Unit MATHEMATICS AND PHYSICS
 Course
 Animal science
 Studyunit Code
 GP004361
 Curriculum
 In all curricula
 CFU
 10
 Course Regulation
 Coorte 2023
 Offered
 2023/24
 Type of studyunit
 Obbligatorio (Required)
 Type of learning activities
 Attività formativa integrata
PRINCIPLES OF PHYSICS
Code  GP004371 

CFU  5 
Teacher  Diego Ciangottini 
Teachers 

Hours 

Learning activities  Base 
Area  Discipline matematiche e fisiche 
Academic discipline  FIS/07 
Type of studyunit  Obbligatorio (Required) 
Language of instruction  Italian 
Contents  The course aims at providing basic knowledge of physics, oriented to applications of specific interest to the course of study and necessary to undertake further training activities. Particular attention is payed to the study of fluids (statics and dynamics) and thermodynamics (temperature, heat transfer and work). Numerical problems and exercises are a fundamental part of the course.Topics:  Kinematics (9 hours);  Dynamics (9 hours);  Fluids and Thermodynamics (18 hours);  Electromagnetism and Optics (9 hours). 
Reference texts  D. Halliday, R. Resnick, J. Walker, Fondamenti di Fisica. ed. Casa Editrice Ambrosiana. Lecture notes by the lecturer, available in digital format. 
Educational objectives  Ability to practically apply the skills acquired in the disciplines of physics to solve numerical problems, to approach reality with scientific method, and to bring the phenomena studied in suitable models. 
Prerequisites  In order to understand the contents and to achieve the objectives related to the module Principles of Physics, it is essential that the student has the following basic knowledge:  physical quantities and their units: the concept of measurable variable, measurement parameters of the main physical characteristics, fundamental and derived quantities, systems of measurement units, multiples and submultiples, orders of magnitude, writing rules, scientific notation, equivalences and conversion factors;  trigonometry: angular measurements (in degrees and radians), sine, cosine and tangent functions, principal relations and operations among these functions;  vectors: magnitude, direction and orientation, components, representation and composition/ decomposition methods, main arithmetic operations (addition, subtraction, scalar and vector product). 
Teaching methods  Frontal lessons and practical exercises. 
Other information  Attendance: optional but strongly recommended. 
Learning verification modality  The exam of Principles of Physics includes a written test and, possibly, an oral test, at the request of the student, which can also be omitted. The written test of Principles of Physics consists of 15 multiple choice questions that will cover both theoretical aspects and exercises in which a short course will be scheduled. This test is aimed at verifying the skills of:  understanding of the main concepts of fundamentals of physics;  understanding of the proposed problems;  correct application and management of acquired knowledge;  analysis of the results obtained. In the case of a written test whose result is at least equal to 18/30, the oral exam of Principles of Physics can be omitted. The oral test can instead be requested by the student concerned to improve the outcome of the written test. In order to access the oral test, however, it is necessary to have obtained a mark of at least 18/30 on the written test. If requested, the oral exam of Principles of Physics consists of an interview and is aimed to test the level of learning reached by the student as well as his ability to use the theoretical and methodological contents of the module of Principles of Physics with reference to the main topics covered. Exposure clarity and an appropriate language property will also be evaluated. For information on support services for students with disabilities and / or DSA visit the page http://www.unipg.it/disabilitaedsa 
Extended program   Kinematics (1 Credit) Physical quantities, samples and units of the International System, scalars and vectors, multiples and submultiples. Motion in one dimension, velocity and acceleration. Uniform rectilinear motion, uniformly accelerated motion and free fall. Motion in a plane, projectile motion and circular motion. Harmonic motion.  Dynamics (1 Credit) Force, mass and laws of Dynamics. Types of force, gravitational force, weight force, elastic force, frictional force, centripetal force and centrifugal force. Work, kinetic energy and power. Conservative forces, potential energy and conservation of mechanical energy.  Fluids and Thermodynamics (2 Credits) Pressure, Stevin's law, Pascal's and Archimedes' principles. Perfect fluid, flow, equation of continuity and Bernoulli's equation. Fundamentals of fluid flow. Wave phenomena, sound and ultrasound. Temperature, heat, specific heat and latent heat. Work and principles of Thermodynamics. Heat transfer: conduction, convection and radiation. Heating and cooling of matter.  Electromagnetism and Optics (1 Credit) Electrification phenomena, conductors and insulators, Coulomb's law. Electric field and potential difference. Intensity of current, Ohm's and Joule's laws and elementary circuits. Magnetic phenomena and magnetic force. Electromagnetic waves. Wave in elastic media: fundamentals, sound and ultrasound. Laws of reflection and refraction and total reflection. Lenses. 
MATHEMATICS
Code  GP004372 

CFU  5 
Teacher  Rita Ceppitelli 
Teachers 

Hours 

Learning activities  Base 
Area  Discipline matematiche e fisiche 
Academic discipline  MAT/05 
Type of studyunit  Obbligatorio (Required) 
Language of instruction  Italian 
Contents  To provide students with basic knowledge about formulating, solving and discussing simple mathematical models in biology, economy, engineering. Elementary functions. Equations and inequalities. Sequences, iterative process. Limit, continuity, derivative. Riemann integral and the area of regions between two graphs. 
Reference texts  James STEWART “CALCOLO Funzioni di una variabile”, Maggioli Editore 2013. (Original english language edition: CalculusConcepts and Contexts, 2nd edition.) Lecture notes available online. 
Educational objectives  Knowledge: 1. Elementary functions, exponential and logarithmic maps. 2. Sequences 3. Limits. 4. Continuity of functions. 5. Derivatives and applications. Some elements of differential calculus. 6. Critical and extremal points. 7. Integrals and applications. Ability: 1. To define and analyze simple mathematical models. 2. To solve equalities and inequalities of various kind. 3. To draw, interpret and study the graphs of functions. 4. To compute limits, derivatives and integrals. 
Prerequisites  The following basic knowledge is required for the student to understand and reach the objectives of the course of Mathematics: Numerical sets: natural numbers, integer numbers, rational numbers and related algebraic structures. Fundamental properties of operations. Oriented line, irrational numbers. The real numbers. Proportions and percentages. Basis of Euclidean geometry: points, segments, halflines, angles. Talete’s Theorem. Triangles. Pitagora’s and Euclid’s Theorems. Powers and scientific representation. Fundamental properties of powers. Powers with random exponent. Roots of numbers. Logarithms and their properties. Fundamental techniques of polynomial calculus: decomposition, product, L.C.M. and G.D.C., divisions. Reduction of a rational polynomial expression. Basic concepts of plane analytical geometry: cartesian coordinate system, midpoint and distance between two points, straight line equations. Firstdegree equations. 
Teaching methods  The course is organized as follows: lectures on all subjects of the course, classroom exercises to prepare the students for the written exams. It is planned a tutor teaching activity. 
Other information  Attendance: optional but strongly recommended 
Learning verification modality  The exam is made of both a written and oral test.The written test consists of the solution of two problems and has a duration of at most ninety minutes. Its objectives are the following: the understanding of the proposed problems; the handling of mathematical instruments; the interpretation of the results obtained. The oral test consists of a talk of about 30 minutes and is aimed at testing the degree of comprehension reached by the student and his skills in handling mathematical objects, with particular attention to his capacity of finding connections between the topics explained. 
Extended program  A  B. Functions, Equations and inequalities. Definition of a singlevalued function. Monotonic and inverse functions. Operation with functions, composite functions. Algebraic functions: linear, quadratic, cubic, rational, nth root, absolutevalue, greatestinteger functions. Trigonometric functions. Geometric transformations : translations and reflections. Using Excel or Computer Algebra Systems to explore the main properties in their graphs. Linear, quadratic, rational, irrational, modulus (absolute value) equations and inequalities. Linear systems, Cramer's rule. C. Iterative processes  Exponential functions. Sequences, recursive formula. Arithmetic and geometric progressions. Logarithmic and exponential functions and their graphs. Logarithmic and exponential equations and inequalities. Applications: mitosis, Fibonacci sequence, simple and compound interest in Economy, radioactive decay. Semilogarithmic coordinate systems. D. Limits. Introduction to limits. Theorem on uniqueness of limits. Infinite limits and limits at infinity. Continuity of a function : definition and basic theorems. The types of discontinuity. The calculation of limits. Some special limits. The squeezing Theorem. E . Derivatives. Tangent lines and derivatives: geometric interpretation. The derivative as the rate of change. Some differentiation formulas. The derivative of composite and inverse functions. The L'Hôpital's Theorem. Estrema of the functions. The Férmat's Theorem. Concavity, convexity, derivative test for convexity. F. Integral. Riemann integral. The method of exhaustion. The area of regions between two graphs. Mean value theorems for integrals. Indefinite integrals. Fundamental theorem of integral calculus. Integration by substitution (elementary integrals). 