First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Engineering
CHEMICAL AND MATERIALS ENGINEERING
Course unit
NUMERICAL ANALYSIS
IN18101050, A.A. 2017/18

Information concerning the students who enrolled in A.Y. 2017/18

Information on the course unit
Degree course First cycle degree in
CHEMICAL AND MATERIALS ENGINEERING
IN1840, Degree course structure A.Y. 2011/12, A.Y. 2017/18
N0
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Number of ECTS credits allocated 9.0
Type of assessment Mark
Course unit English denomination NUMERICAL ANALYSIS
Website of the academic structure http://icm.dii.unipd.it/ingegneria-chimica-e-dei-materiali/
Department of reference Department of Industrial Engineering
E-Learning website https://elearning.unipd.it/dii/course/view.php?idnumber=2017-IN1840-000ZZ-2017-IN18101050-N0
Mandatory attendance No
Language of instruction Italian
Branch PADOVA
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Lecturers
Teacher in charge MICHELA REDIVO ZAGLIA MAT/08

ECTS: details
Type Scientific-Disciplinary 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

Calendar
Start of activities 01/03/2018
End of activities 01/06/2018

Examination board
Board From To Members of the board
6 A.A. 2017/18 01/10/2017 30/11/2018 REDIVO ZAGLIA MICHELA (Presidente)
SOMMARIVA ALVISE (Membro Effettivo)
CIPOLLA STEFANO (Supplente)
MARCUZZI STEFANO (Supplente)
MARTINEZ CALOMARDO ANGELES (Supplente)
4 A.A. 2016/17 01/10/2016 30/11/2017 REDIVO ZAGLIA MICHELA (Presidente)
SOMMARIVA ALVISE (Membro Effettivo)
MARTINEZ CALOMARDO ANGELES (Supplente)
PUTTI MARIO (Supplente)

Syllabus
Prerequisites: Basic knowledge of Mathematical analysis, Linear Algebra and Geometry (vector spaces, vectors, matrices, operations, determinants, inverse matrix and particular matrices, scalar product, norms).
Target skills and knowledge: The student will have the opportunity to acquire basic computer skills and be able to build the model and the numerical solution algorithm for simple problems. At the end of the course he/she will be able to program with the language reference and produce the results in graphic form. The student will acquire knowledge of some basic methods of Numerical Analysis in view of scientific and technological applications, with special attention to the concepts of error, discretization, approximation, convergence, stability, computational cost.
Examination methods: Written examination and laboratory programming work (related to Numerical Analysis problems). Optional oral examination
Assessment criteria: Students must demonstrate that they have acquired the knowledge of the various methods from both theoretical and algorithmic point of view, from the point of view of the applications through simple exercises.
In lab tests, will need to have purchased a relative familiarity in the use and in writing simple programs in Matlab.
Course unit contents: Computer Arithmetic: Floating-Point numbers and arithmetic. Errors in computation. Stability of algorithms. Condition number.

Nonlinear Equations: Iterative methods. Convergent sequences. Existence and unicity theorems. Bisection algorithm. Fixed point iteration. Newton's methods. Methods for multiple roots. Stopping criteria.

Numerical linear algebra: Direct Methods for linear systems: Gauss and matrix factorizations. Cholesky method. Householder (hints). Matrix Inversion. Preconditioning. Iterative Methods for linear systems: Jacobi, Gauss-Seidel, SOR. Convergence theorems. Stopping criteria

Polynomial Approximation: Interpolation (Lagrange, Newton, Chebyshev). Convergence. Least squares: linear and polynomial regression.

Numerical Integration: Interpolatory formulae: Lagrange, Newton-Cotes. Gauss (hints).

Computer Arithmetic: Floating-Point numbers and arithmetic. Errors in computation. Stability of algorithms. Condition number.

Nonlinear Equations: Iterative methods. Convergent sequences. Existence and unicity theorems. Bisection algorithm. Fixed point iteration. Newton's methods. Methods for multiple roots. Stopping criteria.

Numerical linear algebra: Direct Methods for linear systems: Gauss and matrix factorizations. Cholesky method. Householder (hints). Matrix Inversion. Preconditioning. Iterative Methods for linear systems: Jacobi, Gauss-Seidel, SOR. Convergence theorems. Stopping criteria

Polynomial Approximation: Interpolation (Lagrange, Newton, Chebyshev). Convergence. Least squares: linear and polynomial regression.

Numerical Integration: Interpolatory formulae: Lagrange, Newton-Cotes. Gauss (hints).

Ordinary differential equations: Initial Value Problems. Implicit and Explicit one step methods (Taylor, Euler).

Eigenvalue and Eigenvectors (hints)
Planned learning activities and teaching methods: The course consists of lectures and exercises in the classroom (about 50 hours) and lessons in the computer lab (about 22 hours) with exercises on the computer in Matlab.
Many of the basic methods of numerical analysis presented during the lectures, will gradually be used in the laboratory in order to show their actual use and their potential. Gradually the student will also become familiar with a programming environment for numerical problems and at the end of the course should be able to pass a test that is an integral part of the final exam.
Additional notes about suggested reading: There are numerous tutorials and manuals recoverable in the network also related to the programming environment Matlab.
See also the teacher's web site
www.math.unipd.it/~michela
in the Teaching section.
Textbooks (and optional supplementary readings)
  • Michela Redivo Zaglia, Calcolo Numerico: Metodi ed Algoritmi. Padova: Libreria Progetto, 2011. Quarta Edizione riveduta Cerca nel catalogo
  • Michela Redivo Zaglia, Calcolo Numerico: Esercizi. Padova: Libreria Progetto, 2015. Terza Edizione Cerca nel catalogo
  • Michela Redivo Zaglia, Quaderno MATLAB. Padova: Libreria Progetto, 2018. Cerca nel catalogo