AndradeGonzalez-wp2017/07/classes-07.txt

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2017-11-16 13:35:13 +01:00
English:
#+TITLE: Sagemath symbolic calculations
* Topic
+ how to use programme
+ solving equations (numerical)
+ derivatives and integration
+ differential equations
+ matrices (product, determinant, inverse matrix)
* Tasks
+ solve equations
++ x^6-9 x^5+10 x^4+18 x^3+49 x^2+135 x+84 = 0
++ x^3-5 x^2+8 x-40 = 0
++ \cos(x)=x in the interval [0,\pi]
+ Find
++ \int x\sin x dx
++ \int_{-2}^{4} e^{1/x^2}dx
++ (\sqrt{x^2\sin x+2})'
++ ((x e^{\cos x})^{3})'
++ partial derivative of f(x,y)=x^2+\sin (xy)-y for y
+ Solve equation \frac{d^2 u}{dx^2}-x\frac{du}{dx}+u=0
+ Find product of matrices A and B
A= 1 -4 7
14 6 8
-4 -1 2
B= 2 3 9
-1 17 6
0 5 -7
Find determinant of A and inverse of B
Spanish:
# + TÍTULO: Sagemath - cálculos simbólicos
* Tema
+ cómo usar el programa
+ resolver ecuaciones (numéricas)
+ derivados e integración
+ ecuaciones diferenciales
+ matrices (producto, determinante, matriz inversa)
* Tareas
+ resolver ecuaciones
++ x ^ 6-9 x ^ 5 + 10 x ^ 4 + 18 x ^ 3 + 49 x ^ 2 + 135 x + 84 = 0
++ x ^ 3-5 x ^ 2 + 8 x-40 = 0
++ \ cos (x) = x en el intervalo [0, \ pi]
+ Encontrar
++ \ int x \ sin x dx
++ \ int _ {- 2} ^ {4} e ^ {1 / x ^ 2} dx
++ (\ sqrt {x ^ 2 \ sin x + 2}) '
++ ((x e ^ {\ cos x}) ^ {3}) '
++ parcial derivada de f (x, y) = x ^ 2 + \ sin (xy) -y para y
+ Resolver ecuación \ frac {d ^ 2 u} {dx ^ 2} -x \ frac {du} {dx} + u = 0
+ Buscar producto de matrices A y B
A = 1 -4 7
14 6 8
-4 -1 2
B= 2 3 9
-1 17 6
0 5 -7
Encontrar determinante de A e inverso de B