1. Basic concepts, discretisation, error theory.
2. Algebraic equations: Bisection, regula falsi, fixed-point iteration, Newton’s method.
3. Linear systems: Gauss, LU, Jacobi, Gauss-SeidelandSOR methods.
4. Numerical calculation of eigenvalues and eigenvectors.
5. Interpolation, approximation, data fitting: Lagrange’s and Newton’s polynomials, splines, linear regression, least squares.
6. Numerical differentiation: Forward, backward and central differences.
7. Numerical Integration: Rectangle, trapezoidal and Simpson’s rules.
8. Numerical solution of ordinary differential equations: (1) Initial value problems: Euler’s, Runge-Kutta, multistep and predictor-corrector methods. (2)Boundary value problems:Shootingand finite differences methods.