Function expansion, Mathematics

Assignment Help:

The functions

{sinmx; cosmx}; m = 0,....∞

form a complete set over the interval x ∈ [ -Π, Π]. That is, any function f(x) can be expressed as a linear superposition of these with a unique set of coecients. For f(x) = x, we have

883_FUNCTION EXPANSION.png

To show that the above holds for x = 1, study the di erence between the left- and right-hand sides of the equality as a function of the number of terms included in the sum. Write an octave program to compute and plot the truncated sum approximation (expansion vs x) for n =4 and 16 together with the function x. Make a table showing the error (di erence between two sides) for n =1, 2, 4, 16, 64, 256, 1024. Plot the result of the expansion for 2 values of n together with the original function. Comment on your results. You should submit an octave script or function le I can use to reproduce your results and a separate document (plain text le preferred) for your comments.


Related Discussions:- Function expansion

BASIC MATHEMATHICS :AN APPLIED APPROACH BY RATHUS, FIRST OF ALL I WANNA KN...

FIRST OF ALL I WANNA KNOW THECHNIQUES, I CAT DIVIDE BIG BIG NUMBERS , EVERYTHING IN MATH IIS VERY HARD FOR ME I HOPE YOU CAN HELP ME

Problem solving sentence, a cheeseburger cost $6.39 more than a burger of $...

a cheeseburger cost $6.39 more than a burger of $2.29, what is the difference?

2 step equations, What is a two step equation that equals 8 ?

What is a two step equation that equals 8 ?

Solving a system of 2 equations addition-subtraction method, Solving a Syst...

Solving a System of 2 Equations Using the Addition/Subtraction Method To solve a system of linear equations using the addition/subtraction method, both equations should first b

Example of inflection point-differential equation, Example of inflection po...

Example of inflection point Determine the points of inflection on the curve of the function y = x 3 Solution The only possible inflexion points will happen where

Find the equation to the pair of lines - coordinate geometry, 1. Find the n...

1. Find the number of zeroes of the polynomial y = f(x) whose graph is given in figure. 2 Find the circumcentre of the triangle whose vertices are (-2, -3), (-1, 0) and (7,-6).

Correlation, How o make vicariate frequency distribution table

How o make vicariate frequency distribution table

Steps for integration strategy - integration techniques, Steps for Integrat...

Steps for Integration Strategy 1. Simplify the integrand, if possible This step is vital in the integration process. Several integrals can be taken from impossible or ve

Undamped - forced vibrations, We will firstly notice the undamped case. The...

We will firstly notice the undamped case. The differential equation under this case is, mu'' + ku  = F(t) It is just a non-homogeneous differential equation and we identify h

Surds, solve for x: logx9

solve for x: logx9

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