Madrid PAU Tech & Engineering II study plan
Madrid PAU Tech & Engineering II · Give each week a clear focus.
8 weeks · About 7 hours per week
Materials and their properties: types, structure, mechanical and technological properties, selection criteria, and environmental impact & Mechanical systems and structures: static equilibrium, supports and reactions, internal forces, stress and strain, design and calculation of structural elements
Classify the main families of engineering materials (metals, polymers, ceramics, composites) and relate their internal structure to density, conductivity and hardness
Build a comparison table of at least ten materials with mechanical properties (yield strength, toughness, hardness) and typical applications
Solve five selection exercises where a service requirement (weight, corrosion, cost) drives the choice of material and justify each decision in writing
Identify the supports of a simple beam (pin, roller, fixed) and draw the free-body diagram with all reaction forces labelled
Your checkpoint
A two-page materials selection dossier: comparison table of ten materials plus three worked selection cases with written justification, and three correct free-body diagrams of beams with different support types
Mechanical systems and structures: static equilibrium, supports and reactions, internal forces, stress and strain, design and calculation of structural elements
Apply static equilibrium equations to calculate reactions in isostatic beams and frames, checking results by an independent equilibrium condition
Draw axial-force, shear-force and bending-moment diagrams for beams under point loads and uniformly distributed loads
Compute normal and shear stress in structural elements and verify them against an allowable stress
Calculate strain and elastic deformation using Hooke's law and the elastic modulus, and explain the meaning of the safety factor
Design the cross-section of a simply supported beam for a given load and allowable stress, selecting a standard profile
Your checkpoint
A solved problem set of six structures (reactions, internal-force diagrams, stress check) with one full beam-design calculation including safety-factor discussion and a sketch of the chosen profile
Mechanisms and machines: transmission and transformation of motion, velocity ratios, forces and torques, efficiency, and applications
Compute velocity ratios and output speeds for gear trains, belt and chain drives, and worm gears, including compound trains
Analyse mechanisms that transform motion (crank-slider, cam-follower, rack and pinion) and determine the relation between input and output motion
Calculate transmitted torque and power in a mechanism, and estimate overall efficiency as the product of stage efficiencies
Solve five real machine problems (conveyor, winch, bicycle, lifting screw, gearbox) selecting the appropriate transmission and verifying the result
Your checkpoint
A mechanism calculation sheet covering five machines: each with a kinematic diagram, velocity-ratio derivation, torque/power calculation and efficiency estimate, ending with a one-paragraph recommendation per case
Electrical and electronic systems: direct current circuits, laws of electromagnetism, electronic components, digital logic, and power systems
Solve direct-current circuits with series, parallel and mixed resistors using Ohm's law, Kirchhoff's laws and mesh or node analysis
Calculate power and energy consumption in circuits and size a supply or protection element accordingly
Apply the basic laws of electromagnetism (Faraday, Lenz, Lorentz force) to explain induction, transformers and motor action
Analyse the behaviour of diodes and transistors as switches in simple circuits and identify the operating region
Simplify and design combinational logic circuits with truth tables, Boolean algebra and Karnaugh maps
Your checkpoint
An electronics problem portfolio: four DC circuit solutions with full working, one transformer and one induction exercise, plus two combinational logic designs with truth table, simplified expression and gate diagram
Electrical and electronic systems: direct current circuits, laws of electromagnetism, electronic components, digital logic, and power systems & Automation and control: open- and closed-loop systems, sensors and actuators, programmable controllers, and industrial robotics
Distinguish open-loop from closed-loop control systems and identify the controller, sensor, actuator and process in a given block diagram
Select sensors for temperature, position, proximity and light applications, stating the working principle and the signal type produced
Explain how a programmable controller executes a cycle and write a short sequence of instructions or a ladder-style program for a defined task
Describe the main configurations of industrial robots (cartesian, SCARA, articulated, delta) and match each to an application
Convert a verbal automation requirement into a block diagram with sensor, controller and actuator specified
Your checkpoint
A one-page automation design for a small process (for example a bottle-filling or sorting station): block diagram, sensor and actuator selection with justification, and a written control sequence of at least eight steps
Materials and their properties: types, structure, mechanical and technological properties, selection criteria, and environmental impact & Technical expression and projects: graphic representation, standardization, technical documentation, project methodology, and evaluation of technological solutions
Interpret and produce multiview orthographic drawings applying the standard projection system, scale and line conventions
Add dimensions, tolerances and surface-finish symbols to a drawing following standardisation rules for dimensioning
Read and draw a simple electrical and a simple mechanical schematic using standard symbols
Structure a technical project document with memory, plans, specifications and budget, and evaluate alternative solutions against criteria
Assess the environmental impact of a product across its life cycle and propose two concrete improvements
Your checkpoint
A short technical project dossier of four to six pages on a simple product: orthographic drawing with dimensions, one schematic, specification table, budget and an environmental-impact section with two justified improvements
Materials and their properties: types, structure, mechanical and technological properties, selection criteria, and environmental impact & Mechanical systems and structures: static equilibrium, supports and reactions, internal forces, stress and strain, design and calculation of structural elements & Mechanisms and machines: transmission and transformation of motion, velocity ratios, forces and torques, efficiency, and applications
Complete a timed mixed set of materials, structures and mechanisms problems under exam conditions, allocating time per problem
Diagnose and correct the three most frequent errors found in earlier weeks (units, sign conventions, efficiency chains)
Redo every previously failed exercise without consulting notes and confirm the correct result independently
Summarise the key formulas of domains 1 to 3 on a single reference sheet written from memory
Your checkpoint
A timed mock exam of domains 1 to 3 (90 minutes) scored against a marking scheme, plus a corrected-errors log listing each mistake, its cause and the rule to avoid it
Electrical and electronic systems: direct current circuits, laws of electromagnetism, electronic components, digital logic, and power systems & Automation and control: open- and closed-loop systems, sensors and actuators, programmable controllers, and industrial robotics & Technical expression and projects: graphic representation, standardization, technical documentation, project methodology, and evaluation of technological solutions
Complete a timed mixed set of electrical, electronic, control and technical-expression questions under exam conditions
Redraw from memory the standard symbols and conventions most used in the exam and check them against a reference
Review the whole formula sheet and the corrected-errors log, closing any item still unresolved
Plan the exam strategy: order of sections, time budget per section and a rule for when to skip a question
Your checkpoint
A full timed mock exam across all six domains (120 minutes) with self-scoring, a final one-page formula and conventions sheet, and a written exam-day time plan
Milestones
Week 2: You can take an unfamiliar simply supported beam, compute reactions and draw the shear and moment diagrams without notes, and the results pass an independent equilibrium check
Week 4: You solve a mixed DC circuit and a combinational logic simplification in under 20 minutes each with correct final values, and you can explain a closed-loop block diagram aloud in two minutes
Week 6: You produce a dimensioned orthographic drawing and a project dossier section that a third party could read and build from, with no missing views or dimensions
Week 7: Your timed mock on domains 1 to 3 scores at least 65 percent, and every error is logged with its cause and correction rule
Week 8: Your full timed mock scores at least 70 percent overall with no domain below 50 percent, and you have a written exam-day time plan