1. Mathematical Preliminaries
   • Basic Concepts and Taylor's Theorem.
2. Computer arithmetic
   • Floating point numbers and roundoff errors.
   • Absolute and relative errors: Loss of significance.
   • Conditioning: Stable and unstable computations.
3. Numerical methods for nonlinear equations:
   • Bisection, Newton's and Secant methods.
   • Fixed points and functional iterations.
4. Solving systems of linear equations
   • Matrices algebra.
   • LU and Cholesky Factorization.
   • Gaussian elimination with scaled partial pivoting.
   • Norms, and the analysis of errors.
5. Approximation of functions
   • Polynomial interpolation.
   • Divided Differences.
   • Errors in polynomial interpolation.
   • Splines.
6. Numerical differentiation and integration
   • Numerical differentiation
   • Trapezoid rule. Romberg Algorithm.
   • Simpson's rule.
   • Gaussian quadrature formulae.