**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