Unit MATHEMATICS AND PHYSICS

PRINCIPLES OF PHYSICS

Code	GP004371
CFU	5
Teacher	Maurizio Biasini
Teachers	Maurizio Biasini
Hours	45 ore - Maurizio Biasini
Learning activities	Base
Area	Discipline matematiche e fisiche
Sector	PHYS-01/A
Type of study-unit	Obbligatorio (Required)
Language of instruction	Italian
Contents	The course introduces the main concepts of physics that are useful for understanding biological and physiological phenomena and relevant applications. The main topics will be: physical quantities and units of measurement, mechanics, equilibrium, levers, fluids, pressure, circulation, temperature, heat, electricity, waves, sound, ultrasound.
Reference texts	D. Halliday, R. Resnick, J. Walker, Fundamentals of Physics, Zanichelli / Casa Editrice Ambrosiana. The instructor may indicate additional supporting materials during the course.
Educational objectives	The aim of the course is to provide students with the basic knowledge of physics needed to better approach the study of the biological and physiological disciplines of the degree programme in Animal Production. At the end of the course, students should be able to: know the main physical quantities and units of measurement;¿use simple formulas to solve basic problems;¿understand the meaning of force, work, energy, and power;¿describe simple situations of equilibrium and the functioning of levers;¿understand pressure, density, and the behaviour of fluids;¿understand the concepts of temperature, heat, and heat exchange;¿know the basics of electricity;¿understand sound waves and ultrasound;¿interpret simple numerical results using correct units of measurement.
Prerequisites	Basic school-level knowledge of mathematics is required, in particular: proportions;¿percentages;¿powers;¿scientific notation;¿simple equations;¿elementary geometry;¿reading graphs and tables. Advanced knowledge of physics is not required. The topics will be introduced progressively.
Teaching methods	The course will be delivered through lectures and exercises. During the lectures, the fundamental theoretical concepts will be explained and simple examples will be discussed. The exercises will help students learn how to apply formulas and solve basic problems. The following will be used: practical examples;¿guided exercises;¿diagrams and graphs;¿mathematical reminders when necessary;¿connections with physiological and animal-related phenomena. The aim is not to memorize formulas, but to understand when and how to use them.
Other information	Attendance is recommended, especially in order to follow the exercises carried out in class. Teaching materials will be provided by the instructor and may include slides, lecture notes, solved problems, and exercise texts. Students may ask for clarification during office hours, particularly on exercises and on the more difficult topics.
Learning verification modality	The examination will consist of a written test, possibly accompanied by an oral test, if required. The written test may include: simple exercises;¿theoretical questions;¿interpretation of formulas;¿use of units of measurement;¿questions on biological and animal-related applications. The oral test, if required, will assess the understanding of the main topics and the ability to connect physics to relevant examples. The evaluation will take into account: correctness of the answers;¿reasoning ability;¿correct use of units of measurement;¿clarity of explanation;¿understanding of the physical meaning of the results.
Extended program	1. Physical quantities and units of measurement Fundamental and derived physical quantities. International System of Units. Length, mass, time, temperature, force, energy, and pressure. Multiples and submultiples. Scientific notation. Conversions between units of measurement. Orders of magnitude. Correct use of units of measurement in simple problems. 2. Mechanics Motion of a body. Position, velocity, and acceleration. Uniform rectilinear motion and uniformly accelerated motion. Concept of force. Principles of dynamics. Weight force, mass, and gravitational acceleration. Work, energy, and power. Kinetic energy and potential energy. Conservation of energy in simple cases. Examples applied to movement and to the forces acting on the body. 3. Equilibrium and levers Conditions of equilibrium. Moment of a force. Centre of mass and centre of gravity. First-, second-, and third-class levers. Applications to the musculoskeletal system. Examples of levers in joints and movement. 4. Fluids Density. Pressure. Pressure in liquids. Pascal’s principle. Archimedes’ principle. Buoyancy. Flow of a fluid. Flow rate. Relationship between vessel cross-section and fluid velocity. Introduction to viscosity. Difference between ideal and real fluids. Applications to blood circulation. 5. Heat and temperature Temperature and temperature scales. Heat. Heat capacity and specific heat. Changes of state. Heat transfer by conduction, convection, and radiation. Applications to thermoregulation, heat loss, phase transition and methabolism 6. Electricity Electric charge. Electric field. Electric potential. Electric current. Resistance. Ohm’s law. Simple electric circuits. Electric power. 7. Waves and sound Concept of wave. Mechanical waves. Wavelength, frequency, period, velocity, and amplitude. Sound waves. Sound intensity. Ultrasound.

MATHEMATICS

Code	GP004372
CFU	5
Teacher	Michele Piconi
Teachers	Michele Piconi Arianna Travaglini
Hours	27 ore - Michele Piconi 27 ore - Arianna Travaglini
Learning activities	Base
Area	Discipline matematiche e fisiche
Sector	MATH-03/A
Type of study-unit	Obbligatorio (Required)
Language of instruction	ITALIAN
Contents	Functions, equations and inequalities. Geometric transformations. Iterative processes: sequences and progressions. Exponential and logarithmic functions. Limits and continuity of functions. Derivative and its applications.
Reference texts	James STEWART, "Calculus - Concepts and Contexts", 2nd edition (Italian edition: CALCOLO - Funzioni di una variabile, Maggioli Editore, 2013). Lecture notes and worked/proposed exercises available online on the course platform.
Educational objectives	The course aims to provide students with the basic mathematical concepts needed to acquire a mathematical language to be used in applications. In particular, it aims to develop the ability to interpret simple problems in mathematical terms, to formulate elementary mathematical models and to apply the tools developed to derive, interpret and discuss their solutions. Knowledge: elementary functions, exponential and logarithmic-type; linear, second-degree, rational, irrational and absolute-value equations and inequalities; sequences and progressions; limits and continuity of functions; derivatives and their applications. Skills: to formulate and analyse simple mathematical models; to solve equations and inequalities of various kinds; to draw, interpret and study the graphs of functions; to compute limits and derivatives and use them to study functions and to solve simple optimization problems.
Prerequisites	To understand the contents and achieve the objectives of the course of Mathematics, students are required to have the following basic knowledge: numerical sets (natural, integer, rational and real numbers) and their algebraic properties; fundamental properties of numerical operations; oriented line, proportions and percentages; basic elements of Euclidean plane geometry (points, segments, half-lines, angles, Thales' theorem, triangles, Pythagoras' and Euclid's theorems); powers and their properties, roots, logarithms and their properties; polynomial calculus (factorization, notable products, G.C.D. and L.C.M., divisions), simplification of rational expressions; basic elements of plane analytical geometry (Cartesian coordinate system, midpoint, distance between two points, straight-line equation); first-degree equations.
Teaching methods	The course consists of lectures on all the topics of the syllabus and classroom exercises aimed at preparing students for the written exams.
Other information	Attendance is not mandatory but strongly recommended.
Learning verification modality	Learning assessment consists of a written examination, including exercises and questions covering all the topics of the syllabus, aimed at verifying the knowledge acquired and the ability to apply it to problem solving. Two mid-term tests are scheduled, which allow partial exemption from the final written examination.
Extended program	1. Functions, equations and inequalities: the concept of function, monotone, bijective and invertible functions; composition of functions; elementary functions; linear, second-degree, rational, irrational and absolute-value equations and inequalities; geometric transformations; applications. 2. Iterative processes and exponential functions: sequences, recursive and explicit formulas; arithmetic and geometric progressions; exponential and logarithmic functions; exponential and logarithmic equations; applications. 3. Limits and continuity: the concept of limit, definition and graphical representation; uniqueness theorem for limits; asymptotes, continuity, infinities and infinitesimals; standard limits. 4. Derivative: difference quotient and derivative, geometric meaning, equation of the tangent line; derivatives of elementary functions, rules of differentiation, derivatives of composite and inverse functions; Rolle's theorem and Lagrange's theorem; local and global maximum and minimum points; concavity, convexity and inflection points; simple optimization problems.
Obiettivi Agenda 2030 per lo sviluppo sostenibile