First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
Course unit
SCP3050158, 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
SC1158, Degree course structure A.Y. 2014/15, A.Y. 2019/20
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Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination COMPUTATIONAL METHODS IN PHYSICS
Website of the academic structure
Department of reference Department of Physics and Astronomy
E-Learning website
Mandatory attendance No
Language of instruction Italian
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

Teacher in charge PAOLO UMARI FIS/03

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Educational activities in elective or integrative disciplines FIS/02 Theoretical Physics, Mathematical Models and Methods 6.0

Course unit organization
Period First semester
Year 3rd Year
Teaching method frontal

Type of hours Credits Teaching
Hours of
Individual study
Practice 2.0 24 26.0 No turn
Lecture 4.0 32 68.0 No turn

Start of activities 30/09/2019
End of activities 18/01/2020
Show course schedule 2019/20 Reg.2014 course timetable

Examination board
Board From To Members of the board
7 Metodi Computazioniali della Fisica 01/10/2019 30/11/2020 UMARI PAOLO (Presidente)
6 Metodi Computazioniali della Fisica 01/10/2018 30/11/2019 TROVATO ANTONIO (Presidente)

Prerequisites: Physics I, Physics II
Target skills and knowledge: Numerical methods in classical and quantum physics.
Stochastic and deterministic approaches to numerical methods.
Writing simple numerical codes to solve specific computational problems; evaluation and analysis of the obtained results.
Examination methods: Oral exhamination.
A specific computational task will be given to the student a few days before the oral exhamination.
Assessment criteria: A specific computational task will be assigned to the student prior to the oral exhamination, in order to test his/her abilities in independent problem solving and in using the techniques learned throughout the course. The oral exhamination will test the basic knowledge of numerical methods to be used to solve physics problems and the reasoning and comprehension abilities of the student.
Course unit contents: Introduction. Numerical solution to ordinary differential equations (ODE) with Euler's method. Solution of some mechanics problems. Oscillatory motion. Evolution algorithms to solve ODE:
Euler, Euler-Cromer. Mid-point scheme and Euler-Richardson algorithm. Verlet and velocity Verlet algorithms. Runge-Kutta methods: derivation of second order scheme. Discussion of Runge-Kutta higher order methods. Numerical computation of electric potential and field. Solution of Laplace equation:
finite difference and Jacobi methods. Partial differential equations (PDE); geometric classification with examples: wave equations, diffusion equation and Poisson equation. Finite difference solution algorithms: truncation errors, consistency and stability. Hyperbolic (wave) equations: FTCS and LAX methods. Courant-Friedrichs-Lewy criterion. Staggered leapfrog algorithm. Parabolic (diffusion) equations: explicit FTCS algorithm, convergence constraints. Laasonen implicit algorithm. Crank-Nicolson algorithm. Root-finding algorithms for real functions. Bisection, Newton-Raphson and secant methods. Interpolation and extrapolation of functions. Lagrange polynomials. Numerical intergration: Newton-Cotes formulas. Linear system solution. Gauss-Jordan elimination method: froward elimination and bachward substitution. Introduction to pivoting. Solution of tri-diagonal matrix equations. Monte Carlo methods. Random number generators. LCG, Shift-Register and Lagged Fibonacci generators. Generation of statistical samples fron probability distributions: inverse transformation method. Composition and Acceptance/Rejection method. Computation of definite integrals with Monte Carlo methods: Hit-or-Miss, sample-mean and Importance Sampling. Solution of PDE with different boundary conditions (boundary value problems). Shooting method and relaxation method. Fourier transform: Fast Fourier Transform. Deterministic optmization methods: steepest descent, conjugate gradient, downhill simplex methods. Stochastic optimization methods: simulated annealing.
Planned learning activities and teaching methods: Classroom theory lectures and practical classes in front of a pc desk. In the latter, some of the methodologies taught in the classroom will be practiced and applied to specific computational problems
Additional notes about suggested reading: Further bibliographic references will be given throughout the course, more specific to the treated subjects.
Textbooks (and optional supplementary readings)
  • Nicholas J. Giordano, Hisao Nakanishi, Computational Physics. --: --, --. Cerca nel catalogo
  • Benjamin J. Stickler, Ewald Schachinger, Basic Concepts in Computational Physics. --: --, --. Cerca nel catalogo
  • William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian P. Flannery, Numerical Recipes. --: --, --. Cerca nel catalogo

Innovative teaching methods: Teaching and learning strategies
  • Laboratory
  • Problem based learning
  • Questioning
  • Problem solving
  • Loading of files and pages (web pages, Moodle, ...)

Innovative teaching methods: Software or applications used
  • Moodle (files, quizzes, workshops, ...)
  • Latex