Numerical differentiation and integration

From Process Model Formulation and Solution: 3E4
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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
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