PHYSICS LABORATORY WITH ELEMENTS OF STATISTICS AND COMPUTER SCIENCE
Academic year and teacher
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- Versione italiana
- Academic year
- 2018/2019
- Teacher
- ELEONORA LUPPI
- Credits
- 12
- Didactic period
- Annualità Singola
- SSD
- FIS/01
Training objectives
- This is the first course of Laboratory, Statistics and programming. The main goal of the course consists in providing the basis for learning the basics of experimental methods and techniques of analysis of uncertainties. The course consists of classroom lectures, exercises, computer and laboratory experiments (at least 10) and the presentation of results in reports .
At the end of the course the student should:
-know the meaning and importance of measure a physical quantity and its uncertainties;
-be able to monitor and display data in graphs and provide the reliability;
- use probability distributions for testing hypotheses in simple applications;
- write simple programmes for data analysis and simulations. Prerequisites
- Basic knowledge on the topics covered in High school or in parallel courses (Math: derivatives, summations, integrals. Physics: classical mechanics).
Students are supposed to have no previous experience in computing programming or Information Technology Course programme
- Total number od hours for this course: 120. Lectures 48 hours, Tutorials (in laboratory), 72 hours
Statistics for experimental data analysis (lectures, 24 hours):
- The scientific method.
- The measurement of physical quantities. Definition of magnitude and its measurement. Units and systems of units: the international system.
- Presentation of measures and significant figures. Dimensional analysis.
- Errors and / or uncertainties. Systematic and statistical errors.
- The total error in measurements, relative error, degree of accuracy.
- Precision and accuracy in a measurement. Discrepancy between measurements.
- Individual and / or multiple measurements. The best estimate of the error (moda, median or average)
- Deviations, standard deviation, standard deviation of the population, of the sample and of the average.
- Errors propagation.
- Data representation: tables, histograms and graphs.
- Histograms, limit distribution.
- Gauss distribution as limit distribution for measurements affected by random errors.
- Measurement of a physical phenomena influenced by random errors and the best estimation of the expected value.
- Measurement in probabilistic terms.
- Hints on theory of probability.
- Maximum likelihood.
- Probability distributions: Gauss, Binomial, Poisson.
- Chi-square test.
- Charts and functional relations: the method of least squares.
- Description of the lab tutorials
Laboratory experiments and discussion of the data using the theory of errors (laboratory, 36 hours).
Introduction to information technology for data analysis (lectures, 24 hours)
- Basics on computer architecture (CPU, Memories, Mass Storage, I/O peripherals, etc).
- Definition of variables, constants, algebric and logical operators.
- Definition of algorithm and programming structures.
- Introduction to programme analysis.
- Definition of variables type (int, float) and array dimensioning.
- Cycles.
- Pointers.
- Use of Standard I/O library, I/O from an external file.
- Random numbers generators.
- Introduction to MonteCarlo Method.
Data Analysis Programmes (laboratory, 36 hours):
- Mean and standard deviation evaluation;
- linear regression with the squared minimum method;
- data arrangement in class intervals (histogram);
- chi square test applied to a gaussian distribution;
- fit of a data distribution;
- Simulation Programs:
- Pseudo-random numbers generator;
- Pseudo-random generator with non-uniform distribution;
- Simulation of a Physical Phenomenon with MonteCarlo Method;
- Integrals calculation with van Neumann method. Didactic methods
- Organization of the course.
First part:
Statistics for data analysis lectures (24 hours).
Laboratory experiments with related reports (36 hours plus recovery time, if needed).
Students will work in groups of 2 or 3.
At the end of any experiment, groups have to deliver a report with objectives, methods, experimental setup, data analysis and results.
Second part:
- lectures on information technology for data analysis (24 hours)
- programming tutorials for experimental data analysis and simulations (36 hours plus recovery time, if needed). Learning assessment procedures
- Practical test: execution of an experiment (with report).
Programming test.
Final oral examination.
Practical and programming test are needed to access the oral examination.
Final evaluation will be based on the examination and on the laboratory work.
During the oral examination will be
- discussed course topics, to verify the capability to understand and link each other various subjects
- discussed student reports, to verify the comprehension of the related problems and the acquired abilities in laboratory work
- verified the capability to use a programming language to solve simple problems. Reference texts
- P. R. Bevington, D. K. Robinson DATA REDUCTION AND ERROR ANALYSIS FOR PHYSICAL SCIENCES, 3 ed., Mc Graw Hill
J.R. Taylor INTRODUZIONE ALL'ANALISI DEGLI ERRORI - LO STUDIO DELLE INCERTEZZE NELLE MISURE FISICHE, 2 ed. Zanichelli
course slides
Other textbook:
L.BArone, E. Marinari, G. Organtini, F. Ricci-Tesenghi PROGRAMMAZIONE SCIENTIFICA ed Pearson Education
MONTE CARLO: BASICS, (in English) handout provided by the professor
CB. Kernighan, D. Ritchie C PROGRAMMING LANGUAGE Prentice-Hall
