Lineal Algebra, Programming, Calculus I, Calculus II

Using NUMERICAL METHODS (NM) to calculate approximate solutions of mathematical models Study the stability and accuracy of NM. Calculate numerical solution of systems of nonlinear equations. Approximate the minimum of a function of several variables. Developing, analyzing, and implementing finite difference methods. Solving ordinary differential equations and systems by numerical integration methods. Using the software environments to discuss the efficiency, pros and cons of different NM.

1. Fundamentals (floating point, errors, stability, algorithms...). 2. Numerical linear algebra: systems of linear equations, matrix factorization, diagonalization, least squares. 3. Numerical solution of equations and systems of nonlinear equations. 4. Numerical optimization. 5. Interpolation and approximation of functions. 6. Numerical differentiation and integration. 7. Fast Fourier Transform.

One of the purposes of this course is to provide the mathematical foundations of numerical methods, to analyze their basic theoretical properties (stability, accuracy, computational complexity), and demonstrate their performances on examples and counterexamples which outline their pros and cons. The primary aim is to develop algorithmic thinking-emphasizing on long-living computational concepts. Every chapter is supplied with examples, exercises and applications of the discussed theory. The course relies throughout on well tested numerical procedures for which we include codes and test files. Students should write their own codes by studying and eventually rewriting the codes given by the Teacher in Aula Global. The personal codes should be run, tested and given up in ¿Aula Global¿ in the Computer Room classes. Throughout the course we emphasize graphic 2D and 3D representations of solutions. Through this visual approach, students will have a chance to experience the meaning, i.e. to understand what a solution means and how it behaves.