- Linear Algebra - Calculus I - Physics I

Upon successful completion of this subject, students will be able to: 1. Have knowledge and understanding of the physical principles of electricity and magnetism. 2. Have the ability to apply their knowledge and understanding to identify, formulate and solve problems of electricity and magnetism using established methods. 3. To have the ability to design and carry out experiments on electricity and magnetism, to interpret the data obtained and draw conclusions from them. 4. Have skills in handling laboratory equipment for data collection in electricity and magnetism practices. 5. Have the ability to select and use appropriate tools and methods to solve problems of electricity and magnetism. 6. Have the ability to combine theory and practice to solve problems of electricity and magnetism.

RA1.1: Knowledge and understanding of the scientific and mathematical principles underlying their branch of industrial engineering. RA2.1: The ability to apply their knowledge and understanding to identify, formulate and solve engineering problems using established methods. RA4.2: The ability to design and conduct appropriate experiments, interpret the data and draw conclusions. RA4.3: Workshop and laboratory skills. RA5.1: The ability to select and use appropriate equipment, tools and methods. RA5.2: The ability to combine theory and practice to solve engineering problems. CB1: Students have demonstrated possession and understanding of knowledge in an area of study that builds on the foundation of general secondary education, and is usually at a level that, while relying on advanced textbooks, also includes some aspects that involve knowledge from the cutting edge of their field of study. CB2: Students are able to apply their knowledge to their work or vocation in a professional manner and possess the competences usually demonstrated through the development and defence of arguments and problem solving within their field of study. CG1: Ability to resolve problems with initiative, creativity decision-making and critical reasoning skills, and to communicate and transmit knowledge, skills and abilities in the Industrial Engineering area. CG9: Knowledge and capacity to apply computational and experimental tools for analysis and quantification of electronic and automatic engineering problems. CG10: Capacity to design and carry out experiments and to analyze and interpret data obtained. CG12: Understanding and command of the basic concepts of the general laws of mechanics, thermodynamics, electromagnetic fields and waves and application for resolving engineering problems.

1. Coulomb's Law. The Electric Field 1.1 Electric charge. 1.2 Coulomb's Law. Dimensions and Units. The Superposition Principle. 1.3 Definition of the Electric Field. 1.4 Electric Field of Point Charges. 1.5 Superposition Principle. Electric Field Lines. 2. Gauss's Law 2.1 Charge Densities. Electric Field due to different Charge Distributions. 2.2 Electric Flux. Relationship between field flux and electromagnetic fields. 2.3 Gauss's Law. 2.4 Application of Gauss's Law to Calculate Electric Fields in systems with certain symmetry. 3. Electric Potential 3.1 The work done by an electric field on a moving point charge. 3.2 Electric Potential Difference and Electric Potential. 3.3 Electric Potential due to different Charge Distributions. 3.4 Relationship between Electric Field and Electric Potential. Equipotential curves and surfaces. 3.5 Electrostatic Energy of Point Charges. 4. Conductors 4.1 Conductor and Insulator materials; microscopic interpretation. 4.2 Properties of conductors in Electrostatic Equilibrium. Charge Distribution in Conductors. 4.3 Electric Field and Electric Potential in a conductor. 4.4 Electric Fields inside charged conductors. Conductors with charge inside a cavity. The Faraday-s Cage. Corona Discharge. 5. Dielectrics: Capacitance and Energy Storage in electric Fields. 5.1 Microscopic point of view of dielectrics: induced dipoles. 5.2 Dielectric constant and electric susceptibility. Polarization. Electric displacement. 5.3 Definition of Capacitance: Calculation of capacitance. 5.4 Capacitors with Dielectrics. 5.5 Combination of Capacitors. Series and parallel connections. 5.6 Storing energy in a Capacitor. Energy density of the electric Field. 6. Electric Current 6.1 Electric Current: Intensity and Current Density. 6.2 Ohm's Law. Electric Resistance. Conductivity and resistivity of materials. 6.3 Joule-s Law. Power Dissipated in an Electric Conductor. 6.4 Electromotive Force (emf). Combination of resistance. Series and parallel connections. 6.4 RC circuits. Charging and discharging a capacitor. 7. Magnetic Forces and Magnetic Fields 7.1 Introduction. Definition of a Magnetic Field. Lorentz-s Force. 7.2 Charged Particle Movement in a uniform Magnetic Field. Applications: Velocity selector, Mass Spectrometer. 7.3 Magnetic Force on a dipole and on a Current-Carrying conductor wire. 7.4 Torque on a dipole and Current Loop in a constant magnetic field, Permanent Magnets. Magnetic Moment. 8. Sources of Magnetic Field and Magnetic Materials. 8.1 Sources of the Magnetic Field: Current elements. Biot-Savart Law. 8.2 Forces Between Two Current-Carrying parallel wires. 8.3 Magnetic Flux. Ampère-s Law. Application of Ampère-s Law to Calculate Magnetic Fields. 8.4 Magnetic Materials. Microscopic point of view of Magnetism. Magnetization: Magnetic Dipoles. Paramagnetism, Diamagnetism and Ferromagnetism. Magnetic Susceptibility and Permeability. 9. Faraday's Law of Induction 9.1 Faraday's Law of Induction. Lenz-s Law. Applications. 9.2 Motional Electromotive Force. 9.3 Examples of Electromagnetic Induction. 9.4 Mutual Induction and Self-Induction. Energy Stored in a Solenoid. 9.5 Energy Stored in a Magnetic Field. 10. Oscillations. Maxwell's Equations: Electromagnetic Waves 10.1 Introduction to the oscillatory movement. Mathematical description of the oscillatory systems. 10.2 Simple AC circuits: resistive, inductive and capacitive load. The LCR series circuits. Impedance. Resonance. 10.3 Introduction to travelling Waves and Standing Waves: Mathematical Description. Mechanical waves, Sound and Electromagnetic Waves. One-dimensional wave Equation. 10.4 Displacement Current: Gauss´s Law for Magnetism: Maxwell's Equations. Plane Electromagnetic Waves. Energy Flux Density of an Electromagnetic Wave.

- Lectures, where the theoretical concepts are explained and personal work of the student. They are aimed at the acquisition of theoretical knowledge. - The teaching format will be: 1) Master classes (aggregated groups) on-line. Through Video-Conference preferably using BlackBoard Collaborate or Google Meet. 2) Small groups: Face-to-face. - Practical laboratory sessions of mandatory attendance; practical sessions for small groups, with active and direct interaction between the students and the professor; individual tutor supported sessions and students personal work. They are aimed at the acquisition of practical skill related to the syllabus of the subject . 1) Master classes (aggregated groups) on-line. Through Video-Conference preferably using BlackBoard Collaborate or Google Meet. 2) Small groups: Face-to-face.