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

Find the sum of the three coefficient polynomials, Find the quadratic that ...

Find the quadratic that interpolates f(x) = 2x 3 - x + 1 at the nodes x 0 = 0, x 1 = 2, x 2 = 3, a) by solving a set of three equations for the coefficients of p 2 (x) = a 2

Explain the integrated circuits, a. Explain the Integrated Circuits? What a...

a. Explain the Integrated Circuits? What are the benefits of ICs as compared to standard printed circuits? b. Explain in brief, the various steps included in fabrication of ICs.

Substitution method, Answer the following set of simultaneous equations usi...

Answer the following set of simultaneous equations using elimination or substitution method. a) x-y +z= 10 b) 3x+y+2z=34 c) -5x+2y-z=-14

Produce a discrete time series, Produce a discrete time series y(t i ) by s...

Produce a discrete time series y(t i ) by super positioning 5 cosinusoidal components, for your own choice of the amplitudes (a j ) and frequencies (f j ). Add some Gaus

Sinusoidal trigonometrical function, The displacement x meters of a mass fr...

The displacement x meters of a mass from a fixed point about which it is oscillating is given by x=2.3cos?10pt+4.2sin?10pt where t is the time in seconds Express the displaceme

Dynamics, The acceleration of an oscillating particle is defined by the rel...

The acceleration of an oscillating particle is defined by the relation a = -kx Determine the value of k such that v = 15 in./s when x = 0 and x = 3 in. and v = 0, the speed of the

Loop transfer function, Given the loop transfer function G(s)H(s) = k/s(...

Given the loop transfer function G(s)H(s) = k/s(s+3)(s+4)(s+5) (a) Sketch the root locus plot for G(s)H(s). (b) What is the system gain at s = -1+ 2i? (c) Calculate the

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