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