Educational objectives Aim of this module is the achievement, by the students, of the basic means of Mathematical Analysis related to the study of functions of one real variable and their use for the solution of problems in Applied Mathematics, and in particular of Physical and Engineering problems. Special emphasis is devoted to qualitative study and approximate solution of these problems, by virtue of asymptotical techniques, Taylor polynomials etc.
Successful students will be able to study the behavior of numerical sequences and series; to sketch the complete graph of a function of one variable; to develop the Taylor (or MacLaurin) polynomials of functions of one variable; to study the asymptotical behavior of a function when the independent variable approaches infinity or singularities or zeros; to solve optimization problems in one variable, on bounded and unbounded intervals; to solve definite, indefinite and improper integrals; to solve some kinds of ordinary differential equations, characterizing several Physics and Engineering problems.
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Educational objectives The course illustrates the basic principles of object-oriented programming with reference to the Python language.
Attention is paid both to the methodological aspects of software design and to the techniques of information representation and manipulation.
It also intends to provide the student with the knowledge of the technological tools to aid him in programming such as compilers, function libraries, debuggers, etc. For these reasons, the course includes numerous guided exercises to be performed at the computer.
At the end of the course the student will be able to design, implement and test programs of medium complexity in Python.
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Educational objectives The aim of this module is the achievement and the improvement by the students of the basic notions of algbra, geometry and calculus which have been studied during the highschool.
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Educational objectives Basics in linear algebra and geometry. Linear systems and their geometrical interpretation for 2 or 3 unknowns. Familiarity with rigorous reasoning, with numerical and symbolic calculus, with the analysis of problems using an optimal strategy. Familiarity with vectors and matrices, and with geometrical entities in 2 or 3 dimensions in connection with equations of degree 1 or 2. Understanding of linear applications and, in particular, of diagonalization. I expect constant learning as the course goes on; learning will be increased by tutorials and excercises. Little difficulties can be solved also by an email contact. Although the beginning may be difficult, mostly due to faults in the mathematical background, after the first impact one expects a neat improvement.
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Educational objectives The course of Physics I aims to introduce the student to the scientific method. In the first part of the course the student will become familiar with the fundamental principles of classical mechanics and the related physical quantities (force, work, energy); subsequently, he will become familiar with heat and temperature through the first and second laws of thermodynamics, i.e. with the general principles concerning energy conservation and time evolution of physical systems, respectively. Efforts will be made for addressing the student to the realization of models for the solution of physical problems analyzed also in terms of order of magnitude of the physical quantities involved.
Course objectives & learning outcomes.
1) Knowledge and understanding: at the end of the course the student will have to know the principles of classical mechanics and thermodynamics; he will have to master the concepts of force, energy, work, heat and temperature;
2) Applying knowledge and understanding: at the end of the course the student will be able to apply the principles of classical mechanics and thermodynamics to set up the solution of physical problems of medium and low complexity;
3) Making judgements: the student will keep actively involved in lessons and in the solution of exercises through the act of asking question to stimulate critical thinking skills;
4) Communication skills: student’s thinking will be engaged and challenged by focusing on the various methods of problem solving and encouraging the student to supply reasoning for choosing the a specific method;
5) Learning skills: independent learning will be pursued encouraging students to self-monitor to check if the strategies they were using were effective for achieving learning goals
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Educational objectives THE COURSE OF CHEMISTRY HAS A VERY EDUCATIONAL IMPORTANCE FOR ANY FACULTY OF SCIENTIFIC TECHNICAL ADDRESS. THE GENERAL OBJECTIVE IN THIS COURSE IS TO EXPLAIN THE ARGUMENTS OF GENERAL CHEMISTRY, BOTH IN EXPERIMENTAL AND THEORETICAL ASPECTS, TOGETHER WITH THE FOUNDATIONS OF INORGANIC CHEMISTRY. THE STUDENT WILL ACQUIRE THE ABILITY TO INTERCONNECT THE ARGUMENTS TREATING THE PHENOMENA RELATED TO THE BEHAVIOR OF THE MATERIALS DESCRIBED ALSO THROUGH THE PRINCIPLES OF THERMODYNAMICS. A COLLECTIVE TRAINING WILL BE PROVIDED DURING THE COURSE THROUGH WHICH STUDENTS WILL BE ABLE TO DISCUS AMONG THEM RELATIVELY TO WHAT LEARNED UNTIL THAT MOMENT, DEVELOPING IN THIS WAY EVEN COMMUNICATION SKILLS.
THE STUDENT WILL BE MADE IN CONDITION OF UNDERSTANDING AND EVALUATING THE CHEMICAL, THERMODYNAMIC AND STRUCTURE ASPECTS OF THE MATERIALS RELATED TO THE SUCCESSIVE ACADEMIC COURSES.
THE PROGRAM CAN BE STRUCTURED PRINCIPALLY IN 4 MODULES BELOW ILLUSTRATED TOGETHER WITH THE SPECIFIC OBJECTIVES FOR EVERYONE:
1) THE STRUCTURE OF THE MATTER
- ELECTRONIC STRUCTURE OF THE ATOMS AND PERIODIC CLASSIFICATION OF THE ELEMENTS
- CHEMICAL BONDS - MOLECULAR STRUCTURES AND GEOMETRIES
- SUBSTANCES AND STECHIOMETRIC-CALCULATIONS
- OXIDATION STATES OF ELEMENTS AND REDOX REACTIONS
THE STUDENT KNOWS AND UNDERSTANDS THE STRUCTURE OF THE MATERIALS, STARTING FROM THE ATOMS AND PERIODIC CLASSIFICATION OF THE ELEMENTS AND CONSEQUENTLY HE CAN GIVE A PREDICTION ON WHICH TYPE OF CHEMICAL BOND CAN BE FORMED BETWEEN TWO CHEMICAL SPECIES AND WHICH MECHANICAL AND STRUCTURAL PROPERTY THE DERIVING COMPOSITE CAN HAVE. ACCORDINGLY, HE WILL BE ABLE TO PRODUCE, AUTONOMOUSLY, A CLASSIFICATION OF SUBSTANCES ON THE BASIS OF THE CHEMICAL BONDS AND THE PROPERTY CONNECTED TO THEM. THE STUDENT WILL ACQUIRE KNOWLEDGE ABOUT THE CONCEPTS OF STECHIOMETRIC RATIO THAT CHARACTERIZE THE MATTER AND ITS TRANSFORMATIONS AND WILL BE ABLE TO BALANCE ANY CHEMICAL REACTION BY DETERMINING THE QUANTITIES OF THE PRODUCTS KNOWING ALSO THE NON-STECHIOMETRIC QUANTITIES OF THE REAGENTS. HE WILL BE ABLE TO LEARN THE NEXT PART OF THE PROGRAM AND ALL THE CONCEPTS POTENTIALLY PRESENT IN PROGRAMS OF SUBSEQUENT COURSES.
2) THERMODYNAMICS
- STATE OF MATTER AGGREGATION. 1ST AND 2ND PRINCIPLE OF THERMODYNAMICS. PHASE DIAGRAMS.
- CHEMICAL EQUILIBRIUM (VAN T'HOFF EQUATION).
- EQUILIBRIUM BETWEEN DIFFERENT PHASES OF NO CHEMICALLY REAGENT SUBSTANCES (CLAPEYRON EQUATION).
THE STUDENT KNOWS AND UNDERSTANDS THE THERMODYNAMICS APPLIED TO THERMODYNAMIC SYSTEMS AND THROUGH THE FIRST AND SECOND PRINCIPLE OF THERMODYNAMICS HE IS ABLE TO ANALYZE BOTH THE ENERGY EXCHANGES AND TRANSFORMATIONS RESPECTIVELY WITH THE ENVIRONMENT AND INSIDE THE SYSTEM. HE IS, AUTONOMOUSLY, ABLE TO UNDERSTAND THE DIRECTION OF A TRANSFORMATION AND WHICH IS THE MAXIMUM USEFUL WORK EXTRACTABLE FROM ANY REACTIVE SYSTEM. THE STUDENT LEARNS HOW TO ANALYZE, AUTONOMOUSLY THE PHASE DIAGRAMS TO EXTRACT THE THERMODYNAMIC INFORMATION NEEDED TO INTERPRET THE SYSTEM. HE IS ABLE TO CALCULATE THE EQUILIBRIUM COMPOSITION OF A REACTIVE SYSTEM AND TO ANALYZE THE EQUILIBRIUM BETWEEN DIFFERENT PHASES OF NON-REAGENT SUBSTANCES. HE IS ABLE TO LEARN THE NEXT PART OF THE COURSE AS EQUILIBRIUMS IN SOLUTION AND ELECTROCHEMISTRY, AS WELL AS ALL THE CONCEPTS RELATED TO THERMODYNAMICS PRESENT IN THE OTHER SUBSEQUENT COURSE PROGRAMS.
3) IONIC EQUILIBRIUM IN WATER SOLUTION
- SOLUTION PROPERTIES OF NON-ELECTROLYTE AND ELECTROLYTE SOLUTES
- ELECTRICAL CONDUCTIVITY OF ELECTROLYTE SOLUTIONS: SPECIFIC CONDUCTIVITY, EQUIVALENT CONDUCTIVITY AND EQUIVALENT CONDUCTIVITY LIMIT.
- ACID-BASE. SALTS.
- BUFFER SOLUTIONS.
- LOW SOLUBLE ELECTROLYTES: SOLUBILITY AND SOLUBILITY PRODUCT.
THE STUDENT KNOWS AND UNDERSTANDS THE PROPERTIES OF SOLUTIONS OF NON-ELECTROLYTE AND ELECTROLYTE SOLUTIONS AS COLLIGATIVE PROPERTIES, ELECTRICAL CONDUCTIVITY AND ACID-BASE PROPERTIES. HE IS AUTONOMOUSLY ABLE TO REALIZE SOLUTION TITRATIONS, TO CALCULATE THE PH AND TO PRODUCE BUFFER SOLUTIONS TO MAINTAIN CONSTANT THE PH OF A REACTIVE AND NON-REACTIVE SYSTEM. IT IS ABLE TO STUDY AND ANALYZE HETEROGENEOUS CHEMICAL EQUILIBRIUM. ALSO IN THIS CASE HE IS ABLE TO LEARN THE NEXT PART OF THE PROGRAM AND ALL THE CONCEPTS POTENTIALLY PRESENT IN PROGRAMS OF SUBSEQUENT OTHER COURSES.
4) ELECTROCHEMISTRY AND CHEMICAL KINETICS
- CONVERSION OF "CHEMICAL ENERGY" IN "ELECTRIC ENERGY" AND VICEVERSA BY ELECTROCHEMICAL DEVICES.
- NERNST EQUATION. - ELECTROMOTIVE FORCE OF A GALVANIC ELEMENT. -
- ELECTRODIC POTENTIAL AND ELECTRODIC STANDARD POTENTIAL OF A HALF-CELL.
- STANDARD REDOX POTENTIALS TABLE OF REDUCING COUPLE, OXIDING AND REDUCING POWER OF REDOX COUPLES.
- CHEMICAL KINETICS
THE STUDENT KNOWS AND UNDERSTANDS THE PROPERTIES OF ELECTROCHEMICAL SYSTEMS AS PILES AND FUEL CELL OR ELECTROLYZERS CAPABLE OF CONVERTING CHEMICAL ENERGY IN ELECTRIC ENERGY OR VICE-VERSA. HE IS ABLE TO UNDERSTAND AND TO CONCEIVE ELECTROCHEMICAL SYSTEMS BY COUPLING HALF-CELLS BETWEEN THEM IN ORDER TO OBTAIN ENERGY FROM THE RESULTING SYSTEM. IN ADDITION KNOWING THE STANDARD POTENTIALS OF REDOX COUPLES HE IS ABLE TO UNDERSTAND WHETHER A REACTION THROUGH REAGENTS IS POSSIBLE OR NOT. HE KNOWS AND UNDERSTANDS THE BASIS OF CHEMICAL KINETICS. AT THE END OF THE COURSE, HE IS ABLE TO ANALYZE, IN GENERAL, ENERGY SYSTEMS FROM THERMODYNAMIC-KINETIC AND ENERGETIC POINT OF VIEW VALUATING STRENGTHS AND CRITICALITIES.
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Educational objectives The goals consist of a good knowledge of the terminology adopted in the context of Mathematical Analysis.
It is expected that the students will be familiar with the proof techniques, they will have a knowledge of the fundamentals about sequences and serie of functions, Taylor Series, Fourier Series, functions of n real variables, integrals in R^2, R^3, curve, line integrals. differential forms, vector fields, surfaces and integration, complex functions, holomorphy, integration in C, antiderivatives, analytic functions, zeroes and singularities. Laurent series, Laplace Transform.
Crucial achievements are the ability in applying theorems and concepts learned during the course, in developing strategies and methods to solve problems. It is expected to be able to share and communicate information about the topics of the course with a correct formal language, dominating the contents, computing integrals in R^2, R^3, along curves, in the complex plane, along surfaces; making estimates in term of series, detecting critical points of functions of n real variables, expanding regular functions in power series, and periodic ones in Fourier series, solving improper integrals by means of residues, compute Laplace transform and its inverse in basic cases.
It is important to detect the more effective and efficient method for problem solving, also in a way to apply the knowledge to different frameworks than the pure mathematical one.
The learners are expected also to be able to deepen the contents, consulting and using materials other than those offered during the course. It is important the adoption a scientific approach based on the formal evidence and rigorous proofs, devoted to clarify questions also in order to improve general understanding of phenomena.
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