https://dvillers.umons.ac.be/wiki/ 2026-05-03T18:53:54+00:00 https://dvillers.umons.ac.be/wiki/ https://dvillers.umons.ac.be/wiki/_media/favicon.ico text/html 2021-06-11T12:15:10+00:00 Anonymous (anonymous@undisclosed.example.com) https://dvillers.umons.ac.be/wiki/teaching:methcalchim:eigenvalues_and_eigenvectors?rev=1623406510&do=diff Eigenvalues 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$ text/html 2023-04-12T10:08:20+00:00 Anonymous (anonymous@undisclosed.example.com) https://dvillers.umons.ac.be/wiki/teaching:methcalchim:start?rev=1681286900&do=diff Calculation 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) : text/html 2018-10-09T07:59:58+00:00 Anonymous (anonymous@undisclosed.example.com) https://dvillers.umons.ac.be/wiki/teaching:methcalchim:numerical_integration?rev=1539064798&do=diff Numerical 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 text/html 2022-08-25T07:45:38+00:00 Anonymous (anonymous@undisclosed.example.com) https://dvillers.umons.ac.be/wiki/teaching:methcalchim:numerical_methods_for_ordinary_differential_equations?rev=1661406338&do=diff Integration 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 » text/html 2018-10-19T09:58:36+00:00 Anonymous (anonymous@undisclosed.example.com) https://dvillers.umons.ac.be/wiki/teaching:methcalchim:root-finding_algorithm?rev=1539935916&do=diff Root findings : equations f(x) = 0 * Polynomial equations : Bairstow's method is an efficient algorithm for finding the roots of a real polynomial of arbitrary degree * Polynomials in NumPy * polynomial module, including polyroots(c) to compute the roots of a polynomial. * Bisection method (dichotomy) : very simple and robust method, but relatively slow. It assumes continuity of the function, and obtain one roots. The algorithm is based on a text/html 2018-10-18T10:10:41+00:00 Anonymous (anonymous@undisclosed.example.com) https://dvillers.umons.ac.be/wiki/teaching:methcalchim:system_of_linear_equations?rev=1539850241&do=diff System of linear equations Time_complexityi.e. Theory * System_of_linear_equations * Gaussian_elimination, Gauss and Gauss-Jordan eliminations (diagonalization, triangularization) * Pivot_element, pivoting * LU_decomposition * Triangular_matrix * Chapter 2 in the book “Numerical Recipes” : * 2.0 Introduction * 2.1 Gauss-Jordan Elimination