COMPUTATIONAL MATHEMATICS
- Overview
- Assessment methods
- Learning objectives
- Contents
- Full programme
- Bibliography
- Teaching methods
- Contacts/Info
Programming, Linear Algebra, Calculus.
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 the approximation of zeros of functions and a second part on linear systems.
The oral exam can be optional based on the outcome of the written exam.
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.
The representation of numbers on the calculator and floating point arithmetic.
Introduction to the Matlab environment.
Numerical methods for the approximation of zeros of real functions in one variable.
Resolution of linear systems by direct and iterative solvers.
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. (About 10 hours)
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. (About 23 hours)
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. (About 23 hours)
Recommended text: "Scientific Computing with Matlab and Octave", by A. Quarteroni and F. Saleri, Springer.
Teaching material (codes implemented in lectures, exercises, exam texts, etc.) on the e-learning site.
Lectures and in the computer lab.
The lectures are integrated together with the laboratory ones, on average the first are 32 hours and the second 24 hours.
The lectures are on the blackboard, but the slides and recordings of the lessons from previous years are available on the elearning 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 own Laptop, as the Matlab campus license is free for all Insubria students.
Meeting for course discussion by appointment.