Module page

Laboratory of programming and calculus

academic year:	2013/2014
instructor:	Biancamaria Della Vecchia
degree course:	Mathematics - DM 270/04 (triennale), I year
type of training activity:	affine e integrativa
credits:	9 (72 class hours)
scientific sector:	MAT/08 Analisi numerica
teaching language:	italiano
program:	A-H
period:	I sem (30/09/2013 - 17/01/2014)

Lecture meeting time and location

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.

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. Basics on the use of pointers. 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.

Detailed module subject: Weekly list of course lessons

Suggested reading: Materials provided by the teacher on the Web Luis J. Aguilar, "Fondamenti di programmazione in C++", McGraw-Hill, 2008 or equivalent. A. Quarteroni, R. Sacco, F. Saleri, "Matematica numerica", Springer, 2008 As an alternative: A.Quarteroni , "Elementi di Calcolo Numerico", Progetto Leonardo ,1998 J.F. Epperson, "Introduzione all'analisi numerica", McGraw-Hill, 2003

Issues:

Type of course: standard

Exercises:

Examination test: Text of the mid-term exam November 2013

Useful links:

Numerical Recipes in C, Second Edition (1992) Link
Allen B. Downey: How to think like a computer scientist (2012) Link
M. Banahan, D. Brady, M. Doran: The C Book Link
M. Henricson, E. Nyquist and E. Utvecklings: Industrial Strength C++ (1997) Link
B. Eckel: Thinking in C++, 2nd edition, Volume 1 (2001) Link
B. Eckel: Thinking in C++, 2nd edition, Volume 2 (2003) Link
Registration to the course and middle-term exam Link

Knowledge and understanding: Successful students will be able to 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.

Examination dates on Infostud

Statistical data on examinations