
Course unit
INTRODUCTION TO NUMERICAL ANALYSIS
SCP9087940, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2017/18
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Educational activities in elective or integrative disciplines 
MAT/07 
Mathematical Physics 
6.0 
Course unit organization
Period 
First semester 
Year 
3rd Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Laboratory 
2.0 
24 
26.0 
No turn 
Lecture 
4.0 
32 
68.0 
No turn 
Prerequisites:

We assume that the student is confident with basic notions of linear algebra and geometry (vectorial spaces, vectors and matrices, operations on matrices, determinants, norms, etc..) and those of mathematical analysis 1 and 2 (in particular multivariate analysis). 
Target skills and knowledge:

The student will have the opportunity to acquire basic computer and numerical abilities. In particular he/she will be able to understand the numerical model and the underlying algorithm, make a program in Python language, produce results in graphical form. Among the others, he/she will use basic numerical methods (for solving non linear equations, linear systems, approximation of data, integrals and solution of differential equations) and hopefully he/she will be able to use in real examples/applications. 
Examination methods:

The exam will consists of an oral interview plus a second part consisting of a discussion of the lab assignments, to verifiy the Python knowledge. 
Assessment criteria:

The student should show the ability in using numerical methods both from theoretical and algorithmic point of view. He/she will show this by solving (simple) exercises. It will be essential to acquire familiarity with Python. 
Course unit contents:

1) Error analysis (propagation, stability and conditioning): 4h
2) Numerical linear algebra (vectorial and matrix norms, conditioning, matrix factorizations (LU, QR and SVD), iterative solvers): 8h
3) Interpolation (Lagrange and Newton forms, optimal points, and stability): 6h
4) Numerical quadrature( NewtonCotes and Gaussian formulas), numerical derivation: 6h.
5) Difference methods for IVP and for BVP for ordinary and some partial differential equations: 8h. 
Planned learning activities and teaching methods:

The course consists of two main sessions: frontal lectures in the classroom (32 h) and lab exercises (24 h) in Python. Lectures are given in Italian. Many of the numerical methods presented during class lectures, will be implemented during lab hours. The aim is to show the use of a computational tool, like Python, as a tool for better understanding numerical calculus. The hope is that at the end of the course the students will mature a numerical sensitivity and also a good programming ability in Python. 
Additional notes about suggested reading:

Suggested textbook. Lecture notes are available through the website of the course on the elearning platform of the Department of Mathematics "T. Levi Civita" (https://elearning.unipd.it/math/). There are plenty of tutorials and manuals introducing to the language Python. We suggest the following one: https://www.python.it/doc/Easytut/easytutit/index.html 
Textbooks (and optional supplementary readings) 

De Marchi, Stefano, Introduzione al Calcolo Numerico con codici in Matlab/Octave. Seconda Ed.. Bologna: Esculapio, Progetto Leonardo, 2018.

Innovative teaching methods: Teaching and learning strategies
 Lecturing
 Interactive lecturing
 Loading of files and pages (web pages, Moodle, ...)
Innovative teaching methods: Software or applications used
 Moodle (files, quizzes, workshops, ...)
Sustainable Development Goals (SDGs)

