Numerical resolution of linear systems. Direct and iterative methods. Sparseness. Ordering. Storage methods. Eigenvalues ​​and eigenvectors. Applications.

Analysis of the linear stability of steady-state solutions of dynamic systems. Calculation of eigenvalues ​​(asymptotic analysis). Analysis of transient zero-dimensional systems. Algebraic dispersion equation. Analysis of one-dimensional transient systems. Introduction to the concepts of convective and absolute instability. Marginal stability curves and critical points. Two- and three-dimensional disturbances. Transformation and Squire’s theorem. Principle of exchange of instabilities. Differential dispersion equation. Calculation of eigenvalues ​​with direct (matrix formation) and inverse (shot method) methods. Viscous and non-viscous instabilities. Influence of inflection points. Calculation of eigenvectors (initial transient analysis). Energy standards definitions. Initial value problem.

Introduction. Analysis in the phase plan. Existence of limit cycles. Fundamentals of Lyapunov theory: stability, equilibrium points, performance analysis. Advanced stability theory: instability theorem. Barbalat’s motto. Analysis of descriptive functions.

Classification and origins of residual stresses. Main sources and sub-sources of residual stresses. Residual stresses in the welding process. Residual stresses in the machining process. Mechanical surface treatments. Relief of residual stresses. Effects of residual stresses on fatigue and service life of structural components. Destructive and non-destructive methods for evaluating residual stresses. X-ray diffraction tensometry.

Free Vibrations. Forced Vibrations. Systems with Two Degrees of Freedom. Systems with Multiple Degrees of Freedom. Dynamic Absorbers. Energy Method. Continuous Systems. Modal Analysis. Experimental Analysis of Vibrations. Shock and Vibration Isolation.

Types of Fuels, Biofuels, Energy Generation, Tests of: density; viscosity; flash point; corrosion; cloud and pour point; distillation; chromatography; calorific value, Applications for Biomass Oils and Waste.

Polymeric materials. Mechanical properties. Thermal properties. Chemical properties. Optical properties. Electrical properties. Rheological properties. Extrusion. Injection. Blow. Thermoforming.

Transformations in 2D and 3D objects, Projections and perspectives. Curves and surfaces: interpolation, adjustment, free forms. Hermite, Bezier, Splines, Rational, NURBS models. Geometric Modeling: B-rep, CSG. Data Structure for Geometric modeling. Graphical interfaces. Interactive systems. Treatment of hidden lines and surfaces. Visual realism: local and global methods.Radiosity. Tray tracing. Animations. Colors.

Fundamentals of symbolic manipulation. Review of functions for symbolic computation. Introduction to internal representation. Assignments and transformation rules. Tests, models and applications of these. Introduction to pure functions. Definition of new functions for symbolic manipulation. Different types of models. Different shapes to represent arbitrary objects. Restrictions on models. Models name. Alternatives. Repeated Models. Optional arguments. Customization, representation functions and notation. Introduction to representation functions. Introduction to notation and formatting. Contexts and package creation. Changing contexts. Attributes. Structure of a package. I/O. Construction of a package for symbolic manipulation. Transformation, manipulation and notation of representation functions. Applications: derivation of equations and simplification, non-dimensionalization, separation of variables and integral transform, finite differences and other discrete methods.

Control systems concepts. Components and characteristics of open and closed loop control systems. Root locus and Bode diagrams. Classic controller design: Proportional, Integral, Derivative, lead-lag compensators. Design of modern controllers: state feedback, controllability, observability. Ackerman formula.

Review of the basic concepts of fluid mechanics. Structure of non-Newtonian fluids. Constitutive models. Generalized Newtonian and Viscoelastic Fluids. Flow phenomena in non-Newtonian fluids. applications

Simulation of incompressible flows. Artificial compressibility method. Projection method. Boundary conditions for pressure, inlet and outlet. Example problems: cavity with movable lid and flow over a step. Simulation of compressible flows. Euler equations. Different methods for capturing discontinuities. Example problems: Normal and oblique shock tube.

Formulação Variacional de Problemas de Valor de Contorno: Método de Ritz. Método de Galerkin. Aspectos Computacionais. Aplicações em elasticidade, condução de calor e mecânica dos fluidos. Técnicas numéricas especiais. Organização e implementação de programas.

1.Introduction: capture devices, spatial resolution and color depth. Classification, Applications: processing, analysis, synthesis. Hardware for CG and CV. Graphic Primitives. Digital Images. Aliasing (anti-aliasing). Moiré patterns. Human Vision. 2. Image Storage Formats: PCX, GIF, TIFF, EPS, etc. Image Compression Techniques. Lossy vs. Lossless Compression..RLE,Hoffman,LZW,JPEG,FIF DCT, Fractals, Wavelets. 3. Colors in video and printers: RGB, CMY, CMYK, HSV, HLS, YIQ systems. Systems used in industry – PANTONE, MUNSELL, SCOTICK. 4. Image Manipulation:.Contrast Modification..Noise Smoothing..Side Detection..Interpolation and Motion Estimation. Pseudocolor and Falsecolor. Special Effects in Dithering images. Image Segmentation. Line and Point Detection. Thresholding. Understanding Pattern Recognition. Interpolation and Motion Estimation.

Fundamentals of Newtonian Mechanics. Fundamentals of Analytical Mechanics: Principles of Virtual Work, D’Alembert and Hamilton. Lagrange and Hamilton equations. Relative Motion. Rigid Body Dynamics. Geometric Description of Dynamical Systems. Stability of Autonomous Systems. Non-Autonomous Systems. Perturbation methods. Hamilton-Jacobi equation.

High cycle fatigue of metallic structures – S-N method. General notions of elasto-plasticity. Oligocyclic plastic fatigue of metallic structures – E-N method. Neuber’s rule and linear rule for approximating the stabilized cycle. Linear Elastic Fracture Mechanics – Stress Distribution in the vicinity of a crack. Voltage intensity factor. Energetic balance. Energy refund rate. Integral J. Numerical determination of stress intensity factors. Rupture criteria for monotonous loads. Pure mode I. Effect of stress state. Plastic zone. Determination of Kic according to standards. Dynamic cracking. Combined modes. Fatigue failure criteria. Fatigue crack propagation laws. Bifurcation criteria. Elasto-plastic fracture mechanics. Phenomenological aspects. COD. R curve. Equivalent energy.

Uniaxial tests, phenomenological aspects: softening, variation in stiffness in damaged specimens, size effect. Definition of the damage variable and presentation of uniaxial models – Models with and without gradient \[Dash] test simulation, heat conduction, wave propagation, existence and uniqueness, numerical methods for approximating problems. General models – Continuous with microstructure, thermomechanics of damaged solids, fracture and fatigue, numerical methods for approximating problems, comparison with classical theories of Fatigue and Fracture Mechanics.

Phenomenological aspects of fatigue tests on metals and metallic alloys. Introduction to Continuous Damage Mechanics: definition of the damage variable in the uniaxial case and presentation of uniaxial models for oligocyclic fatigue at high and low temperatures. Experimental acquisition of coefficients. Numerical simulation of complex loads on bars and trusses. Extension of models to the three-dimensional context – thermodynamic aspects. Numerical simulation of complex loading on thin-walled pressure vessels and beams. Study of fatigue-creep coupling. General study of the fracture of structures with any geometry and with elasto-plastic or elasto-viscoplastic behavior.

Review of the Basic Principles of Mechanics. Constitutive Theory. Ideal, Elastic and Newtonian Fluids. Navier-Stokes equations. Exact solutions. Potential Flow. Boundary layer. Compressible Flows.

Definition of a continuous medium. Kinematics: configuration, movement and deformation measurements. Basic conservation laws: mass, linear momentum, angular momentum and energy. Second law of thermodynamics. Constitutive equations: thermo-elasticity. Small deformation hypothesis: linear elastostatics, wave propagation in elastic media and heat conduction in elastic media.

Phenomenological aspects of testing on metals and polymers. Uniaxial models for metals and polymers at high and low temperatures – Viscoelasticity, elasto-plasticity and elasto-viscoplasticity – Identification of coefficients. Trusses – Energy method. Extension of theories to the three-dimensional case – Plates with notches, beams and pressure vessels with thin walls – Numerical solution techniques. Review of the principles of Mechanics. Systematic procedure for obtaining thermodynamically admissible constitutive equations – Second law of thermodynamics, Helmholtz free energy and dissipation potential. Quasi-static processes and wave propagation in inelastic media. Heat conduction. General solution by Finite Elements.

Diffusion (introduction). Binary and ternary phase diagrams. Physical metallurgy of carbon and low alloy steels. Tool Steels. Stainless steels. Aluminum and its alloys. Copper and its alloys.

Tensile test: nominal curve, true stress-true strain curve, adjustment equations (Holloman, Ludwick, …), hardening coefficient, plastic instability, sensitivity to strain rate. Impact test: concept of impact toughness, Charpy test, influence of temperature, materials for cryogenic purposes, influence of metallurgical factors, aspects of ductile fracture and brittle cleavage fracture. Understanding Linear Elastic Fracture Mechanics: concept of fracture toughness (KIC). Fatigue: S-N curve, effect of average stress, surface finish and stress concentrators, crack propagation (da/dN x \[Laplacian]K). Creep: creep test, creep curve, creep mechanisms, creep resistant materials.

Matrix Algebra. Resolution of direct and iterative Systems of Equations. Eigenvalues ​​and eigenvectors. Integration Methods. Errors. Approximate Methods for Solving Differential and Integral Equations. Introduction to Discrete Methods.

Function base. Eigenvalue problems. Sturm-Liouville problems. Helmholtz problem. Expansion in eigenfunctions. Classical Integral Transform Technique. Generalized Integral Transform Technique. Methods for accelerating convergence. Approximate analytical methods. Galerkin method. Approaches to Hermite. Technique of Coupled Integral Equations. Applications in diffusion and convection. Applications to solid mechanics problems.

Uncertainty Analysis. Sensors. Force, Pressure and Torque Transducers. Displacement, Speed ​​and Acceleration Transducers. Instrumentation. Signal Conditioning. Data acquisition.

Modeling of Mechanical Systems applying the Newton-Euler and Lagrange equations. Modeling of Electrical Systems applying Kirchhof’s Laws. Modeling of Thermal, Hydraulic and Pneumatic Systems. Linearization. Analysis in the time and frequency domain. Application of Connection Graphs.

Sampled systems, Z transform. Transfer function, zero order stapler, digital filters, open and closed loop systems. Stability. Discretization of the continuous controller. Controller design by discrete methods. Design methods: root locus in the Z plane. Discrete PID. Implementation of numerical algorithms on a computer.

Rheological properties. Uncertainty analysis. Viscosimetry by falling spheres. Capillary viscometer. Rotary rheometer. Capillary rheometer. Extensional rheometer. Rheological characterization of materials.

Review of Basic Principles. First and Second Laws of Thermodynamics. Reversibility and Irreversibility. Energy Availability. Introduction to the Thermodynamics of Irreversible Processes. Applications.

Fusion and Solidification. Latent heat of phase change. Two-phase modeling. Modeling in a single phase in terms of enthalpy. Melting and solidification analytical solutions. Boiling and Condensation. Boiling and condensation models. Boiling in a swimming pool. Convective boiling. Critical heat flux. Saturated and subcooled boiling

General heat conduction equation. Permanent driving: with and without internal generation. Superposition of solutions. Driving in transient mode. Applications.

Convection in laminar regime. Hydrodynamic and thermal boundary layer. Similar solutions in forced convection and natural convection. Dissimilar solutions in forced and natural convection. Mixed convection. Internal drainage. Tubes and channels. Graetz problems. Convection in turbulent regime

Basic laws of radiation. Definitions. Surface properties. Results of electromagnetic theory. Form factors. Heat exchange between black bodies. Heat exchange between gray bodies. Heat exchange between non-ash bodies. Analysis by wavelength ranges. Isothermal and non-isothermal surfaces. Numerical methods. Problems involving radiation, convection and conduction. Study of cavities. Application to the use of solar energy. Beehive type collectors. Reflectors and concentrators. Numerical solutions. Radiation with half participant.

Transient Flows in Pipes. Basic Differential Equations. Anchoring Conditions. Equations in Matrix Form. Eigenvalues. Wave Propagation Speed. Characteristics Method. Boundary Conditions. Control Devices. Transients in Pumps in the four quadrants. Liquid Column Separation. Cavitation.

Membrane theory and bending in shells of revolution. Loadings. Composite shells, nozzles and flanges. Stress concentration, behavior in the plastic phase and collapse loads. Design codes, failure theories and stress classification. External pressure and fatigue in pressure vessels

Fundamental machining concepts. Cutting tools. Tool materials. Machining forces and powers. Tool life. Cutting fluids. Damages and wear of cutting tools. Machinability of materials. Economical machining conditions. Difficult to machine materials. New tool materials. High speed machining.

Binary image processing. Feature extraction. Morphological Operators. Connectivity. Image Analysis. Classification and Recognition: feature extraction, correlation, classification processes. applications

Dynamic Vision. Discrete Fourier Transform. Hough transform. Color. Color System. Texture. Image Quality Control. Image Metrology.