- Introduction to Numerical Analysis.
- Introduction and basic elements of MATLAB and Octave.
- Representation of real numbers in finite precision and the floating-point model of arithmetic.
- Forward and backward stability of algorithms. Condition number of a numerical problem.
- Numerical linear algebra: Direct methods (LU, Cholesky and variants).
- Iterative methods for solving linear systems (Jacobi, Gauss-Seidel, Richardson).
- Brief introduction to projection methods for matrices with symmetric positive definite matrices (steepest descent and conjugate gradients).
- Numerical approximation of eigenvalue problems: Power method, inverse power method, shifted inverse power method. Brief description of the QR algorithm.
- Polynomial interpolation and representations (Lagrange, Newton, barycentric, Hermite), piecewise interpolating polynomials, splines. Brief introduction to Chebfun.
- Function and data-driven approximation. Least squares approximation and solving linear least squares problems. QR factorization by means of Householder reflectors.
- Methods for solving nonlinear equations (bisection, Newton, secant, regular falsi).
- Numerical integration with simple methods (rectangle, trapezoidal, Simpson).
- Finite difference methods for approximating derivatives and brief introduction to the numerical solution of differential equations.
- The role of Numerical Analysis in Computer Science and Engineering.