Floating point representation of numbers and round off errors. Conditioning of the problems and stability of the algorithms. Basic numerical methods for solving nonlinear equations and linear algebraic systems, polynomial interpolation, (composite) quadrature formulas. Basic notions of Matlab.
Course Content - Last names L-Z
Errors and finite representation of numbers, numerical solution of nonlinear equations, numerical methods for linear systems, function approximation by interpolation, quadrature formulae, introduction to programming.
L. Brugnano, C. Magherini, A. Sestini, Calcolo Numerico, Masterbooks, 2019
Learning Objectives - Last names A-K
Being able to write Matlab programming codes and use predefined functions. Knowledge of existing numerical methods for the problems discussed during the lectures and ability to choose the best one for solving a given problem. Being able to compare different methods based on theoretical properties and practice.
Learning Objectives - Last names L-Z
Basic Matlab programming, including the use predefined functions. Knowledge of existing numerical methods for the solution of the most common mathematical problems. Ability to compare methods on the basis of their theoretical properties and practical experience, in order to select the best one to solve a problem.
Prerequisites - Last names A-K
Mathemathics I (mandatory)
Prerequisites - Last names L-Z
Basic knowledge of linear algebra and calculus (Mathematics I mandatory).
Teaching Methods - Last names A-K
Total number of lectures hours: 32
Total number of practice hours: 24
Teaching Methods - Last names L-Z
Lectures devoted to the theoretical analysis of the methods (32 hours), lectures devoted to the programming and implementation of numerical methods in Matlab (24 hours).
Further information - Last names L-Z
Frequency of lectures, practice and lab: Strongly recommended
The exam is an oral test which consists in questions related to the topics addressed by the course lectures and exercises.
Type of Assessment - Last names L-Z
Matlab exercises to be sent before the exam. Final oral exam: Theoretical questions concerning the topics of the course.
Course program - Last names A-K
Introduction to algorithms and their main building components. Floating point representation of numbers and round off errors. Conditioning of the problem and stability of the algorithms. Basic
numerical methods for solving: nonlinear equations (bisection, Newton, quasi-Newton);
linear algebraic systems (Gauss method with and without pivot), conditioning of a linear system, error analysis, iterative methods (Jacobi and Gauss-Seidel); polynomial interpolation (Lagrange polynomial), interpolation error, conditioning of interpolation problem. Integration rules:
Trapezi and Simpson methods, composite quadrature formulas (Trapezoidal formula, Simpson formula, composite formulas). Basic notions of Matlab.
Course program - Last names L-Z
Introduction to numerical analysis. Finite number representation. Iterative methods for the solution of nonlinear equations. Solution of linear systems: gaussian elimination, LU factorization, iterative methods (Jacobi and Gauss-Seidel). Polynomial interpolation, spaces of spline functions. Numerical quadrature with Newton-Cotes formulae.
Introduction to programming and implementation of numerical methods (in Matlab).