====== Numerical integration ======
<note tip>
Calculation of definite integrals implies to replace the function by another one (usually a polynomial form) which is a good approximation and easier to compute. [[wp>Numerical_integration#Conservative_.28a_priori.29_error_estimation|Error estimation]] depends on parameters of the method and refinement of spatial grid discretization. It is interesting to check these errors using various algorithm and mesh resolution.
</note>

  * Equally spaced methods :
    * [[wp>Numerical_integration]]
    * [[wp>Trapezoidal_rule]]
    * [[wp>Newton–Cotes_formulas]]
    * [[wp>Simpson's_rule#Composite_Simpson.27s_rule|Simpson's rule and composite Simpson's rule]]
  * If intervals between interpolation points vary :
    * [[wp>Gaussian_quadrature]]
  * Chapter 4 in the book “Numerical Recipes” : Integration of Functions
    * 4.0 Introduction
    * 4.1 Classical Formulas for Equally Spaced Abscissas
    * 4.2 Elementary Algorithms
    * 4.5 Gaussian Quadratures and Orthogonal Polynomials
  * Python SciPy library : [[https://docs.scipy.org/doc/scipy/reference/|SciPy Reference]]
    * [[https://docs.scipy.org/doc/scipy/reference/tutorial/integrate.html|Integration (scipy.integrate)]]

===== Applications =====
  * Perform better integration calculus compare to [[https://pubs.acs.org/doi/10.1021/acs.jchemed.8b00193|Employing Spreadsheets for Applying Calculus in Upper-Level Chemistry Courses]] Paul D. Cooper, J. Chem. Educ., 2018, 95 (10), pp 1890–1893 DOI: 10.1021/acs.jchemed.8b00193

===== Références =====
  * Numerical recipes, The Art of Scientific Computing 3rd Edition, William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian P. Flannery, 2007, isbn: 9780521880688
    * [[http://numerical.recipes/]]
      * in C : [[http://apps.nrbook.com/c/index.html]]
    * [[http://www2.units.it/ipl/students_area/imm2/files/Numerical_Recipes.pdf]], p 129...
    * [[http://apps.nrbook.com/empanel/index.html#]]