Module page
Laboratorio di Programmazione e Calcolo
| academic year: | 2016/2017 |
| instructor: | Silvia Noschese |
| degree course: | Mathematics - DM 270/04 (triennale), I year |
| type of training activity: | di base |
| credits: | 9 (84 class hours) |
| teaching language: | italiano |
| program: | M-Z |
| period: | I sem (03/10/2016 - 13/01/2017) |
Presence: highly recommended
Module aims: The main goal is to introduce the students to a constructive approach to mathematics also by means of personal computers. In this respect, the course complements other courses of the first year where the logic/deductive point of view is more emphasized. A major part of this course will be devoted to problem solving, to the analysis of basic algorithms and to their implementation in C++.
Detailed module subject: Introduction to C++ language: types of variables, type conversion, arrays, logical operators (or, and, not), read and write statements, conditional statements (if-else) and cycle statements (for, while, do-while). Mathematical functions. Structure of a C++ program. Functions. Passing variables. Representation of integer and real numbers in computers. Error propagation in arithmetic operations. Stable and unstable algorithms: computation of pi. Computation of a polynomial in a point (Horner algorithm). Matrices, vectors and systems of linear equations: Gauss and Jacobi methods. Graphic library Gnuplot: plot of a function. Numerical methods for finding roots of a nonlinear equation: bisection, Newton and secant methods. Taylor formula for computing some mathematical functions. Polynomial interpolation. Numerical methods for computing definite integrals.
Suggested reading:
- Materials provided by the teacher on the Web.
- A. Quarteroni, R. Sacco, F. Saleri, P. Gervasio "Matematica numerica", Springer, 2014 (or 2008 edition). As an alternative: either A.Quarteroni , "Elementi di Calcolo Numerico", Progetto Leonardo,1998 or J.F. Epperson, "Introduzione all'analisi numerica", McGraw-Hill, 2003;
- Luis J. Aguilar, "Fondamenti di programmazione in C++", McGraw-Hill, 2008 or equivalent.
Type of course: standard
Knowledge and understanding: Successful students will have a basic knowledge of programming and of the mathematical properties of simple algorithms. They will also achieve some fundamental notions about convergence, order of convergence, errors and complexity for elementary algorithms.
Skills and attributes: Successful students will be able to write a simple C++ code for scientific purposes and to manage elementary numerical algorithms to solve problems. They will be able to choose the appropriate algorithm for simple problems like finding the root of an equation, computing an integral or solving a linear system. During the laboratory sessions they will learn how to use PCs, graphic tools and a LAN network.
Personal study: the percentage of personal study required by this course is the 65% of the total.