[{"command":"insert","method":null,"selector":".course-modal-ajax-placeholder-952473","data":"\u003Cdiv class=\u0022container content-rte\u0022\u003E\n  \u003Cdiv class=\u0022row\u0022\u003E\n    \u003Cdiv class=\u0022box col-md-6 bg-primary text-white\u0022\u003E\n      \u003Ch2 class=\u0022h1 text-left\u0022\u003E  M\u00e9thodes math\u00e9matiques pour l\u0026#039;ing\u00e9nierie\n\u003C\/h2\u003E\n                  \u003Cdiv class=\u0022field-spacing\u0022\u003E\n        \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EECTS :\n          4\n        \u003C\/div\u003E\n      \u003C\/div\u003E\n                  \u003Cdiv class=\u0022field-spacing\u0022\u003E\n        \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ESemestre calendaire :\n          Semestre 1\n        \u003C\/div\u003E\n      \u003C\/div\u003E\n            \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ED\u00e9tail du volume horaire\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                          \u003Cspan class=\u0022field__label h4 mt-5 \u0022\u003ECours magistraux :\u003C\/span\u003E\n                                      \u003Cspan\u003E18\u003C\/span\u003E\n                      \u003C\/div\u003E\n                                              \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                          \u003Cspan class=\u0022field__label h4 mt-5 \u0022\u003ETravaux dirig\u00e9s :\u003C\/span\u003E\n                                      \u003Cspan\u003E0\u003C\/span\u003E\n                      \u003C\/div\u003E\n                                \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                          \u003Cspan class=\u0022field__label h4 mt-5 \u0022\u003EProjet tutor\u00e9\u003C\/span\u003E\n                                      \u003Cspan\u003E24\u003C\/span\u003E\n                      \u003C\/div\u003E\n                                              \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ELangue d\u0026#039;enseignement\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003EAnglais\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EEnseignement \u00e0 distance\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003Enon\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n      \u003C\/div\u003E\n    \u003Cdiv class=\u0022box col-md-6\u0022\u003E\n            \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EPr\u00e9requis\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003EBachelor level in Mathematics\u003C\/p\u003E\n\u003Cp\u003ENotions of algorithmics\u003C\/p\u003E\n\u003Cp\u003ENotion of Python\u003C\/p\u003E\n\u003Cp\u003ENotions in Linux\u003C\/p\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EProgramme \/ plan \/ contenus\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003EIntroduction to Python\u003C\/p\u003E\n\u003Cp\u003EThe language and existing numerical libraries.\u003C\/p\u003E\n\u003Cp\u003EPart 1 : Simple functions\u003C\/p\u003E\n\u003Cp\u003EElements of floating point numbers : IEEE 754 format, relative uncertainty, single \/ double precision. Catastrophic cancelation, examples with solving the quadratic equation and computing geometric quantities\u003C\/p\u003E\n\u003Cp\u003EEvaluating elementary and special functions : interval reduction, Taylor\u2019s expansion\u003C\/p\u003E\n\u003Cp\u003EEstimating statistical quantities : variance in particular, critical to uncertainties estimations\u003C\/p\u003E\n\u003Cp\u003EPart 2 : Linear algebra\u003C\/p\u003E\n\u003Cp\u003ELinear systems, Cramer\u0027s rule and why one should avoid it,\u003C\/p\u003E\n\u003Cp\u003EGaussian elimination (simple and full pivot), LU factorization, elements of error propagation ; why one should rely on factorization to evaluate determinants and geometric quantities\u003C\/p\u003E\n\u003Cp\u003EEigenvalues and Eigenvectors\u003C\/p\u003E\n\u003Cp\u003EPart 3 : Numerical calculus\u003C\/p\u003E\n\u003Cp\u003E1D integration a.k.a. quadrature : rectangle rule, trapezoidal rule, Simpson rule\u003C\/p\u003E\n\u003Cp\u003EMultidimensional integration : the simple MonteCarlo algorithm\u003C\/p\u003E\n\u003Cp\u003EOrdinary Differential Equations solving : Euler method, Runge-Kutta method\u003C\/p\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EObjectifs d\u0026#039;apprentissage\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003EMathematical method used to rely on tedious hand computation for centuries. The commoditization of computers, of high-level programming languages, of numerical libraries helps greatly in executing these computations fundamental to science and engineering work, but shift the burden to understanding rather than number crunching: after the phenomenon has been translated to equations, how to solve these with a computing system and track the uncertainties that are as present as in experimental work.\u003C\/p\u003E\n\u003Cp\u003EWe will describe families of such algorithms, the numerical issues they poses, how the corresponding libraries tackle with these. We will be using Python for this.\u003C\/p\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EOrganisation g\u00e9n\u00e9rale et modalit\u00e9s p\u00e9dagogiques\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003ELectures will be held at IJCLab\u003C\/p\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n                        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EBibliographie\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cul\u003E\n\u003Cli\u003EMathematical Methods in the Physical Sciences Mary L. Boas\u003C\/li\u003E\n\u003Cli\u003EThe Python Tutorial (\u003Ca rel=\u0022nofollow noopener noreferrer\u0022 target=\u0022_blank\u0022 href=\u0022https:\/\/docs.python.org\/3\/tutorial\/index.html\u0022\u003Ehttps:\/\/docs.python.org\/3\/tutorial\/index.html\u003C\/a\u003E)\u003C\/li\u003E\n\u003Cli\u003ENumpy (https:\/\/numpy.org)\u003C\/li\u003E\n\u003Cli\u003ESimplified Numerical Analysis (Fourth Edition) by Dr. Amjad Ali.\u003C\/li\u003E\n\u003Cli\u003ENumerical Recipes in Python (\u003Ca rel=\u0022nofollow noopener noreferrer\u0022 target=\u0022_blank\u0022 href=\u0022https:\/\/zenodo.org\/records\/8371794\u0022\u003Ehttps:\/\/zenodo.org\/records\/8371794\u003C\/a\u003E)\u003C\/li\u003E\n\u003C\/ul\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ENature de l\u0026#039;\u00e9valuation\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003EEvaluation Continue non Int\u00e9grale\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n      \u003C\/div\u003E\n  \u003C\/div\u003E\n\u003C\/div\u003E\n","settings":null}]