From 84397c580fec604cf91d6b5022f00bd1d8f20fc7 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?F=C3=A9lix=20MARQUET?= Date: Mon, 2 Dec 2024 09:47:10 +0100 Subject: [PATCH] Obisidian vault auto-backup: 02-12-2024 09:47:10 on constellation. 3 files edited --- .../obsidian-table-generator/data.json | 2 +- ISEN/Maths/CIPA3/Fiche de révision DS1.md | 16 ++++++++++++---- ISEN/Maths/CIPA3/Fiche de révision DS1.pdf | Bin 132591 -> 147447 bytes 3 files changed, 13 insertions(+), 5 deletions(-) diff --git a/.obsidian/plugins/obsidian-table-generator/data.json b/.obsidian/plugins/obsidian-table-generator/data.json index 5d97ab6..07ae79b 100644 --- a/.obsidian/plugins/obsidian-table-generator/data.json +++ b/.obsidian/plugins/obsidian-table-generator/data.json @@ -1,7 +1,7 @@ { "rowCount": 8, "columnCount": 8, - "defaultAlignment": "center", + "defaultAlignment": "left", "defaultCardWidth": 160, "defaultCardHeight": 160 } \ No newline at end of file diff --git a/ISEN/Maths/CIPA3/Fiche de révision DS1.md b/ISEN/Maths/CIPA3/Fiche de révision DS1.md index 71021c2..3f47cdb 100644 --- a/ISEN/Maths/CIPA3/Fiche de révision DS1.md +++ b/ISEN/Maths/CIPA3/Fiche de révision DS1.md @@ -18,6 +18,12 @@ title: Fiche de révision DS1 de maths | $\cos(ax)$ | $-a\sin(x)$ | $\frac{1}{a}\sin(x)$ | | $\tan(x)$ | $1 + \tan^2(x) = \frac{1}{\cos^2(x)}$ | | +# 2. Identités trigonométrique: + +| $\cos(a+b) = \cos(a)\cos(b) - \sin | +| :------------: | | + + # 2. **Espaces de Hilbert** Un **espace de Hilbert** est un espace vectoriel normé complet muni d'un produit scalaire. @@ -56,11 +62,11 @@ f(x) = a_0 + \sum_{n=1}^\infty \left[a_n \cos(nx) + b_n \sin(nx)\right]. $$ ## Coefficients de Fourier -- $a_0$ : +- $a_0$ : (tous le temps) $$a_0 = \frac{1}{2\pi} \int_{-\pi}^\pi f(x) \, dx$$ -- $a_n$ : +- $a_n$ : (si paire) $$a_n = \frac{1}{\pi} \int_{-\pi}^\pi f(x) \cos(nx) \, dx$$ -- $b_n$ : +- $b_n$ : (si impaire) $$b_n = \frac{1}{\pi} \int_{-\pi}^\pi f(x) \sin(nx) \, dx$$ ## Propriétés - **Convergence** : La série converge en moyenne quadratique dans $L^2([-\pi, \pi])$. (Pas vu en cours mais je le note la quand même au cas ou) @@ -106,6 +112,8 @@ $$\frac{\partial f}{\partial y} = \lim_{\Delta y \to 0} \frac{f(x, y+\Delta y) - $$\nabla \times f = \frac{\partial f_y}{\partial x} - \frac{\partial f_x}{\partial y}$$ ## Théorème de Schwarz $$\frac{\partial^2 f}{\partial x \partial y} = \frac{\partial^2 f}{\partial y \partial x}, \quad \text{si } f_{xy} \text{ et } f_{yx} \text{ sont continues.}$$ +
+ # Matrice hessienne ## Définition La matrice hessienne d'une fonction $f: R^n \to R$ est une matrice carrée composée des dérivées partielles secondes de $f$. Si $f(x_{1}, x_{2}, x_{3},\dots, x_{n})$ est deux fois continûment différentiable, alors : @@ -133,7 +141,7 @@ H_f(x, y) = \end{bmatrix} $$ ## Analyse -La matrice hessienne $H_{f}(x, y)$ +La matrice hessienne $H_{f}(x, y)$ est définie positive (ses valeurs propres sont toutes positives). 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