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methcalchimplugin-autotooltip__default plugin-autotooltip_bigCalculation methods applied to chemistry

Synopsis (english)

Mathematical prerequisites

Programming bases and tools

* Python programming language * LearnPython.org interactive tutorial with code execution * DataCamp free course "Intro to Python for Data Science" * Python 3 Tutorial, interactive, with code use in web browser * MOOCs (massive open online courses) :
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hm) * Reférences : * [[https://pubs.acs.org/doi/abs/10.1021/acs.jchemed.8b00649|An Open-Source, C... lich, J. Chem. Educ., 2018, 95 (12), pp 2273–2278 DOI: 10.1021/acs.jchemed.8b00649 === Chebyshev appr... Python]] * Arduino * [[http://pubs.acs.org/doi/abs/10.1021/acs.jchemed.6b00639|Fabrication of an... Nollert, J. Chem. Educ., 2017, 94 (4), pp 530–533 DOI: 10.1021/acs.jchemed.6b00639 * PCA (principal c
eigenvalues_and_eigenvectorsplugin-autotooltip__default plugin-autotooltip_bigEigenvalues and eigenvectors

* Eigenvalues and eigenvectors * Important matrix properties * Hermitian, orthogonality,...

* Eigenvalue algorithm * Power iteration, a simple numerical algorithm producing a number $\lambda$, the greatest (in absolute value) eigenvalue of a matrix $A$, and the corresponding eigenvector $v$$Av=\lambda v$
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relaxation * //e.g.// [[https://pubs.acs.org/doi/abs/10.1021/ed066p142|Collisional relaxation via ... endell Forst, J. Chem. Educ., 1989, 66 (2), p 142 DOI: 10.1021/ed066p142 * population dynamics, evolu... * [[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.133.7164&rep=rep1&type=pdf|Leslie Matrix M
numerical_integrationplugin-autotooltip__default plugin-autotooltip_bigNumerical integration

Error estimation

* Equally spaced methods : * Numerical_integration * Trapezoidal_rule * Newton–Cotes_formulas * Simpson's rule and composite Simpson's rule

* If intervals between interpolation points vary : * Gaussian_quadrature

* Chapter 4 in the book “Numerical Recipes” : Integration of Functions * 4.0 Introduction * 4.1 Classical Formulas for Equally Spaced Abscissas
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ration calculus compare to [[https://pubs.acs.org/doi/10.1021/acs.jchemed.8b00193|Employing Spreadsheet... oper, J. Chem. Educ., 2018, 95 (10), pp 1890–1893 DOI: 10.1021/acs.jchemed.8b00193 ===== Références ==
numerical_methods_for_ordinary_differential_equationsplugin-autotooltip__default plugin-autotooltip_bigIntegration of Ordinary Differential Equations

* Ordinary Differential Equations (ODE, ODEs) * Numerical methods for ordinary differential equations * Euler method * Runge-Kutta methods * « most widely known member of the Runge–Kutta family is generally referred to as “RK4”, “classical Runge–Kutta method” or simply as “the Runge–Kutta method »
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cademy of Sciences Jan 2021, 118 (4) e2017463118; DOI: 10.1073/pnas.2017463118 * [[https://www.sympy.