Basic concepts: Basic concepts of numerical analysis, concepts for the behavior of numerical methods for computing approximate solutions.
Roots of nonlinear functions of many variables: Methods for computing zeros of systems of nonlinear equations. Behavior, convergence and complexity issues. The problem of finding all the roots of nonlinear functions of a single variable and nonlinear function of many variables.
Fixed points of nonlinear functions in several variables: Study of fixed points of functions of many variables. Numerical methods for locating fixed points. Behavior, convergence and complexity of numerical methods for computing fixed points.
Generalization of iterative methods for solving linear systems: Iterative methods for the numerical solution of systems of linear and /or nonlinear equations. Solving systems of a large number of nonlinear equations. Behavior, convergence and complexity issues.
Numerical optimization of objective functions in several variables: Importance and usefulness of optimization. Applications. Effective and efficient numerical methods for optimizing objective functions of many variables. Behavior, convergence and complexity issues. Globally convergent methods. The global optimization problem.

Laboratory exercises using the mathematical computing environment Matlab (and/or the General Public License-GNU Octave) to implement the course's methods and algorithms.