
Course unit
NUMERICAL ANALYSIS
SC06101050, A.A. 2017/18
Information concerning the students who enrolled in A.Y. 2016/17
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Core courses 
MAT/08 
Numerical Analysis 
6.0 
Course unit organization
Period 
First semester 
Year 
2nd Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Laboratory 
1.0 
16 
9.0 
No turn 
Lecture 
5.0 
40 
85.0 
No turn 
Start of activities 
02/10/2017 
End of activities 
19/01/2018 
Examination board
Board 
From 
To 
Members of the board 
7 Calcolo Numerico  2017/2018 
01/10/2017 
30/09/2018 
MARTINEZ CALOMARDO
ANGELES
(Presidente)
VIANELLO
MARCO
(Membro Effettivo)
DE MARCHI
STEFANO
(Supplente)
MARCUZZI
FABIO
(Supplente)
PUTTI
MARIO
(Supplente)
SOMMARIVA
ALVISE
(Supplente)

Prerequisites:

Calculus, Basic Linear Algebra. 
Target skills and knowledge:

In this course students learn the essential numerical techniques which are commonly used in scientific applications, when these have to face with mathematical problems that can not be solved analytically. Students are introduced to the basic computational concepts of stability, accuracy and efficiency.
It is also a goal of this course to introduce the students to the fundamental concepts of scientific programming using MATLAB. 
Examination methods:

Written exam and programming test. Oral exams could be possible in some cases. 
Assessment criteria:

Oral exam due for students with overall grade after the written and lab tests in the range 18/3023/30. 
Course unit contents:

Number representation and arithmetic operations on digital computing. Error propagation in arithmetic operations
Introduction to computational complexity
Numerical solution of nonlinear equations
Interpolation and data fitting
Numerical derivation and integration
Numerical linear algebra 
Planned learning activities and teaching methods:

Fundamental principles of digital computing and the implications for algorithm accuracy and stability: Number representation. IEEE standard. Error propagation, cancellation, stability and illconditioning.
Introduction to computational complexity.
Several lectures are devoted to solving nonlinear equations: the bisection method, error estimation. The Newton method, global and local convergence, how to terminate Newton's iterations. Other linearization methods. Fixed point iterations. Stopping criteria for fixed point iterations.
The concept of interpolation and its role as foundation for numerical integration is introduced, emphasizing classical Lagrange polynomial interpolation. Error and convergence analysis. Piecewise polynomial interpolation: Spline. Least squares approximation.
Numerical differentiation and integration: Finite difference approximations to derivatives. Local error, error cancellation, and global error. Extrapolation. Trapezoidal rule, Simpson's rule. Error bounds.
The solution of systems of linear equations, (comprising 90% of numerical effort in science and engineering) is covered extensively, including direct (Gaussian elimination) and iterative techniques: vector and matrix norms, condition number of a system of linear equations, condition number of a matrix.
The LU factorization and it's use for solving systems of linear equations. Computing the factors by Gaussian elimination.
Stability. Pivoting. QR factorization and the accurate solution of overdetermined systems arising from least squares problems.
Classical iterative methods: Jacobi, GaussSeidel and Successive Overrelaxation.
An important component of numerical analysis is computational implementation of algorithms which are developed in the course in order to observe first hand the issues of convergence, accuracy, computational work effort, and stability. Exercises will consist entirely in computational experiments in MATLAB. 
Additional notes about suggested reading:

One of the suggested textbooks and online material provided by the instructors.
Useful links:
www.math.unipd.it/~acalomar (alla voce Didattica)
www.math.unipd.it/~marcov/studenti.html) 
Textbooks (and optional supplementary readings) 

Quarteroni, Alfio; Saleri, Fausto, Calcolo scientifico: esercizi e problemi risolti con MATLAB e Octave.. Milano: Springer, 2012.

Quarteroni, Alfio; Saleri, Fausto, Scientific computing with MATLAB and OctaveAlfio Quarteroni, Fausto Saleri, Paola Gervasio. Berlin: Springer, 2014. For erasmus students.

Rodriguez, Giuseppe, Algoritmi numerici. Bologna: Pitagora, .


