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