Polytechnic Institute of Coimbra (P COIMBRA 02) Coimbra Institute of Engineering  ISEC Electrical Engineering Department ECTS CATALOGUE


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1 Polytechnic Institute of Coimbra (P COIMBRA 02)  ISEC Department ECTS CATALOGUE The main language of instruction at is Portuguese. However, some courses from degree and master programs can be offered in English and/or with a tutorial support in English. During the 1 st semester, the interested students have the opportunity to attend Portuguese Subject Língua e Cultura Portuguesa with 6 ECTS. At the begging of each semester, students can also enroll the EILC Course from IPC. The ECTS catalogue includes subject contents in English. The Students can choose subjects from this Catalogue to the study plan proposal (Learning Agreement) to be analyzed carefully by the Departmental Coordinators and to be adjusted if necessary. This ECTS catalogue contains information which is valid for this academic year. ISEC reserves the right to adjust the courses offered during the academic year and is not responsible for typing errors or printing mistakes. Ms Dália Pires International Relations Office Rua Pedro Nunes Quinta da Nora Coimbra PORTUGAL Tel.: (+351) Prof. Marina Perdigão Department Coordinator Rua Pedro Nunes Quinta da Nora Coimbra PORTUGAL Tel.: (+351) Academic Year
2 Polytechnic Institute of Coimbra (P COIMBRA 02)  ISEC Department ECTS CATALOGUE BACHELOR  Code Title  Portuguese Title  English ECTS Duração 1.º ano / 1 st Year Análise Matemática I Calculus I 6 1º Semester Álgebra Linear Linear Algebra 5 1º Semester Medidas e Instrumentação Instrumentation and Measurement 5 2º Semester Electrotecnia II Electrical Circuit Theory II 5 2º Semester Programação de Computadores Computer Programming 5,5 2º Semester Sistemas Digitais Digital Electronic Systems 5 2º Semester Matemática Aplicada à Electrotecnia Mathematics Applied to 4,5 2º Semester Análise Matemática II Calculus II 5 2º Semester Aplicacionais para a Engenharia Software Tools for Engineering 4 1º Semester Electrotecnia I Electrical Circuit Theory I 5,5 1º Semester Introdução à Programação Introduction to Programming 5 1º Semester Física Geral General Physics 4,5 1º Semester 2.º ano / 2 nd Year Electrónica Electronics I 6,5 2º Semester Sistemas de Energia Eléctrica Electrical Power Systems 5,5 2º Semester Instalações Eléctricas Electrical Installations I 5,5 2º Semester Teoria dos Sistemas Theory of Systems 6,5 1º Semester Máquinas Eléctricas Electrical Machines I 6,5 2º Semester Introdução aos Sistemas de Comunicação Introduction to Communication Systems 6,5 1º Semester Electromagnetismo Electromagnetism 5,5 1º Semester Probabilidades e Estatística Probability and Statistics 5 1º Semester Automação Industrial e Robótica Industrial Automation and Robotics 6 2º Semester Microprocessadores Microprocessors 6,5 1º Semester 3.º ano / 3 rd Year  Ramo de Sistemas de Energia / Specialization in Power Systems Projecto de Instalações Eléctricas Design of Electrical Installations 6 1º Semester Electrónica de Potência Power Electronics 6 1º Semester Complementos de Máquinas Eléctricas Electrical Machines II 6 1º Semester Produção de Energia Eléctrica Electrical Power Generation 6 1º Semester Análise de Sistemas Eléctricos Power Systems Analysis 6 1º Semester Organização e Gestão de Empresas Business Planning and Management 5,5 2º Semester Gestão de Energia Energy Management 6 2º Semester Qualidade de Serviço em Sistemas de Energia Eléctrica Electric Power Systems Quality 5,5 2º Semester Accionamentos Electromecânicos Electromechanical Drives 6 2º Semester Projecto de Sistemas de Energia Eléctrica Electrical Power Systems Project 7 2º Semester Organização e Gestão de Empresas Business Planning and Management 5,5 2º Semester Gestão de Energia Energy Management 6 2º Semester Qualidade de Serviço em Sistemas de Energia Eléctrica Service Quality in Electrical Power Systems 5,5 2º Semester 3.º ano / 3 rd Year  Ramo de Automação / Specialization in Automation Projecto de Instalações Eléctricas Electrical Installations II 6 1º Semester Electrónica de Potência Power Electronics 6 1º Semester Complementos de Electrónica Electronics II 6 1º Semester Complementos de Máquinas Eléctricas Electrical Machines II 6 1º Semester Controlo de Sistemas Systems Control 6 1º Semester Organização e Gestão de Empresas Business Planning and Management 5,5 2º Semester Gestão de Energia Energy Management 6 2º Semester Redes Locais e Industriais Local and Industrial Networks 6 2º Semester Manutenção e Controlo de Qualidade Maintenance and Quality Control 5,5 2º Semester Projecto de Automação Automation Project 7 2º Semester 3.º ano / 3 rd Year  Ramo de Electrónica e Telecomunicações / Specialization in Electronics and Telecommunications Projecto de Instalações Eléctricas Electrical Installations Design 6 1º Semester Electrónica de Potência Power Electronics 6 1º Semester Complementos de Electrónica Electronics II 6 1º Semester Processamento de Sinal Signal Processing 6 1º Semester Comunicação Analógica e Digital Analog and Digital Communication 6 1º Semester Organização e Gestão de Empresas Business Planning and Management 5,5 2º Semester Sistemas de Telecomunicações Telecommunication Systems 6 2º Semester Redes Locais e Industriais Local and Industrial Networks 6 2º Semester Propagação e antenas Propagation and Antennas 5,5 2º Semester Projecto de Electrónica e Telecomunicações Electronics and Telecommunications Project 7 2º Semester Organização e Gestão de Empresas Business Planning and Management 5,5 2º Semester Academic Year
3 Licenciatura em Engenharia Electrotécnica/Degree in Title Linear Algebra Code: Scientific Area: Mathematics Course: Term/Semester: 1 st /1st ECTS: 5 Department: Physics and Mathematics Instructor: Paulo Alexandre Mendes Martins Rosa Study plan: 1. Matrices and Linear Systems Introduction; Matrix operations and their properties; Row echelon form and rank; Classification and geometry of linear systems; Gaussian elimination; Homogeneous systems; Matrix inversion: GaussJordan method; 2. Determinants Definition and properties; Cramer s rule. 3. Linear Spaces Definition, Examples and Properties; Subspaces; Linear combinations; Linear expansion; Linear independence; Basis and dimension. 4. Eigenvalues Eigenvalues, eigenvectors and their properties; Diagonalization; CayleyHamilton Theorem. Language Portuguese Type of instruction: Activities Total Hours Hours/week Comments Theoretical 28 2 Practical: 28 2 Tutorial guidance Learning objectives: Perform basic matrix operations. Compute matrix determinants, eigenvalues and eigenvectors. Understand and apply concepts related to vector spaces. Solve and interpret linear systems using matrix theory. Understand the importance of linear algebra and analytic geometry in engineering. Recognize the importance of the algorithms in linear algebra. Solve real problems which are modelled by matrices and systems.
4 Licenciatura em Engenharia Electrotécnica/Degree in Generic learning outcomes and competences: Develop algorithms using a logical and structured reasoning. Base problem solving on mathematics. Compare, with criticism, the results obtained by analytical means with the ones obtained by computational means. Select appropriately the accessible information (from monographs, textbooks, web, ). Expose, using documents, the problems solution in a clear and simple way. Explain the concepts and problems solution in an appropriated way. Solve practical problems with autonomy using, not only the subjects treated in the class, but also other related topics. Bibliography: ANTON, H.  Elementary Linear Algebra, John Wiley & Sons, Inc, ISBN13: Progress assessment: CABRAL, I., PERDIGÃO, C. e SANTIAGO, C., Álgebra Linear Teoria, Exercícios resolvidos e Exercícios propostos com soluções, Escolar Editora, ISBN CARREIRA, A. ; PINTO, G. Cálculo Matricial Teoria Elementar, Ciência e Técnica, ISBN FIDALGO, C.  Álgebra Linear, Instituto Superior de Engenharia de Coimbra GRAHAM, A.  Matrix Theory and Applications for Engineers, Ellis Horwood Limited, ISBN13: JAMES, G.  Modern Engineering Mathematics, Prentice Hall, ISBN13: PINTO, G.; MONTEIRO, A.; MARQUES, C. Álgebra Linear e Geometria Analítica. Problemas e Exercícios, McGrawHill, ISBN13: NICHOLSON, W. Elementary Linear Algebra with Applications, PWS Publishing Company, ISBN13: SANTANA, A.; QUEIRÓ, J.  Álgebra Linear e Geometria Analítica, Departamento de Matemática, Universidade de Coimbra (2003). Available online (Setember, 2009) at Continuous evaluation: small tests and or quizzes (20%) + final written exam (80%). OR Final written exam (100%).
5 Licenciatura em Engª Electrotécncia / Degree in Title Code: Scientific Area: Course: Year/Semester: ECTS: 5 Department: Instructor: Introduction to Programming 1st /1st Verónica Vasconcelos, MSc; Adelino Pereira, MSc; João Ferreira, Msc; Frederico Santos, Msc Study plan: Basic computer architecture; Programming developing cycle: algorithm, compilation and debugging; Main programming paradigms; Basic C programming language concepts; Structure of a program; Primitive data types, variables, constants and elementary operators; Input and output functions; Control structures; Structured programming: functions; Pointers; Arrays: one dimension and multidimensional, strings; Introduction to Object Oriented Languages; Application Examples. Language Portuguese and English Type of instruction: Activities Total Hours Hours/week Comments Theoretical 28 2 Classroom, Lectures Theoretical Practical Work / Work Group Practical: 28 2 Classroom, Laboratory work Tutorial guidance   Students have weekly voluntary support through instructor s office hours (6 hours availability, overall) Learning objectives: Generic learning outcomes and competences: The main aims of this course unit are: To understand the basic computer architecture; To understand the main algorithmic structures; To learn the programming developing cycle; To understand the basic concepts of programming; To understand the control structures; To understand the concept of structured programming. At the end of this course unit the learner is expected to be able: Acquire the indispensable algorithmic structures and programming techniques / tools to solve, write, debug and test, small applications using the C programming language.
6 Licenciatura em Engª Electrotécncia / Degree in Bibliography: Progress assessment: Luís Marques & Verónica Vasconcelos, "Linguagem C  Textos de apoio", ISEC Luís Damas, "Linguagem C", FCA  Editora de Informática Herbert Schildt, "Teach Yourself C", Osborne Richard Petersen, "Introductory C  Pointers, Functions and Files", Academic Press Final written exam (80%); Two laboratory miniprojects (20%)
7 Licenciatura em Engenharia Electrotécnica/Degree in Title Instrumentation and Measurement Code: Scientific Area: & Mechanical Engineering Course: Term/Semester: 1st / 2nd ECTS: 5 Department: Instructor: Study plan: Electrotechnics Engineering (DEE); Helena Jorge Carvalho da Silva Marto João Cândido Batista Santos Marina Mendes Sargento Domingues Perdigão Introduction to Measurement systems: Functional descriptions of measuring systems; null and deflection methods; inputoutput configuration of instruments and measurement systems; static characteristics. Types of errors. Statistics. The Oscilloscope. Operational Amplifiers, Instrumentation Amplifiers Digital to analog converters and Analog to digital converters. Transducers Fundamental Concepts Interference Signals and Their Elimination or Reduction. Data acquisition systems, Signal conditioning Virtual Instrumentation: introduction to LabVIEW Language Portuguese Type of instruction: Activities Total Hours Hours/week Comments Theoretical 14 1 Practical: 28 2 Tutorial guidance Learning objectives: Generic learning The main aims of this course unit are to: Teach the students the importance of experimental methods in solving engineering problems; Explain the students how to operate, configure and select electronic instruments and measuring systems. At the end of this course unit is the learner is expected to be able to: use electronic instruments and understanding their principles of operation; validate and interpret the results
8 Licenciatura em Engenharia Electrotécnica/Degree in outcomes and competences: of measurements; 3) understand the basics of Metrology; develop and implement automatic data acquisition systems. Bibliography: Progress assessment: ELFRICK, ALBERT D.; COOPER, WILLIAM D, Instrumentação Electrônica Moderna e Técnicas de Medição, PrenticeHall do Brasil, WOLF, S ; SMITH, R., Student Reference Manual for electronic Instrumentation laboratories, Pearson PrenticeHall International, USA, JONES, L.; CHIN, A., Electronic Instruments and Mesurements. PrenticeHall International, Inc. República de Singapura, BISHOP, ROBERT H., Learning with Labview 7 Express, Prentice Hall, International, USA,2004,ISBn b Leonard Sokoloff, Applications in LabVIEW, Pearson  Prentice Hall, 2004, ISBN Final written exam (60%); laboratory work (40%).
9 Licenciatura em Engenharia Electrotécnica / Electrical Engineering Degree Ficha de Unidade Curricular / Course Unit Description Title: Code: Scientific Area: Course: Year/Semester: ECTS: 5,5 Department: Instructor: Electrical Installations I Degree 1 st / 2 nd José Manuel Fresco Tavares de Pina Study plan: Designing, implementing and maintaining electrical installations of public service and private (residential, commercial and industrial). Designing, implementing and maintaining telecommunications facilities in buildings (ITED) Knowing how to apply the Regulation of Energy Systems of conditioning of buildings in the energy section Language: Portuguese Type of instruction: Activities Total Hours Hours/week Comments Theoretical 14 1 Lectures, casestudies presentation Theoretical Practical Practical 42 3 Students have to design electrical installations of public service and private (residential, commercial and industrial). Students have to design telecommunications facilities in buildings (ITED) Learning objectives: The main aims of this course unit are: 1)Technical Rules of Electrical Installations of Low Voltage Sizing electrical conductors Design of electrical circuits Stereo Protection Protections overcurrent and overload on electrical circuits Design of protection of electrical installations System connection to the land masses Protectors sensitive defect current 2. Draft Telecommunications Facilities in Buildings
10 Licenciatura em Engenharia Electrotécnica / Electrical Engineering Degree Ficha de Unidade Curricular / Course Unit Description General information on telecommunications installations in buildings Systems of radio and television Fundamentals of Network Coaxial Cable Fundamentals fiber Fundamentals XTP cables ITED Manual 3. Regulation of Energy Systems of conditioning of buildings in the energy section Generic learning outcomes and competences: Bibliography: Progress assessment: At the end of this course unit the learner is expected to be able: Designing, implementing and maintaining electrical installations of public service and private (residential, commercial and industrial). Designing, implementing and maintaining telecommunications facilities in buildings (ITED) Knowing how to apply the Regulation of Energy Systems of conditioning of buildings in the energy section Regras Técnicas das Instalações Eléctricas de Baixa Tensão Especificações Técnicas Manual ITED. Regulamento de Sistemas Energéticos de Climatização de Edifícios Theoretical part: Test with a maximum score of 20. Minimum required: 4 points. Practical part: Maximum score 20 points. Presentation and discussion of three projects, one corresponding to the electrical installations of a building housing and commercial establishment, other facilities on the telecommunications infrastructure of a building and a third corresponding to a processing plant. Presentation of a paper on the Regulation of Energy Systems of conditioning of buildings in the energy section. The final rating will be obtained using the following formula: CF = (CT +3 CP) / 4 where: CF  Final Results CT  Classification Theoretical part CP  Classification Part Practice
11 Licenciatura em Engenharia Electrotécnica/ Electrotechnical Engineering Title: Calculus II Code: Scientific Area: Course: Year /Semester: ECTS: 5 Department: Instructor: Mathematics Electrotechnical Engineering 1st / 2 nd Department of Physics and Mathematics Deolinda Maria Lopes Dias Rasteiro Study plan: Language: An introduction to ordinary differential equations: Terminology; Firstorder differential equations: Firstorder linear differential equation, Bernoulli equation, separable equation and homogeneous equation. Laplace Transform. Differential calculus in Rn: Real functions of real vector variables (Scalar fields): Notions of topology; Levels sets; Graph of a function of two variables; Limits and continuity; Directional derivatives and partial derivatives; Partial derivatives of higher order; The gradient of a scalar field; Schwarz theorem; Differentiable functions; A sufficient condition for differentiability; Differentials; Chain rule; Derivatives of functions defined implicitly; Geometric relation of the directional derivative to the gradient vector; Maxima, minima and saddle points; Extrema with constraints Lagrange s multipliers. Integral calculus in Rn: Double integrals: Definition of the double integral of a function defined and bounded on rectangle; Geometric interpretation of the double integral; Double integrals extended over more general regions; Applications to the calculation of areas and volumes; Change of variables in a double integral, Special cases of the transformation formula. Triple integrals: Definition and properties; Geometric interpretation; Calculation of the triple integral; Change of variables in a triple integral. Introduction to vector analysis: definition and properties of line integral; Calculus; Applications; Vector fields, work, movement and flow. Portuguese Type of instruction: Activities Total Hours Hours/week Comments Theoretical 28 2 Classroom, lectures Theoretical Practical Practical Tutorial guidance 28 2 Classroom, lectures and problem solving
12 Licenciatura em Engenharia Electrotécnica/ Electrotechnical Engineering Learning objectives: Generic learning outcomes and competences: Bibliography: Progress assessment: The main aims of this course unit are: Learn essential concepts of real valued functions with n variables real or vector values in particular differentiability, directional derivatives, nonlinear optimization, Lagrange multipliers method, multiple integrals, line and surface integrals. At the end of this course unit the student is expected to be able: To explain the concepts, discuss and present each problem solution in an appropriate way; To solve practical problems with an increasing autonomy, using the subjects treated in the classroom and other related topics; To find and select relevant information from different sources such as monographs textbooks and the web. Rasteiro, D. M. L. D., Apontamentos teóricas e exercícios práticos de Análise Matemática II, DFM, ISEC, Stewart,J. ; Cálculo, Vol.2; Pioneira Thomson Learning Jerrold, E. Marsden \&, Tromba, Anthony J., "Vector Calculus", 5th edition, Freeman James, Glyn, "Advanced Modern Engineering Mathematics", 3th edition, Prentice Hall Adams, Robert A., "Calculus, Several Variables", 5 th edition, Addison Wesley Swokowski, E.W. ; Cálculo Com Geometria Analítica, Vol.2; McGrawHill Marsden And Weinstein; Calculus, III ; Springer Leithold, L. ; O Cálculo Com Geometria Analítica, Vol.2; McGrawHill Penney And Edwards. ; Calculus And Analytic Geometry; PrenticeHall International Editions Demidovitch, B.; " Problemas e Exercícios de ANÁLISE MATEMÁTICA". McGrawHill Assessment can be either continuous or by a final exam during the 1 st or 2 nd exams period. Continuous assessment consists of one intermediate test (50%) and a final test (50%). Alternatively, or in the case the student did not succeed the continuous evaluation, the assessment is made through a final examination (100%).
13 Licenciatura em Engª Electrotécncia / Degree in Title Code Scientific Area: Course: Year/Semester: ECTS: 5.5 Department: Instructor: Computer Programming 1st/2nd Verónica Vasconcelos, MSc; João Ferreira, Msc; Frederico Santos, Msc; Teresa Outeiro, Msc Study plan: Sorting and searching algorithms; Memory allocation; Data structures; Text and binary files: function to handle data files; Dynamic data structures; Linked lists: creating, searching, inserting and deleting nodes. Introduction to ObjectOriented Languages. Application Examples. Language Portuguese and English Type of instruction: Activities Total Hours Hours/week Comments Theoretical 28 2 Classroom, Lectures Theoretical Practical Work / Work Group Practical: 28 2 Classroom, Laboratory work Tutorial guidance   Students have weekly voluntary support through instructor s office hours (6 hours availability, overall) Learning objectives: The main aims of this course unit are: To understand and apply sorting and searching algorithms; To understand the concepts of memory allocation; To understand and to apply the different data structures; To understand the concepts of dynamic data structures; To understand the principles of ObjectOriented Languages Generic learning outcomes and competences: Bibliography: At the end of this course unit the learner is expected to be able: Apply the proper data structures to computerbased proposed engineering problems. Acquire the indispensable programming techniques / tools to solve, write, debug and test, small and medium applications using the C programming language. Herbert Schildt, "Teach Yourself C", Osborne Richard Petersen, "Introductory C  Pointers, Functions and Files", Academic Press
14 Licenciatura em Engª Electrotécncia / Degree in Pimenta Rodrigues, Pedro Pereira, Manuela Sousa, Programação em C++, FCA  Editora de Informática Progress assessment: Final written exam (70%); Two laboratory miniprojects (30%)
15 Licenciatura em Engenharia Electrotecnica Degree in Teoria dos Sistemas / Theory of Systems Title Code Scientific Area: Course: Term/Semester: THEORY OF SYSTEMS 2 nd /1 st ECTS: 6.5 Department: Instructor: Department of Nuno Miguel Fonseca Ferreira Study plan: 1. Introduction to Control. Examples motivators. Control openloop versus closed loop control. General Objectives of a monitoring system. 2. Mathematical representation: differential equation, Laplace transform, transfer function. Linearization. Response time from the transfer function: decomposition in partial fractions, transitional arrangements and location of poles. Theorems of the initial and final value. 3. Block diagrams: successive reduction. Canonical form of feedback. Algebra Blocks. Transfer function of the open mesh. Transfer function of closed loop. Characteristic polynomial. 4. Response of the ranking system of order 1 without zero. Static gain and time constant. Response to the step system 2nd order without zeros: schemes subdamped, critically damped and overdamped. Parameters of the response, with the location of the poles and their analytical expressions. Effects of additional pole and zero. Concept of dominant poles. Reduction of order dominant poles and polezero contempt. Zero in semicomplex plane right. 5. Frequency response: concept. Function frequency response Bode diagram: amplitude feature, characteristic of phase, asymptotic approximation. Bode diagram of the basic factors of a frequency response function rational minimumphase: gain, pole / zero at the origin, pole / zero real poles / zeros complex timefrequency ratio. Bode diagram of system is not minimum phase. 6. Stability limited inputoutput limited. Test Hurwitz. Criterion RouthHurwitz  general case  special cases: zero in the first column, row of zeros. 7. Effects of feedback: stability, following the reference, disturbance rejection, sensitivity to parameter variation. Tracking error in steady state: definition. Error permanently for entrylevel, ramp, parabola. Type system. Error in systems with disturbances. 8. Diagram of the locus of the roots (rootlocus). Condition module and condition of argument. Rules for the construction of the diagram of the locus of the roots to gain positive and negative gain. Zeros of the closed loop. Polezero cancellation in the rootlocus. Rootlocus as a function of any parameter. 9. Stability analysis in the frequency domain. Criterion and the Nyquist diagram. Net Gain. Phase margin. Damping coefficient and phase margin. Bandwidth. Relationship between the frequency response in open loop and closed loop. Stability in systems with delay. Project supported by the rootlocus. 10. Study of onoff control and PID. ONOFF controller, with and without hysteresis. The PID controller; Study measures P, I and D, Empirical methods for the calibration of PID controllers, problems associated with the integral action in the presence of saturation (windup). Compensation fever. Compensation for phase advance and PD action.
16 Licenciatura em Engenharia Electrotecnica Degree in Teoria dos Sistemas / Theory of Systems Compensation for phase delay and action PI. Language Portuguese language Type of instruction: Activities Total Hours Hours/week Comments Theoretical 24 2 Practical: 24 2 Tutorial guidance 14 1 Learning objectives: Teaching students with systematic methods for performance analysis of linear dynamic systems, as well as methods for designing algorithms for automatic feedback control for linear systems. Generic learning outcomes and competences: Bibliography: Progress assessment: Systematic methods for performance analysis of linear dynamical systems. Methods for designing algorithms for automatic feedback control for linear systems. 1. Katsyhiko Ogata, System Dynamics, PrenticeHall 2. J. L. Martins de Carvalho, 'Sistemas de Controlo Automático', LTC Editora, G.F. Franklin, J. D. Powell and EmamiNaeini, Feedback Control of Dynamic Systems. AddisonWesley. 4. C. L. Philips and R. D. Harbor, 'Feedback Control Systems', PrenticeHall, Evaluation during the semester is done through four minitests to assess knowledge, with a minimum of 8.5 values. The final grade is calculated by averaging the sum of the three best scores. There will be two written examination (1 st call and time of appeal) within the deadlines set by the Pedagogical Council. All written tests will include questions of theoretical and practical and lasts for 2 hours. The final rating will be assigned to the note written test. In any of these assessments is necessary to obtain a rating equal to or higher than 10.
17 Course Unit Description Subject Title: Scientific Area: Course: Electromagnetism Physics Code: Year/Semester: 2/1 ECTS: 5.5 Department: Instructor: Study plan: Electromagnetism Physics and Mathematics Paulo Jorge Ribeiro da Fonte, Susete Teresa Gaspar do Fetal 1. Recaps of Vector Analysis The mathematical concepts of the scalar field and vector field. Examples of some physical quantities that are represented by fields. Graphic representation of the fields: equipotential surfaces and field lines. Derivation of the fields in a translation and rotation invariant form The operator nabla. Gradient of a scalar field: definition and meaning. Divergence of a vector field: definition and meaning. Rotational vector fields: definition and meaning. The Laplacian and other second derivatives: the most important properties. Irrotational, solenoidal and harmonic fields. Potential vector and scalar potential. Integrals over the fields Volume integrals on scalar fields. Meaning and important special cases. Line and surface integrals on vector fields. Meaning and important special cases. Flow and circulation of a vector field. The Gauss and Stokes theorems Flux tubes. Continuity equation. Differential operators in curvilinear coordinate systems. Spherical and cylindrical coordinates. 2. Introduction to Electromagnetism The phenomenology of Electromagnetism: charges, currents, electric field, magnetic field, electric and magnetic forces, electromagnetic waves. Fundamental electromagnetic relations: Maxwell equations, Lorentz force, law of conservation of electric charge. Main simplified approaches. Linearity of the fundamental equations: the principle of superposition. 3. Electrostatics The Maxwell's equations and Lorentz force in a electrostatic situation. Gauss' law. Electrostatic application to various simple situations. Coulomb's law. Electric dipole and electric dipole moment. Calculation of the electric field of a known charge distribution from the principle of superposition. Volume, surface and linear charge distributions. The electric potential. Equations of Poisson and Laplace and its application to various simple electrostatic situations. Meaning and physical properties of the electric potential. Potential energy. Power and energy in electrical circuits. Kirchhoff's loop rule.
18 Course Unit Description Conductors in the electrostatic situation. Relaxation time. Boundary conditions. Distribution of electrical energy. Systems of conductors in electrostatic equilibrium. Field lines, flux tubes and matching elements. Coefficients of capacity. Insulated conductor. Spherical, cylindrical and plane capacitors. General relationship between current and voltage in a capacitor. Capacitive impedance. Capacity and stored energy. Volumetric density of electrical energy. Dielectrics. Susceptibility electrical permittivity and relative permittivity. 4. Electric Current Definition of intensity and density of electric current. The law of conservation of charge in differential form. Integral form: Kirchhoff's point rule. Influence of the displacement current. Charge transport in ohmic materials. Microscopic Ohm's law. Conductivity and resistivity of materials. Superconductivity. Lines of current flow and flux tubes of the current density. Electrical resistance and Ohm's Law. Resistance of linear conductors. 5. Magnetostatics The currents as sources of magnetic induction. Magnetic forces. The Maxwell's equations and Lorentz force in magnetostatic situation. Mathematical properties of the magnetic field. Magnetic field lines, circulation and flux. Ampere's Law. Application to various simple magnetostatic situations: rectilinear conductor; infinite plane of current; solenoid. Relationship between electrostatic and static magnetic fields. Magnetic field generated by a single moving charge. Calculation of the magnetic induction field generated by a current distribution by applying the principle of superposition: BiotSavart s law. Application to various simple magnetostatic situations. Movement of charged particles in electric and magnetic fields. Gyromagnetic ratio and cyclotron frequency. Analysis of some instruments. Magnetic forces exerted on a straight current. Analysis of some particular situations. Force and moment exerted on a coil. Magnetic dipole moment. Some applications and associated phenomena: universal motor, nuclear magnetic resonance, magnetic attraction of ferromagnetic materials. Magnetic field in materials. Diamagnetic, paramagnetic and ferromagnetic materials. Hysteresis cycle. 6. Electromagnetic induction Electromotive force induced in a conductor in motion and its relationship with Faraday's law. Faraday generator. Faraday generator efficiency. Related Applications: electromagnetic brake, asynchronous motor and generator. The Maxwell's equations in the presence of magnetic fields in varying in time. Quasistatic approximation. Laws of Faraday and Lenz. Law of the meshes in the presence of magnetic fields varying in time. Electromotive force induced in a circuit. Principle of the alternator. Auto induction. General relationship between current and voltage of an inductance. Inductive impedance. Stored energy. Space density of magnetic energy. Calculation of
19 Course Unit Description the coefficient of self induction in several simple situations. Systems of two circuits. Coefficients of mutual induction. The ideal transformer. 7. Electromagnetic Radiation The Maxwell equations in a vacuum. Solution for plane and spherical electromagnetic waves. Polarization. Light as an electromagnetic phenomenon. Harmonic waves. Phase velocity, wave number, wavelength, frequency, period. Electromagnetic spectrum. Energy of the electromagnetic field. Poynting Vector and Poynting flux vector. Field of radiation of the dipole antena. Directivity and polarization. Electromagnetic waves in the material media. Language: Type of instruction: Activities Total Hours Hours/week Comments Theoretical 28 2 Theoretical Practical 14 1 Practical 14 1 Tutorial guidance Learning objectives: Generic learning outcomes and competences: Bibliography: In this course will be acquired competences on the understanding of Nature in the domain of the Electromagnetic phenomena, emphasizing the most technologically more important concepts. The theoretical studies are complemented with laboratory work. It is developed the knowledge and ability to understand the field of electromagnetism, leaning on the highschool level of expertise and on adequate and updated texts of international authors. The knowledge acquired is promoted by conducting theoretical and practical exercises and applied in the laboratories, which develop a professional attitude towards work. The student is compelled to engage in situations of a practical nature (laboratories) or theoreticalpractical (written examinations) where he should carry out judgments and decisions. The subjects taught are largely basic concepts of scientific and technical literacy, relevant to a broad understanding of nature and applications, and in the communication of ideas with scientific basis. The laboratory group work allows exercising interpersonal exchanges of ideas and discussion of problems and solutions. The individual study of the subjects taught, supported by tutorial contacts, forms an important part of the work plan, acquiring the students habits of autonomous acquisition of knowledge. Física para cientistas e engenheiros, v.2, 5ª edição, Mosca e Tipler, Editora LTC, 2007 (english version available) The Feynman Lectures on Physics v.2, R.P. Feynman, R.B. Leighton, M.Sands, Addison Wesley, Reading, Massachusetts, Vector Analysis and an introduction to tensor analysis, M. R. Spiegel, Schaum Publishing
20 Course Unit Description Company, Progress assessment: The laboratory work is evaluated by short written reports, with a maximum of 4 points (L). There will be final written exams required by the ISEC rules, with a maximum of 20 points (E). Approval is granted when L+0.8xE>9.500.
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