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.

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

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 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 mar.eting-mix.
The product. The price.
The place. The promotion.
.
THE PRODUCTION SUBSYSTEM
The production activity: concept and types.
Concept and elements .of the produ.ct.ion subsystem. Types of production processes.
Goals and decisions when administe.ring 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

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.

GENERAL SETTINGS OF THE ELASTIC PROBLEM
Tension test. Hooke law. Transverse deformations. Poisson’s coefficient. Principle of superposition.
Generalised Hooke’s law. Lame’s equation.

THEORIES OF ANELASTIC ACTION
Introduction. Mohr criteria of limit states. Other criteria

THEORY OF FORCES. STATIC CHARACTERISTICS OF THE SECTION
Forces. Moments. Centre of gravity. Static moment. Moment of inertia.

AXIALS
Introduction. Axial diagrams Stresses. Deformations.

SHEAR AND BENDING
Introduction. Shear and bending diagrams.

BENDING STRESSES
Pure bending, Navier-Stokes law. Simple bending. Relation shear and bending.

BENDING DEFORMATIONS
Introduction. The elastics.
Mohr’s Theorems.

BUCKLING
Introduction. Critical load. Effective length.
Buckling according to Eurocodes.

ENVIRONMENTAL MANAGEMENT
Environmental impact assessment. Environmental management systems.
Life cycle analysis. Green labelling.

WATER POLLUTION
The natural water environment and the waste waters Physical operations for waste waters treatment. Chemical processes for waste waters treatment. Biological processes for waste waters treatment. Treatment and management of sludge.
Examples of waste waters treatment plants.

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

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.

SINGLE PHASE AND THREE-PHASES CIRCUITS ANALYSIS SINUSOIDAL SIGNALS
Analysis in the sinusoidal steady state Power in the sinusoidal steady state Three-phases balanced systems.

ELECTROMETRICS
Fundamentals of electrical measurements Analogue and digital instruments Conditioning of signal Measurement methods.

BASIC PRINCIPLES OF ELECTRICAL MACHINES
Basic elements of electrical machines Balance of energy in electrical machines Classification of electrical machines.

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 linear momentum conservation. Integral form.
Differential form Equation of energy conservation. Integral form. Differential form.

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

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

STRESS CONDITIONS IN ELASTIC SOLIDS

DEFORMATIONS IN A CONTINUOUS MEDIUM

DEVIATED BENDING AND COMPOUND BENDING

COMBINED STRESSES

HYDRAULIC AND PNEUMATIC INSTALLATIONS
Resistant characteristic of the network Regulation
Holes, tubes, nozzles and weirs. Measurement instruments of free and level flows. Installations design and calculation.

DISTRIBUTION NETWORKS
Installation of a pipe with a tank Two-tanks systems
Pipes servicing throughout the route Series and parallel pipes systems
Systems of pipelines

OPEN CHANNELS
General

MECHANICAL BEHAVIOUR OF MATERIALS

MATERIALS SERVICING BEHAVIOUR; TRIBOLOGY

SELECTION OF MATERIALS IN THE INDUSTRY

MATERIALS OF SPECIAL INDUSTRIAL INTEREST

MATERIALS PROCESSING

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

CALCULATIONS OF ISOSTATIC TRUSS

CALCULATION OF HYPERSTATIC TRUSS

INFLUENCE LINE

STRUCTURES AND INDUSTRIAL CONSTRUCTION DESIGN

MATRIX ANALYSIS OF STRUCTURES
Elementary matrices.
Coordinates systems. Change of basis rigidity method.
Flexibility method. Non concordant conditions.

ANALYSIS TOOLS

MACHINE TESTING

PREVENTION OF FAULTS

AUXILIARY VIEWS OF INDUSTRIAL FORMS AND THEIR STANDARDISED REPRESENTATIONS.
FURTHER ENSEMBLE AND EXPLODED DIAGRAM

INDUSTRIAL PERSPECTIVES
Dimensioning and cuts
Further pipelines alignment.
Symbols, planes and isometric alignment. Reading industrial planes.

AIDED DESIGN

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 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

REGULATIONS AND LEGISLATION
The rules

MACROSCOPIC BALANCES OF MATTER AND ENERGY Matter balances
Energy balances

STATIC ELECTRICAL MACHINES
Transformers (single phase, three-phases and special)

ROTATIONAL ELECTRICAL MACHINES
Engines (CCE, ACE and SE)

ACTIVATION AND CONTROL OF ROTATIONAL ELECTRICAL MACHINES

ELEMENTS IN LV ELECTRICAL INSTALLATIONS
Design, selection and calculation of elements and circuits of the LV electrical installations (including electrical energy receivers)

CHAPTER 3. RANDOM DATA, MEASUREMENTS AND EXPLORATORY DATA ANALYSIS
1. Sources or errors in electronic measurement equipment.
2. Statistical estimators in measurement:biased and unbiased.
3. Autocorrelation and spectra.

CHAPTER 4. DATA ACQUISITION: THEORY AND PRACTICE
1. Electronic equipment functional blocks.
2. Analog to digital converters.
3. Sampling theorem. Aliasing and leakage effects.
4. Discrete spectra.

CHAPTER 5. INTERFERENCES AND NOISE
1. Types of interferences.
2. Coupling mechanisms.
3. Modeling interferences.
4. Noise in electronic circuits.
5. Short term stability.

CHAPTER 6. SENSORS AND TRANSDUCERS
1. Classification of sensors and transducers.
2. Electronic conditioning.
3. Displacement.
4. Temperature.
5. Accelerometers. Vibration characterization.
6. Force and torque.
7. Flow.
8. Other magnitudes.
9. Smart sensors.

CHAPTER 7. NON-DESTRUCTIVE TESTING (NDT)
1. Acoustic Emission (AE): testing and
monitoring.
2. Piezoelectric acoustic emission sensors.
3. Electromagnetic method.
4. Digital imaging
5. Ultrasonics.
6. Leak testing method.
7. Radiology (X and Gamma) method.
8. Radiology (neutron) method.

CHAPTER 8. NOISE AND VIBRATION CONTROL THROUGH
ELECTRONICS
1. Electronics as the key to vibration
control.
2. Structure of a control electronic system.
3. Electronic mesurement and diagnostics.
4. Vibration transducers: more.
5. Equipment.

LAB EXPERIENCE 1. OSCILLOSCOPES
Elements of the oscilloscope. Calibration of probes.
Measurement of different magnitudes:voltages, time and frequency.
Rise time.Spectral analysis. Function generator synchronization issues.

LAB EXPERIENCE 2. FREQUENCYMETERS AND PULSE COUNTERS
Frequency measurement. Period measurement.
Time-interval counters. Totalizers: event counters.

LAB EXPERIENCE 3. A/D AND D/A CONVERTERS
Design and Simulation of A/D and D/A converters via PSPICE.

LAB EXPERIENCE 4. DATA ACQUISITION
Data acquisition and random data in measurement equipment. Data acquisition boards and MATLAB to
handle data.

LAB EXPERIENCE 5. SENSORS AND TRANSDUCERS
Temperature, position, vibration, ultrasonics transducers, torque sensors, load cells.

COMPONENTS AND STRUCTURES

MODELLING AND SIMULATION OF SYSTEMS

QUALITATIVE ANALYSIS OF THE TIME RESPONSE.

CONTROLLERS DESIGN

INTRODUCTION TO THE CONTROL TECHNIQUES IN THE SPACE OF STATUS

ACTIONS WHEN BUILDING.

THE STRUCTURE. THE ELEMENT. THE JOINTS.

DURABILITY

ULTIMATE LIMIT STATES (ULS)

FATIGUE LIMIT STATE FOR STANDARD STRESS
Fatigue ULS for standard stress. General study of break-related methods.
Sizing and check of the sections. Deviated section.
Instability ULS. Fatigue ULS for shear. Fatigue ULS tensile stresses.

SERVICEABILITY LIMIT STATES (SLS)
SLS cracking
SLS deformation

STRUCTURAL ELEMENTS
T-sections and similar Frameworks layout Foundation elements

CONCRETE STRUCTURES CONSTRUCTION
Introduction to pre-stressed Material for pre-stressing

QUALITY STANDARDS
Standardisation and standardisation entities. General concepts concerning standardisation. UNE Quality Standards.
Elements of an internal quality management system. Elements of an internal quality assurance system. Quality User Guide.

QUALITY WHEN PROVIDING SERVICES
Concept and definition of service.
Service issue on product quality. Different types of services portfolio.
Main characteristics of services. Considerations on the design of services.
Elements of the quality system for services.

CONTROL TECHNIQUES – BASIC FOR IMPROVED QUALITY (7 h)
Purposes of the improvement techniques.
The seven tools for quality (7 H). Data collection sheet. Inspection cause-effect diagram.
Histogram. Stratification. Pareto Diagram. Scatter Diagram. Control Graphics.

OTHER BASIC TECHNIQUES FOR IMPROVED QUALITY (7 h)
Other improvement techniques. Brainstorming.
Flowchart Tree chart Matricial chart, etc.

PLACEMENTS
Introduction. Management Techniques A. Introduction. Management Techniques B.
Control techniques. Data collection and inspection. Control techniques. Metrology
Other Control techniques.

THE WELDING PROCEDURES WELDABILITY

INSPECTION AND CONTROL OF WELDING TYPES OF DEFECTS AND CERTIFICATION

ROBOTS MECHANICS: MORPHOLOGY, CHARACTERISTICS AND COMPONENTS

KINEMATICS OF HANDLERS

NON-CONVENTIONAL MECHANISMS

MECHANISMS OF PNEUMATIC FORCE OR COMMAND PNEUMATIC MECHANICAL CIRCUITS

MODELLING AND DYNAMIC ANALYSIS OF MACHINERY

PRELIMINARY PROJECT ON MECHANICAL TRANSMISSION

INTRODUCTION TO A DIAGNOSIS TECHNIQUE IN MACHINES

COMBUSTION
Characteristics, properties and specifications
Theory, calculations and performance. Control and applicable regulations.

BURNERS
Fireplaces. Draft. Control and regulations.

BOILERS
Types. Applications. Balance and performance.

FURNANCES
Types. Applications. Balance and performance.

CO-GENERATION AND THERMAL FLUIDS NETWORK
Calculations and assessment

ENERGY AUDITS
Methodology, measuring, assessment, identification of potential improvements and profitability assessment.

SELECTION OF AUTONOMOUS EQUIPMENT

TYPES OF THERMAL INSTALLATIONS IN BUILDINGS

TRANSPORT AND DISTRIBUTION OF AIR AND WATER