B027296 - NUMERICAL METHODS FOR PHYSICS

Italian

Italian

Recall of the C language structure and short Python overview as visualization tool.
Creation and implementation of algorithms for the solution with numerical methods of linear algebra problems, interpolation, derivation, ordinary and partial differential equations. Possible applications on heat diffusion problems, molecular dynamics, non-linear oscillators, wave propagation.

Recall of the C language structure and short Python overview as visualization tool.
Creation and implementation of algorithms for the solution with numerical methods of linear algebra problems, interpolation, derivation, ordinary and partial differential equations. Possible applications on heat diffusion problems, molecular dynamics, non-linear oscillators, wave propagation.

Lecture notes and lectures are available on the course web page on the e-l.unifi.it
A recommended reference is
1 Luciano M. Barone - Enzo Marinari - Giovanni Organtini - Federico Ricci-Tersenghi Programmazione scientifica.
Pearson Education Italia (2006)
2 Brian W. Kernighan, Dennis M. Ritchie Linguaggio C, Jakson Libri (1989)
3 Alessandro Bellini, Andrea Guidi, Linguaggio C, Mc Graw Hill (2021)
4 Alessandro Bellini, Andrea Guidi Python & Machine Leraning Mc Graw Hill (2021)

Lecture notes and lectures are available on the course web page on the e-l.unifi.it
A recommended reference is
1 Luciano M. Barone - Enzo Marinari - Giovanni Organtini - Federico Ricci- Tersenghi Programmazione scientifica.
Pearson Education Italia (2006)
2 Brian W. Kernighan, Dennis M. Ritchie Linguaggio C, Jakson Libri (1989) 3 Alessandro Bellini, Andrea Guidi, Linguaggio C, Mc Graw Hill (2021)
4 Alessandro Bellini, Andrea Guidi Python & Machine Leraning Mc Graw Hill (2021)

Provide the basic tools of numerical calculation and simulation of physical systems, data analysis and their visualization. Familiarity with the C language and the basic functioning of a digital computer

Provide the basic tools of numerical calculation and simulation of physical systems, data analysis and their visualisation. Familiarity with the C language and the basic functioning of a digital computer

Basic notions of geometry, linear algebra, analysis 1, differential equations.
The knowledge of a programming language is recommended, preferably the C language

Basic notions of geometry, linear algebra, analysis 1, differential equations.
The knowledge of a programming language is recommended, preferably the C language

Frontal lessons followed by laboratory experiences.
In the laboratory we shall write, compile and execute programs, analyzing the resulting data.
We will use the C language and the gnuplot software or Python for graphic display.
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Frontal lessons followed by laboratory experiences.
In the laboratory we shall write, compile and execute programs, analyzing the resulting data.
We will use the C language and the gnuplot software or Python for graphic display.

Contacts:
simone.landi@unifi.it
franco.bagnoli@unifi.it

Website: e-l.unifi.it

Contacts: simone.landi@unifi.it franco.bagnoli@unifi.it
Website: e-l.unifi.it

Laboratory test. The student will be asked to build a code using C language that solves a physical-mathematical problem with numerical methods addressed during the course.

Laboratory test. The student will be asked to build a code using C language that solves a physical-mathematical problem with numerical methods addressed during the course.

Calling elements of the C language: functions, arrays, pointers, structures. Outline of Python (basic syntax, main types, functions, application packages for mathematical functions and visualization). Input-Output on files and pipes. Generator of (pseudo) random numbers. Histograms and probability distributions. Monte-Carlo method, diffusion, Langevin equation. An example of a numerical experiment. Methods for solving linear algebra problems and applications to systems of ordinary differential equations. Computation systems of derivatives with numerical methods. Numerical methods of integration of ordinary differential equations: stability and precision. Simulation efficiency. Verlet and Runge-Kutta methods. Applications to the harmonic oscillator, pendulum and other non-linear systems. Numerical integration of partial differential equations. Wave propagation. Molecular dynamics, application to a gas in Lennard-Jones interaction.

Elements of the C language: functions, arrays, pointers, structures. Outline of Python (basic syntax, main types, functions, application packages for mathematical functions and visualization). Input- Output on files and pipes. Generator of (pseudo) random numbers. Histograms and probability distributions. Monte-Carlo method, diffusion, Langevin equation. An example of a numerical experiment. Methods for solving linear algebra problems and applications to systems of ordinary differential equations. Computation systems of derivatives with numerical methods. Numerical methods of integration of ordinary differential equations: stability and precision. Simulation efficiency. Verlet and Runge-Kutta methods. Applications to the harmonic oscillator, pendulum and other non-linear systems. Numerical integration of partial differential equations. Wave propagation. Molecular dynamics, application to a gas in Lennard-Jones interaction.