Métodos Numéricos. Evidencia 2. Parte 1
Enviado por karlaquintanar14 • 4 de Marzo de 2016 • Tareas • 599 Palabras (3 Páginas) • 381 Visitas
Evidencia 2. Parte 1
Realicen un mapa conceptual con los siguientes conceptos del módulo 2:
- Ecuación lineal y no lineal
- Sistema de ecuaciones lineales y no lineales
- Ajuste de curvas a funciones lineales y no lineales
- Matlab, C# (C Sharp), Excel
- Métodos numéricos
[pic 1]
. Realicen un mapa conceptual en el que señalen de manera esquemática los procedimientos de los métodos numéricos vistos del módulo 3:
- Interpolación.
- Integración numérica.
- Ecuaciones diferenciales ordinarias.
[pic 2]
[pic 3][pic 4]
b. Resuelvan por eliminación gaussiana los siguientes sistemas de ecuaciones:
[pic 5]
Solution:
3x1 + 12x2 + 3x3 = 10x1 + 10x2 + 14x3 = 15x1 + x2 = 3
Rewrite the system in matrix form and solve it by Gaussian Elimination (Gauss-Jordan elimination)
3123101101415103
R1 / 3 → R{i} (divide the {i} row by {n})
1411031101415103
R2 - 1 R1 → R{n} (multiply {k} row by {m} and subtract it from {n} row); R3 - 5 R1 → R{n} (multiply {k} row by {m} and subtract it from {n} row)
1411030613-730-19-5-413
R2 / 6 → R{i} (divide the {i} row by {n})
14110301136-7180-19-5-413
R1 - 4 R2 → R{n} (multiply {k} row by {m} and subtract it from {n} row); 19 R2 + R3 → R{n} (multiply {k} row by {m} and add it to {n} row)
10-23344901136-718002176-37918
R3 / 2176 → R{i} (divide the {i} row by {n})
10-23344901136-718001-379651
233 R3 + R1 → R{n} (multiply {k} row by {m} and add it to {n} row); R2 - 136 R3 → R{n} (multiply {k} row by {m} and subtract it from {n} row)
100277651010568651001-379651
x1 = 277651x2 = 568651x3 = -379651
Make a check:
3·277651 + 12·568651 + 3·-379651 = 277217 + 2272217 - 379217 = 10
277651 + 10·568651 + 14·-379651 = 277651 + 5680651 - 75893 = 1
5·277651 + 568651 = 1385651 + 568651 = 3
Check completed successfully.
Answer:
x1 = 277651x2 = 568651x3 = -379651
[pic 6]
Solution:
4x1 + x2 = 0.55x1 + x2 = 0.1
Rewrite the system in matrix form and solve it by Gaussian Elimination (Gauss-Jordan elimination)
410.5510.1
R1 / 4 → R{i} (divide the {i} row by {n})
...