Physics I

Physics I
1 YEAR2 semester12 CREDITS
Maria Richetta2019-20
Code: 8037948


1 – Analyze and interpret motion of particles, systems and rigid bodies and perform calculations relative to the different types of motion (rectilinear, curvilinear, rotational, etc.)
2 – Analyze and interpret the above types of motion in relatively moving inertial refernce frames and perform calculations to switch from one reference frame to another.
3 – Analyze and interpret oscillatory motion, simple, forced and damped harmonic motion, and perform calculations of the: i) horizontal and vertical mass-spring systems, ii) simple pendulum, iii) compound pendulum.
4 – Analyze and interpret wave motion, transverse and longitudinal waves, and wave equations, and perform calculations of transverse waves along a stretched string and of longitudinal waves inside pressurized gases.
5 – Formulate the concepts of superposition and interference; analyze standing waves, sound waves, and the Doppler effect.
6 – Analyze and interpret elementary concept of fluid statics and fluid dynamics, and perform calculations of bouyant forces and of motion of fluids in constricted pipes.
7 – Interpret the concepts of temperature, heat, and phase change, and perform calculations with temperature scales, heat capacity, and specific heat.
8 – Conceptualize the model of the ideal gas, perform calculations using the ideal gas law, and analyze and interpret the kinetic theory of ideal gases.
9 – Interpret the first law of thermodynamics, and calculate and predict work, heat, and internal energy change for various thermodynamic processes.
10 – Interpret the concepts of reversibility, second law of thermodynamics, and entropy, and analyze heat engines, heat pumps and refrigerators.

Students acquire understanding and knowledge of the most important phenomena and physical laws concerning the world around us, at the level in which they operated (Physics 1). The teaching approach provides the foundation for this understanding, based on the use of mathematical methods and on the presentation / explanation of historical and recent experiments and examples taken from everyday life. The most important physical topics are learned in terms of logical and mathematical structure, and experimental evidence. At the end of the course students have assimilated a complete knowledge of the basic themes of classical physics. The methods by which these skills are provided include lectures, tutoring, exercises and knowledge are assessed during exercises, tutoring and final exams.

Physics 1 students are capable to create, describe, refine and use representations and models (both conceptual and mathematical) to communicate scientific phenomena and solve scientific problems. Basically, to make a good model, they have to be able to identify a set of the most important characteristics of a phenomenon or system that may simplify analysis. Since the use of representations is fundamental to model introductory physics, they must know how to realize pictures, motion diagrams, force diagrams, graphs, diagrams, and mathematical representations such as equations, and recognize that representations help in analyzing phenomena, making predictions, and communicating ideas.

The training provided for students in Physics is hallmarked by the acquisition of a flexible mentality that helps them to extend the knowledge learned to new concepts, enabling them to introduce elements of innovation. They are capable of assessing orders of size for the physical quantities relevant to the system under study. These activities encourage students to develop their independence of judgement. They become capable to pose, refine and evaluate scientific questions, being an important instructional and cognitive goal. Even within a simple physics topic, posing a scientific question is mandatory.

Students develop the ability to present what they have learnt during the course with clarity, and likewise additional knowledge acquired from textbooks. They are expected to present their knowledge effectively. This skill, which concerns both oral and written presentations, should be based on the capability for analysis and integration of areas of knowledge developed during the course. They necessarily develop a positive attitude to group work.
Assessment of the attainment of written and oral communication skills is performed during classroom exercises, tutoring and through written and oral exams at the end of the course.

Physics 1 students learn how to work with scientific explanation and theories, justify claims with evidence, articulate the reasons that scientific explanations and theories are refined or replaced, evaluate scientific explanations.
On these bases they connect and relate knowledge across various scales, concepts, and representations “in” and “across” domains. For example, after learning the concepts of conservation law in the context of mechanics, students will describe what the concept of conservation means in physics and extend the idea to other context.
This will be assessed by exercises, during tutoring time and exams at the end of the course.


• INTRODUCTION – Measurement. Fundamental quantities and units. Plane angle. Solid angle. Direction. Scalars and vectors. Components. Scalar and vector products. Vector representation of the area. Forces. Composition of concurrent forces. Torque. Torque of concurrent forces. Coplanar forces. Parallel forces.
• KINEMATICS – Rectilinear motion: velocity, acceleration. Curvilinear motion: velocity, acceleration. Motion under constant acceleration (tangential and normal components). Circular motion: angular velocity, angular acceleration. General curvilinear motion.
• RELATIVE MOTION – Relative velocity. Uniform relative translational motion. Uniform relative rotational motion. Motion relative to the earth. Transformation of velocities.
• DYNAMICS OF A PARTICLE – Introduction. The law of inertia. Linear momentum. Principle of conservation of momentum. Dynamic definition of mass. Newton’s second and third laws: the concept of force. Unit of force. Frictional force. Frictional force in fluids. System with variable mass. Curvilinear motion. Angular momentum. Central forces. Equilibrium and rest.
• WORK AND ENERGY – Work. Power. Units of work and power. Kinetic energy. Work of a force constant in magnitude and direction. Potential energy. Conservation of energy of a particle. Rectilinear motion under conservative forces. Motion under conservative central forces. Discussion of potential energy curves. Non-conservative forces.
• DYNAMICS OF A SYSTEM OF PARTICLES – Motion of the centre of mass. Reduced mass. Angular momentum of a system of particles. Kinetic energy of a system of particles. Conservation of energy of a system of particles. Collisions.
• DYNAMIC OF A RIGID BODY – Angular momentum of a rigid body. Moment of inertia. Equation of motion for rotation of a rigid body. Kinetic energy of rotation.
• OSCILLATORY MOTION – Kinematics of simple harmonic motion. Force and energy in simple harmonic motion. Dynamics of simple harmonic motion. The simple pendulum. Compound pendulum. Superposition of two simple harmonic motions. Coupled oscillators. Anharmonic oscillations. Damped oscillations. Forced oscillations.
• MECHANICS OF FLUIDS – Pressure. Variation of pressure with depth. Pressure measurements. Buoyant forces and Archimedes’ Principle. Fluid dynamics: Bernoulli’s Equation. Applications of fluid dynamics.
• MECHANICAL WAVES – Propagation of disturbance. Sinusoidal waves. The speed of waves on strings. Reflection and transmission. Rate of energy transfer. The linear wave equation. The speed of sound. Periodic sound waves. Intensity. The Doppler Effect. Superposition and interference. Standing waves in strings. Resonance. Standing waves in air column. Beats.
• THERMODYNAMICS – Temperature and the Zeroth Law of thermodynamics. Thermometer. Celsius Scale. Gas thermometer. Absolute temperature scale. Macroscopic description od ideal gases. Heat and internal energy. Specific heat. Latent heat. Work and heat. The First Law of thermodynamics. Applications of the First Law. Energy transfer mechanism. The kinetic theory of gases: molecular model Molar specific heat. Adiabatic processes. Equipartition of energy. The Boltzmann Distribution Law. The Second Law of thermodynamics. Heat engines. Pumps and refrigerators. Reversible and irreversible processes. The Carnot engine. Entropy. Entropy changes in irreversible processes. Entropy on macroscopic scale.

Linear Algebra and Geometry

Linear Algebra and Geometry
1 YEAR2 semester9 CFU
Prof. Paolo Salvatore2019-20
Francesca Tovena2021-22
Code: 8037949


LEARNING OUTCOMES: The course provides an introduction to linear algebra and euclidean geoemetry.

KNOWLEDGE AND UNDERSTANDING: The student will learn to solve simple geometric and algebraic problems using the tools provided by the course.

APPLYING KNOWLEDGE AND UNDERSTANDING: Ability to apply knowledge and understanding to concrete problems.

MAKING JUDGEMENTS: The student will learn how to interpret the data of an algebraic or geometric problem without following standard schemes.

COMMUNICATION SKILLS: The student will show, esapecially during the oral exam, her/his ability to describe the logical process that yields the theorems studied in the course.

LEARNING SKILLS: The student will learn to understand the exercises of the written exams, and to develop a method to solve them.


Linear equations and linear systems. Solutions. Consistency of a system. Basic and free variables. Matrix of coefficients. Augmented matrix. Row reduction to echelon matrix. Exercises on linear systems. Numerical vectors. Addition and multiplication by scalars. Linear combinations. Linear systems and vectors. Linearly independent vectors. Finding subsets of linearly independent vectors. Linear systems in matrix form. Exercises on linear systems in vector form. Canonical basis. Linear space. Basis and coordinates of vectors. Steinitz lemma. Dimension of linear spaces. Rank of a matrix. Linear spaces of rows and columns of a matrix. Null space of a matrix. Matrix transformations. Injectivity, surjectivity and rank. Linear transformations and matrices. Multiplication and addition of matrices and their linear transformations. Invertible matrices. Computing the inverse via row reduction Change of coordinates and matrices Vector (linear) spaces. Examples of polynomials and matrices. Linear subspaces. Intersection of linear subspaces. Sum of linear subspaces. Grassmann formula. Basis for intersections and sums of linear spaces. Determinants: definition, properties, computation. Computation of the rank using determinants. Computation of the inverse matrix using determinants. Determinant of a product. Cramer’s formula. Linear transformation between vector spaces. Image and kernel. Matrix of a linear transformation with respect to basis of the domain and of the range. Lines in the plane and in 3-dim. space. Planes in the 3-dim. space. Cartesian and parametric equations. Lines through 2 points. Plane through 3 non collinear points. Relative position of two planes. Relative position of two lines in 3-dimensional space. Inner product. Norm. Distances. Orthogonal vectors, lines, planes. Angles. Cross product in 3-dim. space. Mixed product. Area of parallelogram. Volume of parallelepiped. Eigenvalues and eigenvectors. Characteristic polynomial. Algebraic and geometric multiplicities. Diagonalization of endomorphisms and matrices. Orthogonal subspaces, orthonormal basis, orthogonal matrices.
Gram-Schmidt orthonormalization. Formula for the orthogonal projection. Matrix of orthogonal projections. Spectral theorem for symmetric matrices. Quadratic forms and their classification.Conic curves: classification Rotations and translations that put a conic in normal form.

Fundamentals of Computing

Fundamentals of Computing
1 YEAR2 semester9 CFU
Flavio Lombardi2018-19
Enrico Simeoli 2019-20
Code: 8037947


The course aims to provide students with knowledge and skills for an effective use of computer methodologies and tools in the field of engineering, expecially for the development of algorithms.

Acquire knowledge of the internals of computer architectures.
Acquire knowledge on data structures and algorithms.
Acquire knowledge on the principles of programming languages, including the object-oriented paradigm, and on tools and techniques for software development.

Acquire ability to analyze problems and produce a design and implementation of software artifacts addressing them.
Acquire capability of group working on software development and documentation.

Being able to choose appropriate languages and tools for software development.
Being able to evaluate the correctness and efficiency of a software implementation.

Be able to describe and document software artifacts correctly and effectively.

Being able to use effectively the technical documentation and the reference manuals of systems, products and languages.


  • Introduction to Computer Science; Von Neumann architecture; Computer Architectures; CPU and GPU; Programming Paradigms; Functional and Object Oriented Approaches; Principles of Software Engineering and Modeling; Basic concepts and comparison of Programming Languages; Variables; Control structures (Loops, Conditional Selection), Data structures and algorithms; Computational Complexity; Functions and parameters; Recursion; Sorting algorithms; Input/Output; Concurrency and Parallelism; Networking and Distributed Applications; Version Control; The Art of Documentation; Introduction to Safety, Security and Reliability concepts.
  • The programming languages taught are C, Java and Rust

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
Code: 8037944

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.

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

To Identify the theorems and techniques to apply to the given problems and execute computations correctly.

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.

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

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


– 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
Code: 8037945

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.

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.

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.

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

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.

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


  • 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.

International English for Scientific Studies

International English for Scientific Studies
Prof. Carlotta Dell’Arte 2019-20
Code: 8038849

The course aims at (i) providing 1st year international students with the language skills, critical thinking and learning strategies required to attend a University degree held in English (ii) providing students with the basic vocabulary in the field of mathematics, physics and chemistry (iii) providing students with the basic knowledge in Academic English (iv) raise students’ awareness on English as a Global Language and English as a Lingua Franca (v) developing students’ listening and reading skills.

By the end of the course, students will able to (i) recognise specific vocabulary in the fields of maths, physics and chemistry (ii) have a general understanding of spoken and written texts on engineering and science (iii) recognise different pronunciations of English (iv) interact appropriately with administrative staff and professors.

By the end of the course, students will be able to (i) use specific vocabulary accordingly (ii) identify key ideas and supporting ideas in spoken and written texts (iii) discuss the contents analysed in the texts (iv) address administrative staff and professors appropriately.

By the end of the course, students will be able to (i) assess the coherence of spoken and written texts (ii) classify key ideas and supporting ideas (iii) make conclusions and deduce implications.

By the end of the course, students will be able to (i) summarise key ideas of a text (ii) highlight the logical reasoning behind a test (iii) use specific vocabulary in the field of maths, physics, chemistry and engineering.

By the end of the course students will be able to (i) use online language resources efficiently (ie. dictionaries, word references) (ii) search for and assess new online language resources.

Students are required to have a B1+ level of English to attend the course.
Students who do not have that level, would need to prepare individually in order to attend the course effectively.
Students may use the book below for personal study: Murphy R., English Grammar in Use, with answers, Intermediate, Fourth Edition, Cambridge University Press.

  • English as a Global Language and English as a Lingua Franca
  • Implications of English language learners
  • Native Speakers and Non-Native Speakers
  • Phonology and Phonetics of English as an International Language
  • Register (formal, informal, neutral, colloquial)
  • Specific vocabulary: maths, physics, chemistry, engineering, academic English, communications, statistics and social sciences
  • Summary writing, for and against essays, opinion essay and abstract

Engineering Economics

Engineering Economics
1 YEAR1 semester6 CFU
Prof.ssa Elisa Battistoni 2019-20
Code: 8037946


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 of the topics of the course will be developed mostly through active participation to didactic activities during classes.

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.

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, 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 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.


• 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.