LINEAR AND NON-LINEAR EQUATIONS SYSTEMS
Terminology and notations. Equivalent systems. Gauss removing method. Rouché–Capelli theorem. Homogeneous Systems: Nullspace of a matrix. Systems solving: methods and iterative.

VECTOR SPACE AND EUCLIDEAN SPACE
-Rn Vector Space. Definition and properties. Linear dependence and independence. Properties. Basis and dimension of Rn vector space. Vector’s coordinates. Change of basis in Rn. Vector subspaces. Characterisation. Equations of a subspace. Basis and dimension of a subspace.

-Rn Euclidean Vector Space.Scalar product. Module of a vector and angle between vectors. Orthogonal and orthonormal basis. Method for orthonormalisation of Gram–Schmidt.

DIAGONALIZATION OF MATRICES
Eigenvalues and eigenvectors of a square matrix. Properties. Diagonalizable matrix. Diagonalization.
Diagonalization of symmetric matrices by orthogonal similarity. Powers of a diagonalizable matrix. Jordan canonical form for matrices of order two and three.

CONICS AND QUADRICS
-Conics
Definition of conic. Matricial equation. Reduced equation of a conic. Classification and main elements of conics. Study of ordinary conics.

-Quadrics
Definition of quadric. Matricial equation. Reduced equation of a quadric. Classification of quadrics. Study of ordinary quadrics.

CURVES AND SURFACES
– Flat curves.
Concept of flat curve. Expressions of a curve: parametric, explicit and implicit.
Tangent and normal in a point of a curve. Singular points and Ordinary points. Flat curves in polar coordinates.

– Warped Curves
Definition of a curve in the space. Equations of a curve. Ordinary point and Singular point.
Arc length of a curve. Three-dimension space and Frenet Formula. Tangent, normal and binormal straight line. Curvature and twisting. Normal, rectifying and osculating planes.

– Surfaces
Concept of surface. Tangent plane and normal straight line to a surface. Surfaces of revolution and translation. Conical and cylindrical surfaces.

NUMERICAL METHODS
Numerical equation solving. Polynomial interpolation. Function approximation. Numerical differentiation and integration.

DIFFERENTIAL CALCULUS OF SEVERAL VARIABLES FUNCTIONS
Introduction to several variables functions. Surfaces in the space. Continuity and limits. Partial derivatives. Differentiability. Chain rule. Directional derivatives. Implicit derivative. Optimisation of several variables functions. Lagrange multipliers.

INTEGRAL CALCULUS OF SEVERAL VARIABLES FUNCTIONS
Iterated integrals. Double and Triple integrals. Applications. Variables changes: Polar, cylindrical and spherical coordinates.

FUNDAMENTALS AND APPLICATIONS OF DISTANCES
Auxiliary views.
Rotations. Changes of plances projections of a flat figure angles.
Introduction to the study and representation of regular polyhedral surfaces.
Prism and pyramide cylinder and cone sphere.

DIMENSIONED DRAWING SYSTEM
Fundamentals and applications of distances.
Auxiliary views. Rotations. Angles.
Flat figures representations. Dimensioned representation of bodies and surfaces building roofs
Topographical surfaces.

INTRODUCTION TO AUTOCAD AIDED DESIGN BASIC CONCEPTS
Autocad environment.
Drawing and edition basic commands.

KINEMATICS; GENERAL CONCEPTS; STUDY OF MOVEMENTS PARTICLE DYNAMICS; NEWTON PRINCIPLES; WORK AND ENERGY SYSTEM OF PARTICLES DYNAMICS

RIGID BODY DYNAMICS

THERMODYNAMICS; HEAT AND TEMPERATURE; THERMODYNAMIC TRANSFORMATIONS

STRUCTURE, LAYOUT AND MOVEMENT OF ATOMS.
Crystalline structures Crystalline defaults Diffusion in solids

PROPERTIES OF MATERIALS
Mechanical properties, break and tests. Other physical properties
Chemical properties

CONTROL OF PROPERTIES AND MICROSTRUCTURE
Plastic deformation in metals Phase diagrams
Phase transformations
Handling and controlling thermal, electrical, magnetic and optical properties.

ENGINEERING MATERIALS: PROPERTIES, APPLICATIONS AND PROCESSING.
Metallic alloys
Ceramic materials Polymeric materials Composite materials Functional materials.

SELECTION OF MATERIALS IN INDUSTRIAL DESIGN
Criteria for selecting materials

PRACTICAL UNIT
Thermal treatments: Normalised, hardened, tempered on F114 steel Charpy tests: impact toughness on F114 steel.
Resin deep-drawing of samples for metallographic preparation.
Tension tests on F114 steel: determination of the elastic module, elastic limit, tension resistance, shear stress, ductility, elastic energy and plastic energy.
Vickers, Rockwell and Brinell hardness tests.
Metallographic preparation and microscope observation of deep-drawn samples with different thermal treatment.INTRODUCTION TO MATERIALS SCIENCE AND ENGINEERING
Introduction to Materials Science and Engineering.

STRUCTURE, LAYOUT AND MOVEMENT OF ATOMS.
Crystalline structures Crystalline defaults Diffusion in solids

PROPERTIES OF MATERIALS
Mechanical properties, break and tests. Other physical properties
Chemical properties

CONTROL OF PROPERTIES AND MICROSTRUCTURE
Plastic deformation in metals Phase diagrams
Phase transformations
Handling and controlling thermal, electrical, magnetic and optical properties.

ENGINEERING MATERIALS: PROPERTIES, APPLICATIONS AND PROCESSING.
Metallic alloys
Ceramic materials Polymeric materials Composite materials Functional materials.

SELECTION OF MATERIALS IN INDUSTRIAL DESIGN
Criteria for selecting materials

PRACTICAL UNIT
Thermal treatments: Normalised, hardened, tempered on F114 steel Charpy tests: impact toughness on F114 steel.
Resin deep-drawing of samples for metallographic preparation.
Tension tests on F114 steel: determination of the elastic module, elastic limit, tension resistance, shear stress, ductility, elastic energy and plastic energy.
Vickers, Rockwell and Brinell hardness tests.
Metallographic preparation and microscope observation of deep-drawn samples with different thermal treatment.

REGRESSION AND CORRELATION

THEORY OF PROBABILITY.CALCULATION OF PROBABILITIES

ONE-DIMENSIONAL AND TWO-DIMENSIONAL RANDOM VARIABLES.

DISCRETE AND CONTINUOUS DISTRIBUTIONS

STATISTICAL INFERENCE

POINT AND INTERVAL ESTIMATION

HYPOTHESIS TESTING. PARAMETERS HYPOTHESIS TESTING

INTRODUCTION TO OPTIMISATION

WAVES: CHARACTERISATION; PROPAGATION

FIELDS OF CENTRAL FORCES; ELECTROSTATIC FIELD; GRAVITATIONAL FIELD ELECTRIC CURRENT

MAGNETOSTATIC FIELD ELECTROMAGNETIC INDUCTION

THE COMPANY AS AN ECONOMIC REALITY
Concept of company. Functions of companies
The constituting elements of a company. Classification of companies
The companies according to their legal form. Concept of businessman
The businessman within the current company reality. The entrepreneurs

THE COMPANY AS A SYSTEM
Managing roles
Concept and properties of the systems
Typology of the systems
Conceptual elements of the company as a system
The subsystems within the company
The business environment

THE FINANCIAL FUNCTION
Investment and funding
Fundamental preliminary concepts
The planned investment
Funding sources or instruments in the company
The own resources
The third party’s resources
Profit and profitability

MARKETING IN THE COMPANY
The commercial subsystem. Definition of marketing
The market: concept, segmentation and strategies. The marketing-mix
The product. The price
The place. The promotion

THE PRODUCTION SUBSYSTEM
The production activity: concept and types
Concept and elements of the production subsystem. Types of production processes
Goals and decisions when administering production

THE EFFICIENCY IN THE COMPANY
Efficiency measures. The productivity
Graphical analysis of the productivity functions. Elements affecting productivity
Concept and classification of costs

DIMENSION OF INSTALLATIONS
Concept and criteria for dimension measures
Dimension and scale economies
Dimension and structure of costs
Dimension, occupation rate and hysteresis of costs
Methodology for determining the production capacity

DECISIONS ON INSTALLATIONS LOCATIONS
Decisions on company location and its installations Strategies for multisite location
Procedures and elements for the decision-making process Quantitative methods for location

PHYSICAL DISTRIBUTION OF INSTALLATIONS
Concept, objectives and elements for on-site distribution
Types of on-site distribution
Methods for installations distribution

DESIGNING AND MEASURING WORK
Design of work
Study of work methods Study of times

PROJECT PLANNING, PROGRAMMING AND CONTROL
Concept and stages in project management Concept and types of control
Scope of control
Project planning and control techniques

QUANTITATIVE ASPECTS OF CHEMISTRY

MATTER AGGREGATION STATES

LIQUID STATE AND DISSOLUTIONS

CHEMICAL THERMODYNAMICS

CHEMICAL KINETICS

CHEMICAL BALANCE

ACID-BASE REACTIONS

OXIDATION REDUCTION REACTION

CHEMICAL FUNDAMENTALS OF CORROSION ORGANIC CHEMISTRY

ORDINARY DIFFERENTIAL EQUATIONS (ODE)
Origin, definition and classification of the ODE. Main concepts. Solutions. Type of solutions.

FIRST ORDER ODE:
Existence and uniqueness of solution theorem. Geometric interpretation of the equation. y’=F(x,y)(placements).
Differential equations (DE) with separable to reducible variables. Reducible to homogeneous DE. Exact DE. Reducible to exact: Integrating factor. First order linear DE. Definitions. Resolution. Bernouilli equation. Orthogonal and isogonal trajectories.

INTRODUCTION TO THE PARTIAL DIFFERENTIAL EQUATIONS

LINEAR DE OF SECOND ORDER OR HIGHER
Definitions. Existence and uniqueness theorem. Vector treatment of solutions. Linear Homogeneous Constant-Coefficient ODE: cases for resolution. Full linear ODE: undetermined coefficients method and method of variations of parameters. Variable changes. Euler equation. Converting a linear equations system into a higher order equation

POWER SERIES SOLUTION OF DIFFERENTIAL EQUATIONS
Application of the power series to the solution of equations.

LAPLACE TRANSFORM
Introduction. Definition. Calculation of transforms of elementary functions. Properties. Convolution product. Inverse transform. Properties. Application for the solution of differential equations and integrals and linear equations systems.

KINEMATICS AND DYNAMIC OF THE RIGID SOLID
Kinematics of machines and mechanisms
Dynamics of machines and mechanisms

GENERAL CONCEPTS ON MACHINES AND MECHANICMS

LEVIES AND GEARS

MECHANISMS FOR HEAT TRANSFER
Conduction, convection and radiation
Combined applications of the heat transfer mechanisms heat exchangers

INTRODUCTION TO AUTOMATION
Definitions and structures.
Introduction to logic systems
Combinational and Sequential Systems and Applications.

INTRODUCTION TO MODELLING OF AUTOMATION SYSTEMS AND PROGRAMMABLE AUTOMATES
Introduction to modelling of Automation Systems. Petri networks. The programmable automates. Structure, programming
Industrial applications.

THE BIPOLAR JUNCTION TRANSISTOR (BJT)
Morphology.
Functioning regions. Characteristic curves.
The BJT as an amplifier. The BJT as a switch.
Pulse Wide Modulation (PWM). JOINT FIELD EFFECT TRANSISTOR (JFET)
Morphology.
Functioning regions. Characteristic curves.
The MOSFET as an amplifier. The MOSFET as a switch.

THE OPERATIONAL AMPLIFIER (OA)
Amplification and features. The feedback.
OA ideal model. Basic settings.

DIGITAL ELECTRONICS AND DIGITAL INTEGRATED CIRCUITS
Analogue vs digital. Binary system.
Digital encoding of information. A/D and D/A converters. The clock.
Series/parallel communications. Logic gates.
Design and optimisation of logic circuits. Logic families.

PROBLEMS
Metrology
Forming technologies and processes with material preservation Forming technologies and processes with material removing Joining technologies

THEORY
Manufacturing systems
Manufacturing engineering and processes
CAx Systems and Manufacturing management systems. CIM Production systems. Plant engineering Emerging manufacturing systems

METROLOGY
Fundamentals of metrology Dimensional metrology Metrology of lengths and angles
Metrology of surface finish Metrology of forms
Adjustment and tolerances

FORMING TECHNOLOGIES AND PROCESSES
Forming technologies and processes with material preservation
Introduction to forming with material preservation
Consolidation processes
Deformation processes. Advanced processes

FORMING TECHNOLOGIES AND PROCESSES WITH MATERIAL REMOVING
Introduction to forming processes with material removing Conventional machining processes
Cutting tools Machining fundamentals

JOINING TECHNOLOGIES
Introduction to forming with provision of material Welding joining processes
Symbolic representation of welding Advanced processes with provision of material

ONE DIMENSIONAL LAMINAR FLOW IN LIQUIDS IDEAL FLUIDS

BASIC PRINCIPLES IN FLUID MECHANICS
Statics of fluids Kinematics
Integrals applied to finite volumes.

CONSERVATION OF MASS EQUATION
Continuity equation
Equation of conservation of quantity of momentum. Integral form.
Differential form Equation of conservation of energy. Integral form. Differential form.

PROPERTIES OF FLUIDS AND DIMENSIONAL ANALYSIS
Introduction.
Forces acting on a fluid Thermodynamics. Transport phenomena Dimensional analysis.

DIMENSIONING
General on dimensioning.
Dimensioning according to manufacturing process.

SIGNS FOR SURFACE FINISHES
Surfaces finishing symbols of surface status.

TOLERANCES
Dimensional tolerances. Geometric tolerances.

CONSTRUCTION ELEMENTS: NON DETACHABLE JOINTS
Riveting and welding.

CONSTRUCTION ELEMENTS: dETACHABLE JOINTS
Flange and threads.
Screws, nuts and washers.
Supplementary security systems. Keys and keyseats. Hinge pins.

ORGANS OF MACHINES
Trees. Couplings. Spring bases. Pulleys
Toothed wheels.

ENSEMBLE AND EXPLODED DIAGRAM
General considerations.

USEFUL CONSIDERATIONS FOR INDUSTRIAL DESIGN ALIGNMENT. SYMBOLS AND STANDARDISATION

basic concepts for isometric alignment of pipes in processes plants. symbols
and standardisation
basic concepts for alignment of electrical schemes. symbols and standardisation basic concepts for alignment of printed circuits. symbols and standardisation

AIDED DESIGN
Design aids and edition dimensioning
Blocks and attributes

INTRODUCTION TO ELECTRICAL INSTALLATIONS

DISTRIBUTION LINES AERIAL LINES FOR MV AND LV

MV AND LV UNDERGROUND LINES

SWITCHGEAR FOR MANOEUVRE AND PROTECTION OF MV AND LV

TRANSFORMATION CENTRES

INSTALLATIONS OF LINKS AND INTERIORS

LIGHTING INSTALLATIONS

ELECTRICAL PRICING

POWER TRANSFORMERS

ASYNCHRONOUS MACHINES

SYNCHRONOUS MACHINES

CONTINUOUS CURRENT MACHINES

SPECIAL ELECTRICAL MACHINES

STEADY STATE AND TRANSITIONAL STATE OF THE CONTROL SYSTEMS
Operative states: transitional state and steady state. Steady state, study of error in the steady state.
Transitional response in first order system. Transitional response in second order system. Higher order systems.
Routh-Hurwitz stability criterion.

PLACE OF THE ROOTS
Introduction. Definition and concepts. Alignment method.
Response of systems through the analysis of the place of roots.

DESIGN AND COMPENSATION TECHNIQUES
Introduction.
Preliminary considerations in design. PID controllers setting. Compensation in the place of roots.

INTRODUCTION TO DIGITAL CONTROL OF SYSTEMS
Basic concepts
Basic techniques on analysis and design of digital control systems.

COMPOSITION OF A POWER ELECTRICAL SYSTEM

MODELLING OF A POWER ELECTRICAL SYSTEM; QUANTITIES PER UNIT

ANALYSIS OF THE POWER ELECTRICAL SYSTEM ;FLOW OF CHARGES

ECONOMIC DELIVERY

OPERATION UNDER MALFUNCTIONS: SHORT CIRCUITS

AGGREGATE PLANNING MASTER PROGRAMMING COMPONENTS PROGRAMMING

VERY SHORT TERM PLANNING AND CONTROL

ORGANISATION OF THE PREVENTION IN-COMPANY

RESPONSIBILITIES AND PENALTIES CONCERNING PREVENTION. PERSONAL PROTECTION EQUIPMENT.

MINIMUM PROVISIONS ON SAFETY AND HEALTH SIGNALLING. SAFETY AND PREVENTION IN ELECTRICAL AND OXY ACETYLENE WELDING HANDLING, MOVING AND TRANSPORTING LOADS.

MACHINES SECURITY AGAINST MECHANICAL RISKS SECURITY PROVISIONS AT WORK PLACES PREVENTION AND PROTECTION AGAINST FIRES. ELECTRICAL RISKS

ASSESSMENT OF POLLUTANTS. CHEMICAL POLLUTANTS. RADIATIONS SECURITY AND HEALTH STUDIES IN CONSTRUCTION WORKS

ELECTRICAL MACHINES DRIVERS
General concepts.
Drivers for alternate current engines. Drivers for continuous current engines.

STATIC CONVERTERS FOR ELECTRICAL MACHINES DRIVERES
General considerations.
Characteristics of the devices. Classification and type of converters.

CONTROL OF CONTINUOUS CURRENT MACHINES
General concepts. Power circuit. Control circuit.
Speed variators in continuous.

CONTROL OF ALTERNATE CURRENT MACHINES
General concepts. Electronic starters. Speed variators in alternate.

THE GENERATOR AT THE POWER STATIONS. REGULATION OF THE VOLTAGE
The synchronous generator. Types. Construction provisions. Functional characteristics. Functioning flowcharts. Ventilation and cooling.
Alternators excitation systems. Basic parameters. Regulation of the voltage. Regulators.
The asynchronous generator. Load behaviour. Converters and controls.

FUNCTIONING IN GENERATION. STABILITY.
Operating synchronous machines in parallel. Static stability of the operation in parallel. The synchronous machine coupled to a network.
Active and reactive power compensation.

Regulation of the speed and the frequency. Types of regulation. Phase swingings of the synchronous machine.

EXTERNAL SHORT CIRCUIT FAULTS AFFECTING THE GENERATOR
Short circuit in the synchronous machine. Symmetrical permanent short circuit.
Symmetrical components. Direct, inverse and homopolar reactances. Asymmetrical permanent short circuit.
Abrupt short circuit of an alternator.
Subtransitional and transitional reactance. Time constant.

ELECTRICAL SYSTEMS OF THE POWER STATIONS. PROTECTIONS
Auxiliary services. Power transformers. Substation for network connection.
Command, control and protections in power stations. Protections for the synchronous generator, engines and transformers. Protection for bars, lines and networks.

HYDRAULIC AND THERMAL POWER STATIONS
Hydraulic power stations. Water Resources Exploitation. Building elements of the hydraulic power stations. Characteristics of the generator according to the type of turbine.
Hydraulic power stations with pump accumulators. Types. Starting methods. Thermal Power Stations. General composition and constitutive elements.
Conventional Thermal Power Stations. Combined cycle power stations.
Nuclear Thermal Power Stations. Nuclear fission and fusion. Nuclear reactors. Co-generation power stations.

GENERATION OF ELECTRICITY BY RENEWABLE ENERGIES EXPLOITATION OF RENEWABLE ENERGIES.
Wind systems. Photovoltaic systems.
Generation of electricity out of other renewable energy sources

OTHER METHODS TO GENERATE ELECTRICITY OR MAINTAIN THE SUPPLY
Electrical power-unit and Uninterruptable power supply systems. Galvanic or voltaic batteries. Hydrogen and fuel cells.
Storage of energy.

FUELS AND COMBUSTION
Theoretical and real process.
Enthalpy of formation and combustion. First and Second law of reactive systems. Thermal installations. Boilers.

GAS POWER CYCLES
Engines: OTTO, DIESEL, STIRLING, ERICSSON cycles.
Gas turbines: BRAYTON (Regeneration, Intercooling, Reheating, Regeneration) Deviation of real cycles from idealized ones.
Second law of gas power cycles.

CYCLES OF POWER STEAM AND COMBINED CYCLES. STEAM TURBINES.
Rankine’s cycle.
The reheat steam cycle, open and closed heaters. Second law of steam power cycles.
Co-generation, combined and binary.

ELECTRICAL CALCULATION OF DISTRIBUTION LINES
High voltage aerial lines. Electrical and mechanical calculation. Switchgear and protection.

TRANSFORMERS AND DISTRIBUTION SUBSTATIONS

DOCUMENTS OF THE PROJECT
Documents of the project: table of contents report and annexes. Documents of the project: planes.
Documents of the project: tender specifications. Documents of the project: status of measurements. Documents of the project: budget.
Documents of the project: reliable studies construction works management.

REGULATIONS AND LEGISLATION
The rules

MATRICIAL CALCULATION OF STRUCTURES
General concepts on matricial methods. Coordinates systems. Elementary matrices.
The direct method of rigidity. Actions not focused on nodes.

STRUCTURES FOR ELECTRICAL STRINGING SUPPORTS
Introduction. Stringing support structure Foundation

PRESSURE CONTAINERS
Definition of concepts. Calculation by internal pressure.

TANKS AND PIPES
Design of tanks
Design of pipes for processes

REGULATORY SCHEME
ASME Boiler and Pressure Vessel Code. Section 8 Division 1 for designing of pressure containers ANSI B31.3.
Process piping for designing process piping

REGULATIONS ON HIGH VOLTAGE LINES
RD 223/08 on the design of supports for electrical lines API-650 for tanks design ASTM/ISO
Standards for materials

UNIT OPERATIONS IN THE CHEMICAL INDUSTRY.
Unit operation. Classification. Operations of matter transfer. Operations of heat transfer.
Operations of transport of quantity of movement. Supplementary operations.
Chemical unit operation.

MACROSCOPIC BALANCES OF MATTER AND ENERGY Matter balances
Energy balances

POWER PLANTS

ALTERNATIVE INTERNAL COMBUSTION ENGINES

PRODUCTION OF COLD

TURBO-MACHINES

HYDRAULIC INSTALLATIONS

STRESS, TENSION AND DEFORMATION

FAULTS BY STATIC CHARGE

FAULTS BY FATIGUE

AXLES AND SHAFTS

SCREWS AND DETACHABLE JOINTS

WELDING AND NON-DETACHABLE JOINTS

SPRINGS

BALL BEARINGS

LUBRICATION AND DISPLACEMENT FLANGE

GEAR WHEELS AND GEAR WHEELS REDUCERS

BRAKES AND CLUTCHES

STRAPS, CHAINS AND WIRES

OTHER RENEWABLE ENERGY SOURCES
Geo-thermal and marine
The hydrogen, the energy of the future

PROGRAMMING OF GENERATION
Classic economic delivery
Programming starts and stops in thermal power stations
Hydrothermal coordination

OPTIMAL CHARGES FLOW
Equations and variables Restrictions
Optimisation problems

WINDING. CALCULATION AND CONSTRUCTION. ISOLATIONS.

ISOLATING MINERAL OILS. HEATING AND COOLING.

PROTECTION LEVELS OF ELECTRICAL MACHINES.

DESIGN OF STATIC ELECTRICAL MACHINES. DESIGN OF ROTATIONAL ELECTRICAL MACHINES.

TESTS ON ELECTRICAL MACHINES. DIAGNOSIS ON ELECTRICAL MACHINES.

ASPECTS OF INSTALLATION AND MAINTENANCE AFFECTING THE CHOICE OF ELECTRICAL MACHINES.

BASIC FUNCTIONS, GOALS AND DATA OF ELECTRICAL MAINTENANCE. THE MAINTENANCE AND ITS ORGANISATION.

STANDARDISATION OF ELECTRICAL MAINTENANCE. THE MAINTENANCE COSTS.

CONTRACTED ELECTRICAL MAINTENANCE. PLANNING OF MAINTENANCE.

CONTROL OF THE ELECTRICAL MAINTENANCE ACTIVITIES. MANAGEMENT OF COMPUTER AIDED MAINTENANCE.

TRAINING, MANAGEMENT AND QUALITY IN MAINTENANCE. RECEPTION AND ELECTRICAL MAINTENANCE TESTS. RCM.

MAINTENANCE BASED ON RELIABILITY.CURRENT ISSUES IN ELECTRICAL MAINTENANCE.