Mathematical Analysis I

Mathematical Analysis I
1 YEAR 1 semester 12 CFU
Prof. Fabio Ciolli e Prof. Roberto Longo 2018-19
Prof. Sebastiano Carpi 2019-20
TANIMOTO YOH 2020-21
2021-22
Code: 8037944
SSD: MAT/05

LEARNING OUTCOMES:
One learns real numbers, limits and continuity of functions, derivative of functions, their properties and examles, Taylor series and some applications, Riemann integral, complex numbers, real numerical series and separable differential equations. One obtains the ability to calculate various limits, derivatives and integrals of functions, to discuss the convergence numerical series and improper integrals, and solve separable differential equations.

KNOWLEDGE AND UNDERSTANDING:
To know the definitions of basic conepts (limit, continuity, derivative, integrale, convergence of series, differential equations) and apply various theorems to execute concrete computations.

APPLYING KNOWLEDGE AND UNDERSTANDING:
To Identify the theorems and techniques to apply to the given problems and execute computations correctly.

MAKING JUDGEMENTS:
To understand mathematical concepts for the given problems and to divide them into smaller problems that can be solved with the knowledge obtained during the course.

COMMUNICATION SKILLS:
To frame the problems in the obtained concepts, express the logic and general facts that are used during the computations.

LEARNING SKILLS:
To know precisely basic mathematical concepts and apply them to some simple examples in physics.

PROGRAMME:

– real numbers
– sequences of real numbers and their limits
– real functions of one real variable
– limits and continuity of functions
– properties of continuous functions
– differentiability and first derivative
– properties of derivative
– higher order derivatives and Taylor series
– Riemann integral
– fundamental theorem of calculus
– real numerical series
– seprable differential equations

Fundamentals of Chemistry

Fundamentals of Chemistry
1 YEAR1 semester9 CFU
Prof. Roberto Paolesse 2019-20
2020-21
PAOLESSE ROBERTOLVOVA LARISA 2021-22
Code: 8037945
SSD: CHIM/07

LEARNING OUTCOMES:
To provide students with basic chemical skills, in order to facilitate the understanding of the subsequent class of the course. To provide a solid basic knowledge of chemistry, preparatory to the understanding of a wide range of phenomena. To provide the tools for a proper interpretation of matter and its transformations, both at a microscopic (atomic/molecular) and macroscopic (phenomenological) level.

KNOWLEDGE AND UNDERSTANDING:
At the end of the lectures, the student must have acquired the knowledge necessary to understand and apply general chemistry concepts, in particular concerning reactivity and structure of matter in its different states of aggregation, with specific regard to relevant issues of Engineering Science. The acquired skills will be employed by the student to carry out more advanced studies.

APPLYING KNOWLEDGE AND UNDERSTANDING:
At the end of the teaching period the student must have matured the ability to apply the theory of basic chemistry to the resolution of exercises and problems, with specific reference to engegneering science.

MAKING JUDGEMENTS:
Judgment skills are developed through individual or group works. The student will have to self-evaluate (self assessment-test) and compare with colleagues.

COMMUNICATION SKILLS:
At the end of the teaching sessions the student will be able to use a rigorous chemical language, both in written and oral form, together with the use of graphic and formal languages to represent the descriptive models of the matter.
Inoltre lo studente avrà la possibilità di dimostrare di saper operare efficacemente nel gruppo di pari utilizzando supporti informatici per raccogliere e divulgare informazioni.
In addition, the student will have the opportunity to demonstrate that he / she can work effectively in the peer group using IT support to collect and disseminate information.

LEARNING SKILLS:
At the end of the teaching sessions the student will be able to understand and predict the outcome of the most common inorganic reactions, as well as correlate structure-reactivity properties of the fundamental inorganic compounds and of selected simple organic molecules

COURSE SYLLABUS

  • The scientific method. Elements and compounds. Chemical formulas. The balancing of chemical reactions. Chemical nomenclature (notes). Stoichiometric calculations. The principal chemical reactions. Atomic Theory. Sub-atomic particles. Isotopes. Quantum Theory. Particles and waves. Quantum numbers. Atomic orbitals. Pauli and Hund principles. Electronic structures of atoms. The periodic system and periodic properties.
  • Chemical bonds. Ionic and covalent bonds. Valence bond theory: hybridization and resonance. Determinationof meolecular structuresbased on the repulsion of the valence electron pairs (VSEPR). Molecular orbitals theory (LCAO-MO). Application of MO theory for homo- ed heteronuclear diatomic molecules of the I and II period. Dipolar interactions. Hydrogen bond. Metallic bond. Band theory. Structure and conductivity.
  • Solid state. Crystal and amorphous solids. Metals. Ionic crystals and lattice energy. Insulators and semiconductors.
  • The gaseous state. Ideal gas laws. Ideal gas equation. Dalton law. Real gases: van der Waals equation.
  • First principle of thermodynamics. State functions: Internal Energyand Enthalpy. Thermochemistry. Hess law. Secondand third principleofthermodynamics. Entropyand Free Energy. Equilibrium and spontaneity criteria. Molar free energy: activityand standard states.
  • Vapour pressure. Clapeyron equation.
  • Solutions: Phase equilibria. State diagrams. Fractional distillation.Colligative properties for ideal solutions.
  • Chemical equilibrium: Le Chatelier principle. Equilibrium constant. Law of mass action. Gaseous dissociation equilibria.
  • Electrolytic systems: electrolytic dissociation equilibria, electric conductivity. Colligative properties of electrolytic solutions. Low soluble electrolytes: solubility product.
  • Acid-base equilibria. Autoionizationof water: pH. Monoprotic and polyprotic acids and bases. Buffer solutions. Indicators. Titrations. pH dependent solubility.
  • Chemical kinetics: Chemical reactions rate, activation energy, catalysis.
  • Red-ox systems: electrode potentials. Galvanic cells: Nernst equation. Electrolysis: Faraday law; electrode discharge processes.
  • Electrochemical applications: Fuel cells, batteries. Metal corrosion.
  • Nuclear Chemistry. Notes of Organic chemistry. Polymers.

Engineering Economics

Engineering Economics
1 YEAR1 semester6 CFU
Prof.ssa Elisa Battistoni 2019-20
BATTISTONI ELISA 2020-21
Code: 8037946
SSD: ING-IND/35

OBJECTIVES

LEARNING OUTCOMES
The aim of the course is to provide students with basic knowledge about microeconomic models (demand and supply functions, market structures, consumers and producers’ choices, perfectly competitive markets and monopolistic markets), as well as about investment analysis (comparison and choice between investment alternatives, basing on the most used parameters like Present Worth, Internal Rate of Return and payback period).

KNOWLEDGE AND UNDERSTANDING
Knowledge and understanding of the topics of the course will be developed mostly through active participation to didactic activities during classes.

APPLYING KNOWLEDGE AND UNDERSTANDING
The ability of applying knowledge and understandings is developed by encouraging active participation of students to classes, by questioning students during classes, by flipped classroom situations and by facilitating educational conversations.

MAKING JUDGEMENTS
The ability of making judgments on the topics of the course will be developed through theoretical and practical classes and by involving students in analysing the results obtained in simulations and exercises.

COMMUNICATION SKILLS
Communication skills, acquired knowledge and ability to make judgments on the topic of the course will be tested through the exam. During exams, students will face theoretical as well as practical questions.

LEARNING SKILLS:
Learning skills will be sustained by the teacher with the possibility of having appointments in which students can ask questions to solve doubts – both theoretical and practical – coming from individual study.

COURSE SYLLABUS

Microeconomics
• use of microeconomic theory; positive and normative economic analysis; why to study microeconomics; what is a market
• market mechanism; demand and supply curves; elasticity, both in the short and in the long run
• consumer’s preferences, utility function, budget line and consumer’s optimal choice
• production function, production isoquant, production in the short and in the long run
• cost structures in the short and in the long run and their determinants, optimal production choice
• profit maximization, marginal revenues and marginal costs, conditions for a perfectly competitive market
• average and marginal revenues in a monopolistic market, production decision making in a monopolistic market

Investment analysis
• time value for money, interest and interest rate, simple and compound interests
• nominal and effective interest rates
• economic equivalence and financial factors
• difference between investments and loans, investment projects, investment alternatives
• the “not to invest” alternative and the MARR
• choice between investment alternatives: PW, AE, FW, IRR, payback period

Lecture notes and practical classes are integral part of the program, as well as elements coming from discussions during classes.
Please note that lecture notes do not cover all the program, but are meant to integrate and complete what is explained on suggested textbooks.