Geometric construction of numerical integration, Engineering Mathematics

Assignment Help:

The integral

1725_Geometric construction.png

has an exact answer, viz., sinc(pfT). As T®¥ the sinc function tends to zero. Divide the region from -T/2 to T/2 into N equal parts and sum the rectangles on bases Δt =T/N , showing that

1378_Geometric construction1.png

Observe that this function is periodic. For a given choice of f and T construct a table to show by how much the discrete version of the integral differs from the true value. Does inclusion of only half the areas of the end rectangles make much difference? Note that you have included N+1 points in your sum. What happens if you have only N points, i.e., if you do not include one of the end rectangles. A geometric construction may assist.


Related Discussions:- Geometric construction of numerical integration

Fast fourier transform, From this point on it is assumed that any problem a...

From this point on it is assumed that any problem amenable to solution with the aid of the Discrete Fourier Transform (or DFT) will in fact be treated computationally with a fast r

Compute the linear arc distance, Question Assume the earth is a sphere ...

Question Assume the earth is a sphere with a radius of 6,371,000.000 meters. Three points are defined by their latitude and longitude. Point Latitude (N) Longitude (W) A

Geometric construction of numerical integration, The integral has a...

The integral has an exact answer, viz., sinc(pfT). As T®¥ the sinc function tends to zero. Divide the region from -T/2 to T/2 into N equal parts and sum the rectangles on b

Fourier series, b) State by inspection (i.e. without performing any formal ...

b) State by inspection (i.e. without performing any formal analysis) all you can about each of the periodic waveforms shown in FIGURE 1 in terms of their Fourier series when analys

Solve the following logarithmic equations, 1. Joe and Sam each invested $20...

1. Joe and Sam each invested $20,000 in the stock market. Joe's investment increased in value by 5% per year for 10 years. Sam's investment decreased in value by 5% for 5 years and

Some children are afraid of snakes, change each of the following propositio...

change each of the following propositions into symbolic form. De ne the universe of discourse and the predicates you use. (i) Some children are afraid of snakes. (ii) All com

MUPAD, I have some work in Mupad i need doing. Its on Diff equations. Canb ...

I have some work in Mupad i need doing. Its on Diff equations. Canb you guys help?

Temperature function, If a temperature function is given in the x,y plane b...

If a temperature function is given in the x,y plane by T(x,y) = x+y, what is the value, to 3 decimal places, of the corresponding temperature function T1(u,v) at the point (u,v) =

Estimate lowest and highest byte memory, What are the lowest and highest a...

What are the lowest and highest addresses in a 2 20 byte memory in which a four-byte word is the smallest addressable unit?

Harmonic function, Let z 0 = a + ic, z 1 = b + id, z 2 = -id, and z =...

Let z 0 = a + ic, z 1 = b + id, z 2 = -id, and z = [z 0 + z 1 ]. Let z 0 be the apex of the wedge with one ray passing through z 1 and the other passing through z 2 , and

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd