# MATHEMATICS

STATISTICS (2 credits) | COMPUTER SCIENCE (2 credits) |

APPLIED PHYSICS (A) (1 credits) | APPLIED PHYSICS (B) (5 credits) |

## Learning outcomes of the course unit

Provide basic mathematical and physical tools to approach issues of increasing complexity; introduce the student to the study and application of the scientific method, the basic research tool in any field of science; illustrate the most significant aspects of natural phenomena, with particular reference to the measurement of magnitudes that comprise them; describe, within a context of logical continuity, the most common physical properties that provide support and interpretation for biomedical-related magnitudes.

## Course contents summary

Mathematics

Overview of set theory. Review of equations and inequalities.

Exponential, logarithmic and trigonometric functions. Overview of complex numbers.

Real functions of a real variable. Operations between functions. Inverse function. Concept of limit and rules of calculation. Infinite and infinitesimal. Derivability of functions and principal related theorems. Study of monotony and convexity; maximum and minimum search.

Integration theory. Ordinary differential equations.

Physics I

Introduction to the methodology of physical sciences. International system of units of measure. Samples of time, length and mass. Overview of instruments and errors of measurement. Scalar magnitudes and vector magnitudes. Operations with vectors.

Reference systems. Uniform rectilinear motion and uniformly accelerated motion. Motion of bodies in free-fall. Speed and acceleration in three-dimensional motion. Uniform circular motion. Period and frequency. Reference systems in motion in relation to each other.

Concept of force. Three principles of dynamics. Mass and weight. Inclined plane. Frictional force. Simple harmonic motion. Simple pendulum. Motion of a material point under the action of elastic force. Elastic waves.

Work and energy. Spring. Weight force. Kinetic energy. Theorem of kinetic energy. Power. Potential energy. Conservative and non-conservative forces. Principle of conservation of mechanical energy.

Quantity of motion of a particle system. Conservation of the quantity of motion in an isolated system. Impact in two- and three-dimensions.

Definition of fluid. Density. Pressure and its units of measure. Pressure variation in a fluid at rest: Stevino’s law. Pascal’s principle. Archimede’s principle. Pressure measurement: Torricelli’s barometer and open tube manometer. Lines of flow and continuity equation. Bernoulli’s equation. Real liquids and Poiseuille’s theorem.

Thermometry, calorimetry and zero principle of thermodynamics. The first law and the conservation of energy. Ideal gases and real gases. The second law of thermodynamics and entropy. Thermodynamics applied to thermal machines.

Statistics

Introduction : medical statistics and related disciplines. Logic and statistical planning. Overview of combinatorial calculations: permutations, distributions, combinations. Applications.

Overview of probability calculations: simple and compound probability. Bayes theorem. Odds. Odds ratios. Likelihood ratios. applications.

Probability distributions : binomial distribution, Poisson distribution, normal and standard normal distribution. Tables and their use.

Summarising data. Units of measure. Measurements of position, order and variation. Indices of central tendency, mean, median, mode. Indices of variability, variance, standard deviation, CV. Percentiles and their use.

General principles of statistical inference. Sampling distribution. Hypothesis and hypothesis testing. Type 1 and type 2 error. Power of a test and operating curve. Parametric test : Student t-test, Variance analysis with 1 and 2 classification criteria. Non-parametric test: Wilcoxon test, Mann-Whitney test, Kruskal-Wallis test, Friedman test, mean test, Chi-square test, Fisher exact test.

Computer Science

Overview of linear regression and historical correlation from their first invention in the 1600s to the present.

Introduction to computer science and use of the computer. General principles of operation – Functional analysis of the structure of a computer

Hardware: CPU, Memory, I/O devices – Binary system and Boolean operators.

Data (text, numbers, images, sound) in digital form.

Software, basic software and operating systems – applications software.

Overview of programs and algorithms – Computer networks &ndas

## Recommended readings

1. Lecture notes

2. J. W. Kane , M. M. Sternheim: Fisica Biomedica, ed. E.M.S.I. (Roma).

3. D.Halliday-R.Resnick-J.Walker: Fondamenti di Fisica,Casa Ed. Ambrosiana (Milano).

4. Stanton A. Glantz : Statistica per discipline Bio-mediche ed. McGraw