Difference between revisions of "Numerical differentiation and integration"
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pdf_file = E-Numerical-integration-08-Nov-2010.pdf | pdf_file = E-Numerical-integration-08-Nov-2010.pdf | ||
</pdfreflow> | </pdfreflow> | ||
=== Source code used in slides === | |||
{| class="wikitable" | |||
|- | |||
! MATLAB | |||
! Python | |||
|- | |||
| width="50%" valign="top" | | |||
<syntaxhighlight lang="matlab"> | |||
function In = trapezcomp( f, a, b, n ) | |||
% INITIALIZATION | |||
h = (b-a)/n; | |||
x = a; | |||
% COMPOSITE RULE | |||
In =f(a); | |||
for k=2:n | |||
x = x + h; | |||
In = In + 2. * f(x); | |||
end | |||
In = ( In + f(b) ) * h * 0.5; | |||
% end of function | |||
</syntaxhighlight> | |||
Then use this function as follows: | |||
<syntaxhighlight lang="matlab"> | |||
>> f = @(x)sin(x); | |||
>> I1 = trapezcomp( f, 0, pi/2, 1 ) % 0.7854 | |||
>> I2 = trapezcomp( f, 0, pi/2, 2 ) % 0.9481 | |||
</syntaxhighlight> | |||
| width="50%" valign="top" | | |||
<syntaxhighlight lang="python"> | |||
</syntaxhighlight> | |||
|} | |||
Revision as of 13:15, 10 November 2010
Part A: Numerical differentiation
<pdfreflow> class_date = 01 to 04 November button_label = Create my course notes! show_page_layout = 1 show_frame_option = 1 pdf_file = E-Numerical-differentiation-01-Nov-2010.pdf </pdfreflow>
Part B: Numerical integration
<pdfreflow> class_date = 08 to 15 November button_label = Create my course notes! show_page_layout = 1 show_frame_option = 1 pdf_file = E-Numerical-integration-08-Nov-2010.pdf </pdfreflow>
Source code used in slides
| MATLAB | Python |
|---|---|
function In = trapezcomp( f, a, b, n )
% INITIALIZATION
h = (b-a)/n;
x = a;
% COMPOSITE RULE
In =f(a);
for k=2:n
x = x + h;
In = In + 2. * f(x);
end
In = ( In + f(b) ) * h * 0.5;
% end of function
Then use this function as follows: >> f = @(x)sin(x);
>> I1 = trapezcomp( f, 0, pi/2, 1 ) % 0.7854
>> I2 = trapezcomp( f, 0, pi/2, 2 ) % 0.9481
|