Concepts of the transcendental functions and their applications. Solutions localization and isolation. Topological degree theory. Methods for computing the topological degree. Methods of Stenger and Kearfott. Existence theorems of Kronecker and Picard. Computing the exact number of solutions. Computing all solutions. Existence of fixed points. Banach’s theorem. Theorems of Brouwer and Poincaré-Miranda. Computation of fixed points. Knaster-Kuratowski-Mazurkiewicz covering Lemma. Lemma of Scarf-Hansen. Sperner’s Lemma. Triangulations. Scarf’s method. Computing solutions of nonlinear systems of algebraic and transcendental equations. Methods of Newton, type Newton, generalized secant, Broyden. Nonlinear methods of Successive Overrelaxation (SOR), Gauss-Seidel and Jacobi. Generalized bisection method. Numerical optimization methods of transcendental functions.

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