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School of Science
ASTRONOMY
Course unit
INTRODUCTION TO NUMERICAL ANALYSIS
SCP9087940, A.A. 2019/20

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

Information on the course unit
Degree course First cycle degree in
ASTRONOMY
SC1160, Degree course structure A.Y. 2008/09, A.Y. 2019/20
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Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination INTRODUCTION TO NUMERICAL ANALYSIS
Website of the academic structure http://astronomia.scienze.unipd.it/2019/laurea
Department of reference Department of Physics and Astronomy
Mandatory attendance
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 STEFANO DE MARCHI MAT/08
Other lecturers FABIO MARCUZZI MAT/08

ECTS: details
Type Scientific-Disciplinary 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

Calendar
Start of activities 30/09/2019
End of activities 18/01/2020
Show course schedule 2019/20 Reg.2008 course timetable

Syllabus
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( Newton-Cotes 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 e-learning 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/easytut-it/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. Cerca nel catalogo

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, ...)

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