Numerical Analisys

Theoretical-Practical lessons are taught using both the expository and inquisitive methods during the explanation of the theoretical subjects and the settlement of exercises in groups and individually. Students should perform a practical work of scientific-technical interpretation and collaborative research.

Provide the student with tools enabling him to gather one or more approximate solutions of problems whose resolution cannot be obtain using exact analytical form.
Generic skills: application of knowledge and understanding; Realization of judgment and decision making; Communication; Self-learning Mode;
Specific Skills: ability to use mathematical techniques; develop the capacity of concept’s perception, abstract reasoning, interpretation of results and their application to problem solving; understanding the details of the algorithms studied for the resolution of specific problems in the field of Civil Engineering.

1. Brief introduction to the theory of errors.
2. Roots of Nonlinear Equations: Introduction and motivation. Location of roots. Bisection and Newton methods. Stopping criteria. Computational aspects.
3. Polynomial interpolation: Introduction and motivation. Interpolador polynomial Lagrangian. The polynomial Newton interpolador (divided differences and finite). Polynomial interpolation inverse. Study of interpolation
error.
4. Numerical integration: Introduction and motivation. Newton’s rules: rules of trapezes and Cotes of Simpson (simple and compound). Study of the integration error. Computational aspects.
5. Numerical integration of Initial value problems of first order: Introduction and motivation. Euler’s method and Runge-Kutta methods of second and fourth order. Study of error. Computational aspects.
6. Methods of solving linear systems: iterative Methods of Jacobi and Gauss-Seidel.

NAO