Trying to learn matlab (Taylor Series)

kalen

I'm supposed to be writing some code in matlab that will allow me to solve the Taylor series of e^x to a minimum term value of M.

The taylor series is
e^x= 1 + x/1! + x^2/2! +.....

I've been using matlabs help and google for about 6 hours trying to figure this out.

[FONT=Courier New][SIZE=2]x=input([/SIZE][/FONT][FONT=Courier New][SIZE=2][COLOR=#a020f0]'You are computing e^x, what number is x?'[/COLOR][/SIZE][/FONT][FONT=Courier New][SIZE=2]);[/SIZE][/FONT]
[SIZE=2][FONT=Courier New]d=input([/FONT][/SIZE][FONT=Courier New][SIZE=2][COLOR=#a020f0]'What degree of accuracy would you like?'[/COLOR][/SIZE][/FONT][FONT=Courier New][SIZE=2]);[/SIZE][/FONT]
 
 
[SIZE=2][FONT=Courier New]c=0;[/FONT][/SIZE]
[FONT=Courier New][SIZE=2][COLOR=#0000ff]for[/COLOR][/SIZE][/FONT][FONT=Courier New][SIZE=2] b=0:1:1100[/SIZE][/FONT]
[FONT=Courier New][SIZE=2][COLOR=#0000ff]while[/COLOR][/SIZE][/FONT][FONT=Courier New][SIZE=2] b/(x^b/factorial(b))>1 [/SIZE][/FONT]
[SIZE=2][FONT=Courier New]c=c+((x^b)/factorial(b));[/FONT][/SIZE]
 
[FONT=Courier New][SIZE=2][COLOR=#0000ff]end[/COLOR][/SIZE][/FONT]
[FONT=Courier New][SIZE=2]disp(sum(c))[/SIZE][/FONT]
[FONT=Courier New][SIZE=2][COLOR=#0000ff]end[/COLOR][/SIZE][/FONT]
 

I thought that this would cause it to set c as 0. Then run integers in order (1,2,3..) until it reached an answer that was less than the specified d value. Then it would stop and display the total of those values.

This isn't working and I can't figure out what I'm doing wrong.
Help, Please!

drasnor

First off, that is a Maclaurin series expansion for e^x which is equivalent to the Taylor series expansion of e^x about a=0. Just letting you know in case a is not necessarily 0 (see MathWorld entry on Taylor series.)
Questions:
What are the variables 'b', 'c', and 'd' supposed to do? You take 'd' as an input but never use it for anything.
You talk about M but what is M in terms of the code you created?

-drasnor

drasnor

This code is provided for educational purposes only.

disp('Icrontic.com MATLAB Team Sample Code.');
disp('Copy at your own peril, many teachers/professors are proficient with Google.');
disp('This code evaluates a Taylor series approximation of e^x about the point a=0.');

% Variable definitions:
% x: power of e to be solved.
% d: desired accuracy evaluated as the value of the n-term Taylor series
%       approximation - the (n-1)-term Taylor series approximation.
% n: number of terms in the Taylor series.
% t_n: nth term in Taylor series.
% e_approx: solution to the n-term Taylor series.

x=input('Enter x: ');
d=input('Enter accuracy of approximation: ');

n=1;            % approximation begins with single-term solution
t_n=x^(n-1)/factorial(n-1);
e_approx=t_n;   % initial approximation
while t_n > d                      % accuracy reached?
    n=n+1;                         % add another term.
    t_n=x^(n-1)/factorial(n-1);    % evaluate the new term.
    e_approx=e_approx+t_n;         % add the new term to the approximation.
end
disp('Approximate solution of e^x:');
disp(e_approx);
disp('Number of terms in Taylor series:');
disp(n);
disp('Accuracy achieved:');
disp(t_n);

-drasnor

shwaip

i swear we've had this exact question before.

moved to matlab help subforum

kalen

Drasnor, thanks a ton man I think I understand what I was doing wrong,
Seeing your code really helped me understand how to approach it.

Thanks again.