Prof. Paolo Fornasini

A.A. 1998/99

PROGRAMME

PHYSICAL QUANTITIES AND THEIR MEASUREMENT

- Physical quantities and their measurement. Direct and indirect measurements. Time dependence of physical quantities.
- Systems of units. Fundamental and derived units. Natural and artificial standards. The International System. Other systems. Dimensions of physical quantities. Dimensional analysis.
- Measuring instruments and their functional elements. Operative characteristics. Static and dynamic characteristics. Basic instrumentation for length, time and mass measurement. Thermometers and calorimeters.
- Presentation of measurement results. Tables: significant digits and rounding of decimal places. Graphs and histograms.
- Uncertainty in measurements with low resolving power. Repeated measurements with high resolving power: casual errors and statistical distributions. Systematic errors. Unbias, precision, accuracy. Propagation of uncertainty in indirect measurements.

STATISTICAL REDUCTION OF EXPERIMENTAL DATA

- Random phenomena. Probability of an event. Dispositions, permutations and combinations. Sum of events (incompatible and not): probability of the sum. Multiplication of events (indipendent and not): probability of the product.
- Discrete and continuous random varables and their distribution laws. Numerical characteristics of a distribution: average, variance, coefficients of asymmetry and flatness. Binomial distribution. Poisson distribution. Gauss normal distribution.
- Estimate of theoretical parameters from experimental distributions. Criterion of maximum likelihood. Distributions of the averages and variances. Confidence. Data rejection. Weighted averages.
- Approximation of experimental data with theoretical curves. Least squares method. Linear regression. Other particular cases.
- Statistical tests. Covariance and linear correlation coefficient. "Chi square": definiton, degrees of freedom, reduced chi square.
- Introduction to the use of the computer for the analysis of measurements.

 During the course the students will make laboratory experiments on mechanics and thermology.
 The attendance at the laboratory is compulsory.
 

REFERENCE TEXTS

Lecture notes (in Italian)
J. R. TAYLOR Introduction to Error Analysis, University Science Books
P. R. BEVINGTON, Data Reduction and Error Analysis for the Physical Sciences, McGraw Hill