التحليل العددي (1) Math-352

Numerical Methods for Solving Nonlinear Equations: Bisection method, fixed point method, Newton’s method, secant method, multiple roots, modified Newton’s method, rate of convergence (error analysis), Newton's method for solving nonlinear systems. Solving Systems of Linear Equations:

Direct methods: Gaussian elimination, Gaussian elimination with partial pivoting, LU-decomposition.

Iterative methods: Jacobi method, Gauss-Seidel method.

Error analysis for solving Linear system.

Interpolation and Polynomial Approximations

Lagrange interpolation formula, divided differences, Newton's interpolation formula, error in polynomial interpolation, interpolation using linear splines. Numerical Differentiation and Integration

First derivative: two-point formulas (forward and backward) and three-point formulas (forward, central and backward).

Second derivative: the central method.

Trapezoidal, Simpson's rules, and the error bounds.