• Italiano
  • English

Department of Mathematics and Applications
"Renato Caccioppoli"


Programming and Computing Laboratory

Home > Exams > Programming and Computing Laboratory

Programming and Computing Laboratory

Credits

9

Prerequisites

Programming Laboratory, Mathematical Analysis 1, Geometry 1.

Scientific-disciplinary sector (SSD)

MAT/08 Numerical Analysis.

Examination method

Laboratory test (on the theoretical aspects of numerical methods and on their design, implementation, testing and evaluation), oral exam on the topics and proofs presented in the course.

Learning
objectives

The course aims to provide students with the basic knowledge and methodological tools needed to analyse the main numerical methods for solving scientific computing problems, with particular attention to the issues arising from the use of a finite-precision arithmetic system.
The laboratory activity aims to develop skills in the use of high-level programming languages to implement the main methods studied, and of an interactive environment for solving scientific computing problems.

Syllabus

Sources of error in computational models; conditioning of a mathematical problem; stability of numerical methods. Direct and iterative methods for solving linear systems. Polynomial interpolation and spline interpolation. Least-squares data approximation. Iterative methods for solving non-linear equations. Numerical integration: simple and composite formulae; automatic integrators. Introduction to numerical methods for solving ordinary differential equations. Scientific computing libraries: development and documentation of mathematical software.

Expected learning
outcomes

At the end of the course, students must demonstrate that they:

  • know and understand the ideas underlying numerical methods, and can analyse and compare the different methods, also in relation to the applied problem to be solved;
  • are able to apply the knowledge acquired by independently designing and implementing algorithms, taking into account the influence of the finite-precision computing environment on the results;
  • are able to communicate ideas and solutions clearly, rigorously and effectively to both specialist and non-specialist audiences;
  • are able to identify the most appropriate methods to analyse and solve a problem related to the course topics and to interpret the results correctly.

Learning outcomes
to be assessed

Assessment of independence in developing algorithms and programs of varying difficulty. Clarity, correctness and completeness in the presentation of the topics of the course.