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

All.., Ask question #Minimum 100thank you words accepted#

Ask question #Minimum 100thank you words accepted#

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

Set up a scatter diagram for speed, A research analyst for an oil company w...

A research analyst for an oil company wants to develop a model to predict miles per gallon based on highway speed. An experiment is designed in which a test car is driven at speeds

Evaluate the fermat''s method algorithm, 1. (i) How many digits does the nu...

1. (i) How many digits does the number 101000 have when written to base 7 ? (ii) Use the prime number theorem to estimate the proportion of prime numbers among the positive inte

Assingment , application of mathematics in engineering

application of mathematics in engineering

Calculus, Ask questioA mass on a spring vibrates. Its position at time t fr...

Ask questioA mass on a spring vibrates. Its position at time t from its starting point is x(t) = 2 cos(t) e t Find the velocity and acceleration at time t. What is the behavior of

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

., parabola

parabola

Find the polynomial, a) Use divided differences to ?nd the polynomial (in n...

a) Use divided differences to ?nd the polynomial (in nested form) that interpolates the data b) Add the data point x = 6, y = -20 and hence estimate y for x = 2.

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