9 credits

Mathematical Analysis II

Simona Ranieri 1 semester, 2 Year, 9 credits, Subjects
Mathematical Analysis II
2 YEAR 1 semester 9 CREDITS
Prof. TANIMOTO YOH –
Prof. BUTTERLEY OLIVER JAMES		 2019-20

BUTTERLEY OLIVER JAMES

2020-21 to 2022-23

BUTTERLEY Oliver James – butterley@mat.uniroma2.it
Greenblatt Rafael Leon – greenblattt@mat.uniroma2.it

 2023-24

 

Mathematical Analysis II

Code: 8037950
SSD: MAT/05

OBJECTIVES

LEARNING OUTCOMES:
One learns power series, differential calculus of several variables, line integral, multiple integral and surface and volume integral. One obtains the ability to calculate partial derivatives of elementary and composed functions, calculate various integrals and apply theorems of Green, Gauss and Stokes to facilitate the computations.

KNOWLEDGE AND UNDERSTANDING:
To know the definitions of basic conepts (convergence of series, partial derivatives, extremal points, multiple integral, line integal, surface integral and volume integral) 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.

COURSE SYLLABUS

  • Sequences and series of functions, Taylor series
  • Differential calculus of scalar and vector fields
  • Applications of differential calculus, extremal points
  • Basic differential equations
  • Line integrals
  • Multiple integrals
  • Surface integrals, Gauss and Stokes theorems

Electrical Network Analysis

Simona Ranieri 1 semester, 2 Year, 9 credits, Subjects
Electrical Network Analysis
2 YEAR 1 semester 9 CREDITS
Prof. Vincenzo Bonaiuto

2019-20 to 2022-23
Silvano Cruciani 2023-24
 

silvano.cruciani@uniroma2.it

Code: 8037951

Electrical quantities and SI units. Electrical energy and electrical power. Passive and active sign convention. Passive and active elements. Ideal voltage and current sources. Basic ideal electric components: resistance, inductance, capacitance. Models of real components. Ohm-s law. Series and Parallel connection of components. Topological circuital laws: Kirchhoff’s Voltage Law (KVL) and Kirchhoff’s Current Law (KCL). Mesh Current Method, Node Voltage Method. Sinusoidal functions: average and RMS (Root Mean Square) values.

Sinusoidal steady state circuit analysis. Phasors. Impedance and admittance. Analysis of circuits in AC steady state. Electrical power in the time domain and in sinusoidal steady state: active power, reactive power, complex power. Power factor correction. Maximum power transfer in AC. Application of superposition theorem in circuit analysis. Thevenin’s and Norton’s theorems.

Frequency response: first order electrical filters. Resonance: series and parallel resonant circuits.

Mutual inductance and ideal transformer. Three-Phase systems. Introduction to the power distribution and transportation grid. Time response and transient analysis. The unit step function, unit impulse function, exponential function, first-order circuits. Laplace transform method, Laplace transform of some typical functions, initial-value and final-value theorems, partial-fractions expansions, analysis of circuits in the s-domain. Network functions and circuit stability.

Electrical measurement bridges. Introductions to the electrical safety and electricity distribution system: description and prospects. Basics of designing a power plant. Effects of electricity on the human body and relative protection systems. Introduction to electrical machines: Tranformer and DC motor.

Linear Algebra and Geometry

Simona Ranieri 1 Year, 2 semester, 9 credits, Subjects
Linear Algebra and Geometry
1 YEAR 2 semester 9 CFU
Prof. Paolo Salvatore 2019-20
SALVATORE PAOLO –
LHOTKA CHRISTOPH HEINRICH		 2020-21
Francesca Tovena – tovena@mat.uniroma2.it
Andrea Santi

since 2021-22

Andrea Santi  (6 cfu)- santi@mat.uniroma2.it
Filippo Viviani (3cfu) – viviani@mat.uniroma2.it

 since 2023-24
  Code: 8037949
SSD: MAT/03

OBJECTIVES

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.

COURSE SYLLABUS

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

Simona Ranieri 1 Year, 2 semester, 9 credits, Subjects
Fundamentals of Computing
1 YEAR 2 semester 9 CFU
Flavio Lombardi 2018-19
Enrico Simeoli 2019-20

Walter Liguori

since 2020-21
Gianluca ROSSI 2023-24

Cesare ROSETI

Mauro DE SANCTIS

Tommaso ROSSI

 2024-25
  Code: 8037947
SSD: ING-INF/05

OBJECTIVES

LEARNING OUTCOMES:
The course aims to provide students with knowledge and skills for effectively using computer methodologies and tools in the engineering field, especially for developing algorithms.

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

APPLYING KNOWLEDGE AND UNDERSTANDING:
Acquire the ability to analyze problems and design and implement software artifacts addressing them.
Acquire the capability of a group working on software development and documentation.

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

COMMUNICATION SKILLS:
Be able to describe and document software artifacts correctly and effectively.

LEARNING SKILLS:
Using the technical documentation and the reference manuals of systems, products and languages effectively.

COURSE SYLLABUS

  • “Introduction to the computational method. Von Neumann architecture. Programming languages: assembler, compiled, and interpreted languages. Basic concepts of programming languages: variables; data types and assignment; control structures (loops, conditional selection); basic data structures; input and output. Functions and recursion. Searching and sorting algorithms. Computational complexity. Dynamic data structures: array; linked lists; trees; hash tables. Object-oriented programming.

     

    The programming languages taught are Python and C.”

Fundamentals of Chemistry

Simona Ranieri 1 semester, 1 Year, 9 credits, Subjects
Fundamentals of Chemistry
1 YEAR 1 semester 9 CFU
Prof. Roberto Paolesse 2019-20 to 2020-21
2021-22
PAOLESSE ROBERTO – LVOVA LARISA 2021-22
LVOVA LARISA

2022-23

2023-24
 

larisa.lvova@uniroma2.it

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.