
Course unit
NUMERICAL ANALYSIS (Numerosita' canale 3)
IN18101050, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Basic courses 
MAT/08 
Numerical Analysis 
9.0 
Course unit organization
Period 
Second semester 
Year 
1st Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Lecture 
9.0 
72 
153.0 
No turn 
Prerequisites:

Basic knowledge of mathematical analysis. 
Target skills and knowledge:

Learning the base of numerical computing in view of scientific and technological applications, with special attention to the concepts of error, discretization, approximation, convergence, stability, computational cost. 
Examination methods:

Written exam and Matlab laboratory exam. 
Assessment criteria:

The mark is the weighted average of the written and laboratory test. 
Course unit contents:

Floatingpoint system and error propagation:
truncation and rounding error, floatingpoint representation of real numbers, machine precision, arithmetical operations with approximate numbers, conditioning of functions, error propagation within iterative algorithms by examples, the concept of stability
Numerical solution of nonlinear equations:
bisection method, error estimate by weighted residuals; Newton method, global convergence, order of convergence, local convergence, error estimate, other linearization methods; fixedpoint iterations
Interpolation and approximation of functions and data:
polynomial interpolation, Lagrange interpolation, interpolation error, the convergence problem (Runge's counterexample), Chebyshev interpolation, stability of interpolation; piecewise polynomial interpolation, spline interpolation; leastsquares polynomial approximation
Numerical integration and differentiation:
algebraic and composite quadrature formulas, convergence and stability, examples; instability of differentiation, derivatives computation by difference formulas; the concept of extrapolation
Elements of numerical linear algebra:
vector and matrix norms, matrix and system conditioning; direct methods: Gaussian elimination and LU factorization, computation of inverse matrices, QR factorization, leastsquares solution of overdetermined systems; iterative methods: Jacobi and GaussSeidel methods, general structure of stationary iterations
Laboratory: implementation and application of numerical codes in Matlab 
Planned learning activities and teaching methods:

Classroom lessons and laboratory exercises.
In particular, slides are used during the lectures, to simplify the lessons, and Matlab exercises are assigned, pointing out the relevant difficulties. 
Additional notes about suggested reading:

Suggested textbook and online teacher notes
(www.math.unipd.it/~alvise/didattica.html) 
Textbooks (and optional supplementary readings) 

A. Quarteroni et al., Introduzione al Calcolo Scientifico. : Springer, 2016.

Innovative teaching methods: Teaching and learning strategies
 Lecturing
 Laboratory
 Problem based learning
 Interactive lecturing
 Working in group
 Problem solving
 Loading of files and pages (web pages, Moodle, ...)
Innovative teaching methods: Software or applications used
 One Note (digital ink)
 Latex
 Matlab
 Slides and PDFs
Sustainable Development Goals (SDGs)

