ewce09.azraftaohid.me/L2T1/EWCE 205/SA/Syllabus coverage.md

Created: 2024/10/28 01:58

Linear system of algebraic equations

• Background

Direct elimination method

• Matrix inversion method
• Cramer's rule
• Gauss Elimination method
• Gauss Jordan method

Iteration method

• Jacobi method
• Gauss-Seidel method

Finite differences method

• Background
• Taylor series expansion
• Approximation of first derivative
• Approximation of second derivative

Numerical differentiation

• Background
• Differentiating tabulated function (forward difference)
• Differentiating tabulated function (backward difference)
• Differentiating tabulated function (divided difference)
• Difference formulae

Numerical integration

• Background
• Trapezoidal rule
• Simpson's 1/3 rule
• Simpson's 3/8 rule
• Richardson's extrapolation based on trapezoidal rule
• Romberg rule

Euler formula

• Background
• Method based math

Taylors series

• Method based math

Runge-Kutta method

• Background
• Method based math