Numerical calculation in one variable

Description

Subject objectives: - Introduction to the knowledge and handling of basic concepts and techniques of Numerical Calculus. - To know and apply the basic algorithms of Numerical Calculus for functions of one variable for computing the polynomial interpolant of a function, approximating the derivatives of a function at a point, approximating the value of a definite integral and studying the existence and approximation of the roots of a nonlinear equation. - To practice computer programming by implementing the algorithms studied in MATLAB. Contents: T1. Introduction to Numerical Analysis. Floating point systems. Errors in numerical calculus. Order of a numerical method. (Theory: approximately 3 hours) T2. Approximation of roots of a numerical equation: dichotomy algorithms, functional iteration and Newton-Raphson. (Theory: approximately 12 hours) T3. Lagrange polynomial interpolation. Introduction to other types of interpolation. (Theory: approximately 7 hours) T4. Introduction to numerical derivation. Introduction to numerical integration: simple and compound trapezoid and Simpson rules. (Theory: approximately 6 hours)