27216 - Calculus for Astronomy

Course Unit Page

Academic Year 2017/2018

Learning outcomes

At the end of the course, the student will have the basic knowledge of the numerical algorithms commonly used in physical and astronomical applications. In particular the student will be able to write numerical codes using a high-level language: to solve linear algebric equations; to interpolare and integrate functions; to find roots of equations; to integrate differential equations.

Course contents

Introduction to the programming Language Fortran90.  
Numerical algorithms for:  roots of equations; systems of linear algebraic equations; statistical description of data;  interpolation of data;   numerical differentiation and integration; generation of random numbers; ordinary differential equations;   partial differential equations.   Case studies in Fortran90.

Readings/Bibliography

Chapra,     Canale  , "Numerical Methods for Engineers, McGraw-Hill  

Press et al. "Numerical Recipes", Cambridge University Press
Lectures notes prepared by the teacher.

Teaching methods

Part of the lectures (4 CFU) will be done in a teaching room using the blackboard and the videoprojector.

Part of the lectures  (4 CFU) will be done in the computing lab, with worstations which will be used by the students to solve the exercises under the supervision of the teacher


Assessment methods

The final exam is based on: 1) implementation of numerical codes in Fortran90 to solve specific problems presented during the lectures; 2) written reports on the results, discussing: the scientific problem, the numerical methods applied to solve it, the available data, the obtained results and their significance.  The codes and the reports must be sent by email to the teacher at least 2 working days before the date fixed for the oral exams. The oral exam will include a discussion of the projects (codes and reports) and of the other algorithms discussed during the course. The level of knowledge of the programming language will be also verified.

Teaching tools

Programming techniques are illustrated by specific projects which are designed and implemented in class. During the laboratory hours problems referring to the subject of the lectures are presented to the students for the solution.

Office hours

See the website of Lauro Moscardini