Problem 2.12,

by Nasser Abbasi

Source code

function nma_HW_2_12(problemPart,x)

%function nma_HW_2_12

%

% finds the error in calculation of derivatives for a number

% of functions as a function of delta, at some specific points

% using the centered derivative formula

% f(t+TAO) - f(t-TAO)

% f'(t) = ---------------------

% 2 TAO

% INPUT

% problemPart : a character of the name of the part, a-e

% x : the value to evalute the derivative at.

%

% This is the solution to problem 2.12, parts a-e.

%

%

%HW 5, 2.12 parts a-e

%Nasser Abbasi, phy 240, Sam Jose State Univ.

%Feb 11, 2002

% struct to hold the data as we iterate

struct err { ...

value : 0 ...

delta : 0 };

switch(problemPart)

case 'a'

deriveExact=2*x;

process('fa',problemPart,x,deriveExact);

return;

case 'b'

deriveExact=5*x^4;

process('fb',problemPart,x,deriveExact);

return;

case {'c','d','e'}

deriveExact=cos(x);

process('fc',problemPart,x,deriveExact);

return;

error('invalid part number');

end

%%%%%%%%%%%%%%%%%%%%%%%%%%

%

%

%%%%%%%%%%%%%%%%%%%%%%%%%%

function process(functionName,problemPart,x,exact)

delta =1;

for i=1:21

deriveApprox = ( feval(functionName,x+delta) - feval(functionName,x-delta)) / (2*delta);

err.value(i) = abs(exact - deriveApprox);

err.delta(i) = delta;

delta = delta/10;

end

p=loglog(err.delta,err.value,'.');

title(sprintf('Showing abs error in evaluation of derivative for part %c at x=%d',problemPart,x));

xlabel('Delta, or step size, drawn on a log scale.');

ylabel('Absolute error, drawn on a log scale');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% function x^2, for part a

%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function [y]=fa(x)

y=x^2;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% function x^5 for part b

%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function [y]=fb(x)

y=x^5;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% function sin(x) for part c

%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function [y]=fc(x)

y=sin(x);

Run output

» clear all

» help nma_HW_2_12

function nma_HW_2_12

finds the error in calculation of derivatives for a number

of functions as a function of delta, at some specific points

using the centered derivative formula

f(t+TAO) - f(t-TAO)

f'(t) = ---------------------

2 TAO

INPUT

problemPart : a character of the name of the part, a-e

x : the value to evalute the derivative at.

This is the solution to problem 2.12, parts a-e.

» nma_HW_2_12('a',1)

nma_HW_2_12('b',1)

» nma_HW_2_12('c',0)

» nma_HW_2_12('d',pi/4)

» nma_HW_2_12('e',pi/2)