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

The definition of the derivative, The Definition of the Derivative : In t...

The Definition of the Derivative : In the previous section we saw that the calculation of the slope of a tangent line, the instantaneous rate of change of a function, and the ins

Find the slope of a line given two points on it, Finding the Slope of a Lin...

Finding the Slope of a Line, Given Two Points on it ? Find the slope of the line passing through the pairs of points (-5, -2) and (2, 4). One way to find the slope is

Find out the determinant, Find out the determinant: Find out the deter...

Find out the determinant: Find out the determinant of the following 3 x 3 matrix, expanding about row 1. Solution:

Retail price index, Retail price index This is weighted average of pri...

Retail price index This is weighted average of price relatives based on an average household in the base year. The items consumed are divided into groups as liker food, transp

If there are 75 students in the play how many are boys, 64% of the students...

64% of the students within the school play are boys. If there are 75 students in the play, how many are boys? To ?nd out 64% of 75, multiply 75 by the decimal equivalent of 64%

What is the probability that the integer chosen is divisible, An integer i...

An integer is chosen at random from the first two hundreds digit. What is the probability that the integer chosen is divisible by 6 or 8.                    (Ans : 1/4 ) Ans:

Linear programming, Chelsea has been facing some financial problems which e...

Chelsea has been facing some financial problems which even caused her daily expenses for food, at the same time, she hasn''t receive the money from the bank loan yet. Therefore, sh

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