \int_{t = 0}^{t = 1} (1-y) dt ## [1]
The LHS evaluates to ## ln \frac{(x(t_0+T))}{x(t_0)} ##, where ##t_{1}=t_{0}+T##
My issue is that, asked to write out the intermediatary step, I could not. I am unsure how you do this when the...
I would like to prove that
##\displaystyle{\int dx'\ \frac{1}{\sqrt{AB}}\exp\bigg[i\frac{(x''-x')^{2}}{A}\bigg]\exp\bigg[i\frac{(x'-x)^{2}}{B}\bigg]=\frac{1}{\sqrt{A+B}}\exp\bigg[i\frac{(x''-x)^{2}}{A+B}\bigg]}##
Is there an easy way to do this integration that does not involve squaring the...
Homework Statement
We need to write an integrator for the Chandrasekhars Equation (CE) for White Dwarfs (WD) using python3/NumPy/Matplotlib. We then need to compute the structure of a WD made of our varying elements. We also need to compute and plot the mass-radius relation for WD.
Homework...
Consider the partition function ##Z[J]## of the Klein-Gordon theory
##Z[J] =\int \mathcal{D}\phi\ e^{i\int d^{4}x\ [\frac{1}{2}(\partial\phi)^{2}-\frac{1}{2}m^{2}\phi^{2}+J\phi]}
=\int \mathcal{D}\phi\ e^{-i\int d^{4}x\ [\frac{1}{2}\phi(\partial^{2}+m^{2})\phi]}\ e^{i\int d^{4}x\...
Homework Statement
Hi, I'm doing a variation of parameters problem for my differential equations class. It requires solving the integral:
∫ex t-2 dt
I am sure my professor did not give me an impossible integral and that there is some algebraic "trick" to solving it, but despite going through...
I would like to evaluate the following integral:
##\displaystyle{\int_{-\infty}^{\infty} dp^{0}\ \delta(p^{2}-m^{2})\ \theta(p^{0})}##
##\displaystyle{= \int_{-\infty}^{\infty} dp^{0}\ \delta[(p^{0})^{2}-\omega^{2}]\ \theta(p^{0})}##
##\displaystyle{= \int_{-\infty}^{\infty} dp^{0}\...
I have been reading through "Complex Analysis for Mathematics & Engineering" by J. Matthews and R.Howell, and I'm a bit confused about the way in which they have parametrised the opposite orientation of a contour ##\mathcal{C}##.
Using their notation, consider a contour ##\mathcal{C}## with...
Homework Statement
http://imgur.com/a/qlQ5z
Homework Equations
i=i(o)+1/L integration(v0) dt formula is in the attemp at a solution.
The Attempt at a Solution
http://imgur.com/a/HVjl1
For the interval 2<t<infinite . I understand...
Homework Statement
Homework Equations
spherical Jacobean
The Attempt at a Solution
I have (sorry, have to capture my work, too hard to type)
then the integration of p3 ep2 = 1/2 ep2 (p2-3/2) ??
Homework Statement
Minimize the functional: ∫01 dx y'2⋅ ∫01 dx(y(x)+1) with y(0)=0, y(1)=aHomework Equations
(1) δI=∫ dx [∂f/∂y δy +∂f/∂y' δy']
(2) δy'=d/dx(δy)
(3) ∫ dx ∂f/∂y' δy' = δy ∂f/∂y' |01 - ∫ dx d/dx(∂f/∂y') δy
where the first term goes to zero since there is no variation at the...
Is their a tutorial or a reference on how to decompose a function, specifically Fourier and Legendre decomposition, for numerical integration? The method I am going to use for the numerical integration is the Gauss Quadrature, and I suppose I need to decompose my function for the rule to work...
Homework Statement
An object of mass m is initially at rest and is subject to a time-dependent force given by F = kte^(-λt), where k and λ are constants.
a) Find v(t) and x(t).
b) Show for small t that v = 1/2 *k/m t^2 and x = 1/6 *k/m t^3.
c) Find the object’s terminal velocity.
Homework...
Homework Statement
in this problem , i couldn't express all the x any y in terms of u( refer to the circled part ) ... so , i have problem to proceed my subsequent steps ...
Homework EquationsThe Attempt at a Solution
i let u = (x^2) + (y^2) ... [/B]
$$\int(1-y^2)^\frac{1}{2}\,dy$$
I did trig substitution
$$y=\sin\theta$$
$$dy=\cos\theta\,d\theta$$
$$\int(1+\cos2\theta)d\theta$$
$$\arcsin\,y+\frac{1}{2}\sin(2\arcsin\,y)+c$$
How do I get rid of the arcsins?
I need some help with this integran
$$\int\frac{2x^2}{2x^2-1}dx$$I can't seem to solve this using the techniques that I know.
What method should I use?
So I need to compare the results of the volume formula of a cylinder to the results of the integration.
In geometry, you learn that the volume of a cylinder is given by V = πr2h, where r is the radius and h is the height of the cylinder. Use integration in cylindrical coordinates to confirm the...
For part of a proof of a differential equations equivalence, we needed to use that $$\int_0^t [\int_0^s g(\tau,\phi(\tau))\space d\tau]\space ds = \int_0^t [\int_\tau^t ds]\space g(\tau,\phi(\tau))\space d\tau$$
I understand that the order is being changed to integrate with respect to s first...
Homework Statement
Find the value of the integral ## \int_0^\infty dx \frac{\sqrt{x}}{1+x^2} ## using calculus of residues!
Homework EquationsThe Attempt at a Solution
This is how I did it:
##\int_0^\infty dx \frac{\sqrt{x}}{1+x^2}=\frac 1 2 \int_{-\infty}^\infty dx \frac{\sqrt{|x|}}{1+x^2} ##...