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. Solution of linear systems of equations. 3. Numerical solution of equations and systems of nonlinear equations. 4. Interpolation and approximation of functions. 5. Least squares problems. 6. Numerical optimization. 7. Numerical integration. 8. Numerical differentiation. 9. Fast Fourier Transform.

This is a "hands on" course. In the large-group lectures the theoretical contents will be introduced, and they will be delivered in a blackboard standard room. However, the small-group lectures will take place in the computer Lab, and students are supposed to follow the explanations of the instructor performing in real time the exercises, examples and other proposed activities. Students must become acquainted with MATLAB. The course will start learning how to program MATLAB. After and introduction to the course, every two weeks (as a general rule), one of the topics of the course will be discussed in the classroom and practices related to these topics will be proposed to the students. Usually the practices involve to solve a simple problem by writing the appropriate code.