The purpose of the teaching within the CdS is to provide the student with basic skills for the definition, analysis and implementation of numerical methods on the computer, developing the ability to evaluate their stability and computational complexity. At the end of the course, the student is able to: 1. Understand the representation of numbers on the calculator 2. Apply mathematical reasoning in the definition of numerical algorithms. 3. Solve some problems of scientific calculation on the computer with stable algorithms and low computational cost.
Course Prerequisites
No prior knowledge required
Teaching Methods
Lectures and in the computer lab. The lectures are integrated with the laboratory ones. The lectures are on the blackboard, but the slides and recordings of the lessons from previous years are available on the e-learning site. The laboratory is held by the teacher himself, while additional exercises held by an exerciser may be proposed. In the computer lab, each student has a fixed station available or can bring their Laptop, as the Matlab campus license is free for all Insubria students.
Assessment Methods
Written and oral exam. The 3-hour written exam includes a part of the definition and analysis of the numerical methods proposed on the sheet and then a subsequent implementation in Matlab to verify the analysis made. The exam includes a first part on approximating zeros of functions and a second part on linear systems. The oral exam can be optional based on the outcome of the written exam. Two intermediate tests can replace the written exam if both are passed.
Contents
The representation of numbers on the calculator and floating point arithmetic. Introduction to the Matlab environment, scripts and functions. Recursion and graphic design. Representation of numbers and error analysis. Evaluation of a polynomial at a point. Numerical methods for the approximation of zeros of real functions in one variable: bisection method, functional iteration methods with convergence and convergence order, stopping criteria, Newton's method and its variants. Resolution of linear systems: conditioning, triangular linear systems, Gauss elimination with pivoting and LU factorization, definition and convergence of stationary iterative methods, Jacobi and Gauss-Seidel iterative methods.
