# Gestione e Valorizzazione delle Risorse Agrarie e delle Aree Protette | MATHEMATICS AND PHYSICS

## Gestione e Valorizzazione delle Risorse Agrarie e delle Aree Protette MATHEMATICS AND PHYSICS

 0712200047 DIPARTIMENTO DI FARMACIA EQF6 GESTIONE E VALORIZZAZIONE DELLE RISORSE AGRARIE E DELLE AREE PROTETTE 2020/2021

 OBBLIGATORIO YEAR OF COURSE 1 YEAR OF DIDACTIC SYSTEM 2016 PRIMO SEMESTRE
 SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY 1 ELEMENTI DI MATEMATICA MODULO DI MATEMATICA E FISICA MAT/04 3 21 LESSONS BASIC COMPULSORY SUBJECTS 2 FISICA MODULO DI MATEMATICA E FISICA FIS/07 6 42 LESSONS BASIC COMPULSORY SUBJECTS
 FAUSTO ACERNESE21
Objectives
THE FIRST UNIT OF THE COURSE AIMS TO PROVIDE THE ACQUISITION OF BASIC TOOLS OF MATHEMATICS AND GEOMETRY WHICH ALLOW TO FACE MATHEMATICAL PROBLEMS AND TO STUDY THE APPLICATION OF MODELS BASED ON MATHEMATICAL STRUCTURES.
THE SECOND UNIT OF THE COURSE AIMS TO PROVIDE THE KNOWLEDGEMENT OF THE MAIN PHYSICAL MODELS AND HYPOTHESIS ON WHICH SUCH MODELS ARE FOUND; ABILITY TO APPLY THESE MODELS IN REAL CASES RELATING TO AGRICULTURE.

KNOWLEDGE ACQUIRED:
- BASIC TOOLS OF CALCULUS AND GEOMETRY
- BASIC KNOWLEDGE OF THEORETICAL CLASSICAL PHYSICS AND HYPOTHESIS ON WHICH SUCH MODELS ARE FOUNDED;

THE MAIN SKILLS ACQUIRED ALLOW STUDENTS:
- TO FACE A MATHEMATICAL PROBLEM SELECTING PROPER TOOLS;
- ABILITY TO APPLY BASIC MODELS IN CASES REAL, TO ASSESS THE RELIABILITY OF RESULTS OBTAINED IN CONNECTION WITH MEASUREMENT ERRORS;
- CAPABILITY TO REFORMULATE THE CONCEPTS EVEN IN DIFFERENT CONTESTS.
Prerequisites
IT IS REQUIRED THE KNOWLEDGE OF BASIC CONCEPTS OF MATHEMATICS.
Contents
UNIT I: MATHEMATICS (3 CFU)
COMBINATORIX. REAL NUMBERS. PRIMARY FUNCTIONS. FIELD OF EXISTENCE AND GRAPHICS OF REAL VARIABLE. THE FUNCTIONS POWER N-MA, ROOT N-MA, POWER WITH REAL EXPONENT, EXPONENTIAL, LOGARITHMIC, TRIGONOMETRIC (SINE, COSINE, TANGENT AND COTANGENT). OPERATIONS ON LIMITS AND THEIR PROPERTIES. PROPERTY ON CONTINUOUS FUNCTIONS. DISCONTINUITY. INCREASING AND DECREASING FUNCTIONS. DERIVATIVES AND DIFFERENTIALS OF THE FUNCTIONS OF A VARIABLE. DERIVATIVE OF ELEMENTARY FUNCTIONS. DERIVATIVES OF COMPOSITE FUNCTIONS. FORMULA AND RULES OF DERIVATION. THEOREMS : ROLLE, LAGRANGE AND OF DE L'HOSPITAL. ASYMOPOTES. MAXIMUM, MINIMUM AND INFLECTIONS. STUDY OF A FUNCTION GRAPH. THEOREMS, RULES AND PROPERTY OF INTEGRATION. INDEFINITE INTEGRAL IMMEDIATE.

UNIT 2: PHYSICS (6CFU):
INTRODUCTION TO PHYSICS: PHYSICAL QUANTITY, UNIT MEASUREMENT SYSTEMS, MEASUREMENT ERRORS, VECTORS. VELOCITY AND ACCELERATION. STUDY OF ONE DIMENTIONAL AND BIDIMENTIONAL MOTIONS. PRINCIPLES OF DYNAMICS. CONCEPT OF FORCE AND ITS APPLICATIONS. WORK, MECHANICAL ENERGY AND ITS CONSERVATION. MOMENTUM AND ITS CONSERVATIONS. DYNAMICS OF PARTICLE SYSTEMS. SOLID BODY DYNAMICS. (2,5CFU)
PRESSURE, STATIC AND DYNAMICS OF IDEAL FLUIDS: STEVINO LAW, ARCHIMEDE LAW, PRINCIPLE OF PASCAL, EQUATION OF CONTINUITY AND THEORY OF BERNOULLI. VISCOSITY AND REAL FLUIDS. SEDIMENTATION AND CENTRIFUGING. SUPERFACE PRESSURE, LAPLACE LAW, BAGNESSABILITY, CAPILLARY. DIFFUSION AND OSMOSIS. (2CFU)
TEMPERATURE AND HEAT. HEAT TRANSMISSION. PRINCIPLES OF THERMODYNAMICS AND THEIR APPLICATIONS TO IDEAL GAS. COULOMB FORCE, ELECTRIC FIELD. DIELETRICS AND POLARIZATION. ELECTRIC POTENTIAL, ELECTRIC CURRENT, OHM LAW. MAGNETIC FIELD, LORENTZ FORCE, MAGNETIZATION. INDUCTION FENOMENA. INTERPRETATION OF THE MAXWELL LAWS, THE ELECTROMAGNETIC SPECTRUM. (1,5CFU)
Teaching Methods
THE TWO UNITS ARE BASED ON 63 HOURS OF CLASS LECTURES: 21 HOURS OF MATHEMATICS AND 42 OF PHYSICS.
THE TWO UNITS INCLUDE THEORETICAL LECTURES AND PRACTICAL LECTURES (MAINLY BASED ON EXERCISES AND CASE STUDIES).

Verification of learning
THE ACHIEVEMENT OF THE OBJECTIVES OF THE TEACHING IS CERTIFIED BY EXCEEDING AN EXAMINATION (MINIMUM 18/30) THAT IT HAVE TO BE OCCURRED IN THE ROUNDS ESTABLISHED BY THE CALENDAR, COMPOSED BY:
1) A WRITTEN TEST, CONSTITUTED BY 18 QUESTIONS WITH MULTIPLE RESPONSE, SO DIVIDED:
- 6 MATHEMATICAL QUESTIONS (VECTOR CALCULATION, COMBINATORIAL CALCULUS, GEOMETRY, FUNCTIONS, INTEGRAL CALCULATION).
- 12 PHYSICAL QUESTIONS (KINEMATICS, DYNAMICS, FLUID-DYNAMIC AND THERMODYNAMIC).
THE STUDENT WILL HAVE TO ANSWER AT LEAST THREE QUESTIONS OF THE FIRST PART AND AT LEAST SIX QUESTIONS OF THE SECOND PART, A SCORE OF 2 POINTS WILL BE ATTRIBUTED FOR EACH EXACT ANSWER AND A PENALIZATION OF -0.5 FOR EVERY WRONG ANSWER.
THE STUDENT WILL BE ADMITTED TO THE ORAL EXAMINATION IF HE HAS REPORTED A SCORE AT LEAST EQUAL TO 18/30 IN THE WRITTEN TEST. DURING THE WRITTEN TESTING, USE OF THE SCIENTIFIC CALCULATOR IS ADMITTED ONLY. THERE IS A WRITTEN TEST AT THE END OF MATHEMATICS UNIT: IF THE STUDENT HAS PASSED THIS MATHEMATICAL TEST, THERE WILL BE DISCLAIMED FROM THE CORRESPONDING QUESTIONS PRESENTED IN THE WRITTEN TEST OF EXAMINATION.
2) AN ORAL EXAMINATION CONCERNING THE PHYSICS UNIT (AT LEAST FOUR QUESTIONS).
THE FINAL VOTE IS DEFINED CONSIDERING THE SCORE ACHIEVED AT THE WRITTEN TEST AND THE EVALUATION OBTAINED AT THE ORAL EXAM.

AN ADDITIONAL “CUM LADE” MAY BE ATTRIBUTED TO STUDENTS WITH THE MAXIMUM SCORE (30/30) WHO HAVE DEMONSTRATED AUTONOMY AND ABILITY TO FACE MATHEMATICAL AND STATISTICAL PROBLEMS.
Texts
UNIT I:
TOM M.APOSTOL, CALCULUS I,1975 JOHN WILEY & SONS, INC.
UNIT 2:
KESTEN-TAUK, FONDAMENTI DI FISICA, ZANICHELLI; E. RAGOZZINO, PRINCIPI DI FISICA, EDISES;

ADDITIONAL TEACHING MATERIAL: THE PROFESSOR PROVIDES SLIDES CONCERNING THE COURSE SUBJECTS.