1 - It covers first-order differential equations, their existence and uniqueness theorems, and solution methods. The nth-order differential equations, their existence and uniqueness theorems, and solution methods. The systems of differential equations, their existence and uniqueness theorems, and solution methods.

1 - This course aims to provide a space for the student to begin the research work which will be developed throughout the Master's Program. In this context, the research project is defined with respect to the delimitation of the topic, the identification of the research problem, as well as the collection of material that will support the research and the literature review. To earn the credits for this course, the master's student must present proof of the publication of an article—based on the research begun in this course—in a scientific event and/or a quality journal, as established in Table 5 of the Program’s Regulations.

1 - This course provides a space for the graduate student to participate in undergraduate-level activities as a complement to their pedagogical training. The Teaching Internship is mandatory for all doctoral students in the PPGMM who receive scholarships of any type from CAPES, CNPq, FAPERGS, UNIJUÍ, or other funding agencies, and optional for the other doctoral and master's students.

1 - It addresses mathematical modeling applied as a scientific method for research and as a teaching and learning methodology for education. The research topics, developed by the Research Groups that make up the Graduate Program in Mathematical and Computational Modeling, are presented, covering different areas of knowledge such as engineering, agronomy, physics, computer science, and health.

2 - The general principles of Programming Logic. The conceptualization and design of programs and algorithms. Basic components (variable, constant, assignment, instruction, operators, and expressions). Use of control structures (selection and iteration). Basic data types (variable types, strings, vectors, arrays). Construction and declaration of new types. Subalgorithms. Application in a high-level programming language.

3 - Computational modeling at the system and subsystem level. Block diagrams. Use of computational tools with graphical block diagramming and customized libraries. Simulation of continuous-time and discrete-time systems. Simulation of dynamic systems applied in different areas of science. Interfacing with high-level programming languages.

4 - Introduction. Porous Media (Basic concepts, definitions, classification). Porosity. Fundamental Equations in Porous Media (Conservation of Mass, Momentum, and Energy). Tortuosity and Permeability. Equations of Motion for Homogeneous Fluid. Darcy’s Law, Isotropic and Anisotropic Permeability. Derivatives of Darcy’s Law. Continuity and Conservation Equations in Homogeneous Flow. Initial Value and Boundary Value Problems.

5 - Basic concepts in nonlinear systems: definitions, types of nonlinearities (dynamic vs. static, soft vs. hard), motivation and justification for application, autonomous and non-autonomous systems. Typical examples of nonlinearities. Behavior of nonlinear systems: comparison with linear systems, equilibrium points and classification, limit cycles, bifurcations, chaos. Characterization of nonlinear system dynamics: multiple attractors, limit cycles, chaotic dynamics. Analysis of nonlinear systems: phase plane, trajectory, phase portrait, singular points, stability, Lyapunov method. Methods for controlling nonlinear systems.

6 - Fourier Series and Integrals. Partial Differential Equations. Existence and Uniqueness Theorems. Boundary Value Problems. Sturm–Liouville Problems. Expansion in Eigenfunctions. One-Dimensional Wave Equation. One-Dimensional Heat Diffusion. Method of Separation of Variables (Product Method): Homogeneous and Non-Homogeneous Problem.

7 - Partial Differential Equations. Vibrating Membrane. Two-Dimensional Wave Equation. Two-Dimensional Heat Diffusion. Method of Separation of Variables (Product Method): Homogeneous and Non-Homogeneous Problem. Laplacian in Polar Coordinates. Circular Membrane. Bessel’s Equation. Laplace’s Equation. Potential.

8 - Introduction. Main concepts. Heat, mass, and linear momentum transfer. Control of physical quantities. Fourier’s, Fick’s, and Newton’s laws; Fluid Statics. Heat transfer by radiation. Fluid fields and basic equations (Euler): conservation of mass, linear momentum, and energy. Navier –Stokes equations. Laminar flow of incompressible fluids. Turbulent flow of viscous fluids. Reynolds analogy. Mass transfer by convection. Heat transfer by natural convection. Flow through porous media.

9 - Global scenario of electric power generation; Introduction to renewable energy sources; Solar thermal and photovoltaic generation systems; Wind power generation systems; Fuel cells and hydrogen-based power generation; Geothermal energy; Small Hydroelectric Power Plants; Engine–generator sets and biodigester systems; Energy storage; Conversion, control, and grid integration

10 - Introduction. Difference equations. Z-transform. Time series. System classification. Linear system identification. Linear estimators: types and properties. Data processing. Linear models and model structures. Model validation. Case studies.

11 - Introduction. Identification of nonlinear systems. Nonlinear estimators: types and properties. Data processing. Nonlinear models and structures. Model validation. Case studies.

12 - Energy Conversion. Metrology. Laboratory environment and standardization. Constructive aspects of test benches. Measurement of physical quantities. Measurement techniques and methods. Theory of errors and uncertainties. Basic methods for data processing. Use of software for information processing and presentation. Measurement systems. Instruments. Basic principles of transduction. Transducers: sensors and actuators. Conditioning and basic signal-conditioning structures. Electroelectronic instruments: analog and digital. Automatic, intelligent, and virtual instruments. Instrument characterization. General aspects of instrumentation. Data acquisition and transduction techniques in instrumentation. Computerized instrumentation systems. Data acquisition boards. Applications and design.

13 - What is Artificial Intelligence (AI)? An overview of AI, problems, problem spaces, and basic problem-solving methods. Introduction to AI techniques: artificial neural networks, genetic algorithms, fuzzy logic, and intelligent agents.

14 - Introduction to the Discrete Element Method. Particle modeling. Particle collision detection. Force application and method iteration. Time integration. Post-processing of results.

15 - Basic Concept of the Finite Element Method; Variational Formulations and Approximations; Discretization of a Structure; Elements and Interpolation Functions; Computation of the Element Matrix; Assembly of Element Matrices; Solution of the System of Equations; Applications in Structural Analysis, Heat Transfer, and Magnetic Field Evaluation; Execution of a Finite Element Program.

16 - Formulation of the linear programming problem; Geometric interpretation; Applications of linear programming: a production problem, a diet problem; Convex sets; Simplex method; The dual of the linear programming problem; Duality theorems.

17 - Solution methods for large-scale linear systems. Eigenvalues and eigenvectors. Eigensystems, decompositions (Schur, QR, singular value decomposition). Conditioning of eigensystems. Gerschgorin circles. Unitary and orthogonal transformations. Pseudo-inverse (generalized inverse) matrix. Greville’s method. Quadratic forms. Symmetric and Hermitian matrices.

18 - The best approximate solution of a system of algebraic linear equations. Least-squares method. Quadratic forms. Lagrange method. Rank of a quadratic form. Sylvester’s law of inertia for quadratic forms. Gram–Schmidt process. Symmetric and Hermitian matrices. Theorems on eigenvalues of symmetric matrices. Reduction of a quadratic form to canonical form by orthogonal transformation. Theorem on the extremal property of eigenvectors. Positive-definite quadratic forms. Sylvester’s criterion (with proof). Matrix functions. Regular functions. Application to ODEs. Calculation of the matrix exponential eAt. Two quadratic forms. Eigenvalues and eigenvectors of two matrices. D-orthogonalization of two vectors. Simultaneous reduction of two quadratic forms to canonical forms.

19 - Covers numerical methods with their computational implementation for the solution and optimization of linear and nonlinear systems. Errors and sources of error. Direct and iterative methods for solving linear systems of equations. Convergence criteria. Solution of nonlinear systems of equations. Local optimization by gradient descent. Global optimization. Curve fitting.

20 - Numerical methods with their computational implementation for solving problems in differential and integral calculus. Numerical differentiation and integration. Methods for ordinary differential equations and systems of ordinary differential equations. Consistency, stability, and convergence of methods. Boundary value problems. Finite difference method.

21 - Physical and Mathematical Classification of PDEs. Well-posed problems. Dirichlet, Neumann, and Robin problems. Evolution problems. Application of finite differences for solving PDEs. Methods for obtaining difference equations. Local and global approximation errors. Concepts of consistency, stability, and convergence. Lax’s theorem. Numerical schemes for solving PDEs (explicit and implicit schemes for parabolic, hyperbolic, and elliptic equations). Methods for stability analysis (Neumann method, Lax method, matrix methods), convergence. Methods for nonlinear equations.

22 - Basic concepts in industrial robotics: definitions, types of kinematic chains, types of joints, justifications and potential applications. Denavit–Hartenberg convention and tracing of reference coordinate systems of the links. Calculation of homogeneous transformation matrices. Mathematical formulation of the forward kinematics equation. Mathematical formulation of the inverse kinematics equation. Calculation of the Jacobian matrix. Mathematical formulation of the differential kinematics equation. Examples of kinematic modeling of typical serial robots. Computer-aided kinematic modeling.

23 - Fundamentals of Robot Dynamic Modeling, Importance, and Applications. Main components of an industrial robot: mechanism (serial, parallel, hybrid structure, types of joints), actuation (electric, pneumatic, or hydraulic), and control system. Methods for the mathematical formulation of the robot dynamic model. Representation of the dynamic model in compact matrix form: inertia matrix, matrix of centrifugal and Coriolis effects, vector of gravitational effects, vector of friction dynamics effects, and vector of joint torques and/or forces. Properties of the dynamic model of industrial robots and its application in control and stability analysis. Computational simulation of the robot dynamic model.

24 - Atomic Arrangements: Molecular structures, crystal structure, metallic structures, noncrystalline structures, phases. Structural Imperfections: impure phases, crystalline imperfections, atomic movements, vibrations in crystals. Phases and Material Properties, Material Deformation, Material Fracture. Mechanisms of atomic movement (diffusion). Reactions in the solid state, reaction rate, metastable phases. Modification of Properties through Microstructural Changes: physical properties (mechanical, thermal, and electrical) of materials, microstructure control. Solid-State Device Models, Band Theories. Structure of solids. Physical properties of materials. Properties of polymers and ceramics. Microstructural characterization of materials. Materials physics and semiconductor devices.

25 - Basic Concepts, Fundamental Principles, Overview, and Brief History of Feedback Control Systems. Modeling and linearization of dynamic systems for control. Transfer function, block diagram algebra, and dynamic response analysis. Design using the root locus method. Design based on frequency response. State-space control design. Computer-aided control system design.

26 - Introduction to Artificial Neural Networks. The biological neuron and the artificial neuron. Interconnection structures. Supervised and unsupervised learning. Learning algorithms. Error backpropagation. Competitive learning. Evolutionary neural networks. Self-organizing maps. Applications of neural networks.

27 - Introduction to Sensor and Actuator Microsystems. Introduction to MEMS and basic fabrication techniques for sensor and actuator microstructures. Introduction to physicalmathematical models of semiconductor devices at the meso-, micro-, and nanoscales. Development technology for micrometer-scale sensor and actuator devices. Historical aspects, main applications, and technological and commercial importance of MEMS. Main microfabrication techniques and compatibility with CMOS processes. Application examples. Substrate Microfabrication: silicon as a mechanical material; wet corrosion, isotropy and anisotropy, corrosion mechanisms; plasma corrosion, corrosion mechanisms; isotropic versus anisotropic corrosion and its relation to Si crystallography and other thin semiconductor films. Surface Microfabrication: structural and sacrificial layers; materials and properties of films used as structural and sacrificial layers; mechanical properties of films used as structural layers. Communication protocols. Integration of radio-frequency systems. Application examples. Encapsulation techniques and materials used. Specific applications. Methodologies for integrating microelectronics with sensors and actuators. Electronic compatibility and signal conditioning. Integration of microsystems with communication systems.

28 - Probability can be defined as the degree of belief in the occurrence of any event. Thus, statistics is the science that uses probabilistic theories to explain the frequency of occurrence of these events. These conditions are addressed in both observational and experimental studies, aiming to apply concepts and methods to support decision-making under uncertainty, scientifically justify such decisions, and enable the prediction of future phenomena. Therefore, the course Probability Theory and Statistics covers the study of descriptive statistics, probability calculation, and statistical inference, including processes related to the planning, execution, data analysis, and interpretation of results for a research hypothesis.

29 - Introduction to Heuristics and Metaheuristics; Search Heuristics; Genetic Algorithms; Simulated Annealing; Hill Climbing; Genetic Programming.

30 - The syllabus, course content, and bibliography for the course Special Topics will be defined by the Program Coordination for each edition of the course, upon request by a professor or a student’s request for credit transfer from a course taken in another program.

31 - Stack, Queue, and Tree Structures; Search Trees; Brute Force Method; Exhaustive Search; Greedy Algorithm; Divide and Conquer.

32 - Covers the Laplace transform, the inverse Laplace transform, and applications of the Laplace transform to ordinary differential equations and systems of ordinary differential equations.

1 - It covers first-order differential equations, their existence and uniqueness theorems, and solution methods. The nth-order differential equations, their existence and uniqueness theorems, and solution methods. The systems of differential equations, their existence and uniqueness theorems, and solution methods.

1 – This course aims to provide students with an opportunity to begin the research work to be developed throughout the Doctoral Program. In this context, the research project is defined in terms of the delimitation of the topic, formulation of the research problem, as well as the collection of materials to support the research and the literature review. To receive credits for this course, the doctoral student must provide proof of the publication of an article resulting from the research initiated in this course in a scientific event and/or a high-quality journal, as established in Table 5 of the Program’s Regulations.

2 – This course aims to provide students with an opportunity to continue the research work initiated in the Research Work I course and presented in the Thesis Seminar course. The activities developed in this course are intended to enhance the researcher’s training and may take the form of seminars, the preparation and publication of articles, presentations at scientific events, exchanges with research lines and programs, or other activities that make a significant contribution to the training process of researchers. To receive credits for this course, the doctoral student must provide proof of the publication of an article in a scientific event and/or a high-quality journal, as established in Table 5 of the Program’s Regulations.

3 – This course aims to provide students with an opportunity to continue the research work initiated in Research Work I and II, which is being developed throughout the Doctoral Program. The activities developed in this course are intended to enhance the researcher’s training and may take the form of seminars, the preparation and publication of articles, presentations at scientific events, exchanges with research lines and programs, or other activities that make a significant contribution to the training process of researchers. To receive credits for this course, the doctoral student must provide proof of the publication of an article in a scientific event and/or a high-quality journal, as established in Table 5 of the Program’s Regulations.

4 – This course aims to provide students with an opportunity to carry out the practical and theoretical activities defined in the Qualifying Examination, related to the implementation of the research and the writing of the final dissertation document.

1 – This course provides graduate students with an opportunity to participate in undergraduate activities as a means of complementing their pedagogical training. The Teaching Internship is mandatory for all doctoral students in the PPGMM who receive scholarships of any kind from CAPES, CNPq, FAPERGS, UNIJUÍ, or other funding agencies, and is optional for other doctoral and master’s students.

1 - It addresses mathematical modeling applied as a scientific method for research and as a teaching and learning methodology for education. The research topics, developed by the Research Groups that make up the Graduate Program in Mathematical and Computational Modeling, are presented, covering different areas of knowledge such as engineering, agronomy, physics, computer science, and health.

2 - The general principles of Programming Logic. The conceptualization and design of programs and algorithms. Basic components (variable, constant, assignment, instruction, operators, and expressions). Use of control structures (selection and iteration). Basic data types (variable types, strings, vectors, arrays). Construction and declaration of new types. Subalgorithms. Application in a high-level programming language.

3 - Computational modeling at the system and subsystem level. Block diagrams. Use of computational tools with graphical block diagramming and customized libraries. Simulation of continuous-time and discrete-time systems. Simulation of dynamic systems applied in different areas of science. Interfacing with high-level programming languages.

4 - Introduction. Porous Media (Basic concepts, definitions, classification). Porosity. Fundamental Equations in Porous Media (Conservation of Mass, Momentum, and Energy). Tortuosity and Permeability. Equations of Motion for Homogeneous Fluid. Darcy’s Law, Isotropic and Anisotropic Permeability. Derivatives of Darcy’s Law. Continuity and Conservation Equations in Homogeneous Flow. Initial Value and Boundary Value Problems.

5 - Basic concepts in nonlinear systems: definitions, types of nonlinearities (dynamic vs. static, soft vs. hard), motivation and justification for application, autonomous and non-autonomous systems. Typical examples of nonlinearities. Behavior of nonlinear systems: comparison with linear systems, equilibrium points and classification, limit cycles, bifurcations, chaos. Characterization of nonlinear system dynamics: multiple attractors, limit cycles, chaotic dynamics. Analysis of nonlinear systems: phase plane, trajectory, phase portrait, singular points, stability, Lyapunov method. Methods for controlling nonlinear systems.

6 - Fourier Series and Integrals. Partial Differential Equations. Existence and Uniqueness Theorems. Boundary Value Problems. Sturm–Liouville Problems. Expansion in Eigenfunctions. One-Dimensional Wave Equation. One-Dimensional Heat Diffusion. Method of Separation of Variables (Product Method): Homogeneous and Non-Homogeneous Problem.

7 - Partial Differential Equations. Vibrating Membrane. Two-Dimensional Wave Equation. Two-Dimensional Heat Diffusion. Method of Separation of Variables (Product Method): Homogeneous and Non-Homogeneous Problem. Laplacian in Polar Coordinates. Circular Membrane. Bessel’s Equation. Laplace’s Equation. Potential.

8 - Introduction. Main concepts. Heat, mass, and linear momentum transfer. Control of physical quantities. Fourier’s, Fick’s, and Newton’s laws; Fluid Statics. Heat transfer by radiation. Fluid fields and basic equations (Euler): conservation of mass, linear momentum, and energy. Navier –Stokes equations. Laminar flow of incompressible fluids. Turbulent flow of viscous fluids. Reynolds analogy. Mass transfer by convection. Heat transfer by natural convection. Flow through porous media.

9 - Global scenario of electric power generation; Introduction to renewable energy sources; Solar thermal and photovoltaic generation systems; Wind power generation systems; Fuel cells and hydrogen-based power generation; Geothermal energy; Small Hydroelectric Power Plants; Engine–generator sets and biodigester systems; Energy storage; Conversion, control, and grid integration.

10 - Introduction. Difference equations. Z-transform. Time series. System classification. Linear system identification. Linear estimators: types and properties. Data processing. Linear models and model structures. Model validation. Case studies.

11 - Introduction. Identification of nonlinear systems. Nonlinear estimators: types and properties. Data processing. Nonlinear models and structures. Model validation. Case studies.

12 - Energy Conversion. Metrology. Laboratory environment and standardization. Constructive aspects of test benches. Measurement of physical quantities. Measurement techniques and methods. Theory of errors and uncertainties. Basic methods for data processing. Use of software for information processing and presentation. Measurement systems. Instruments. Basic principles of transduction. Transducers: sensors and actuators. Conditioning and basic signal-conditioning structures. Electroelectronic instruments: analog and digital. Automatic, intelligent, and virtual instruments. Instrument characterization. General aspects of instrumentation. Data acquisition and transduction techniques in instrumentation. Computerized instrumentation systems. Data acquisition boards. Applications and design.

13 - What is Artificial Intelligence (AI)? An overview of AI, problems, problem spaces, and basic problem-solving methods. Introduction to AI techniques: artificial neural networks, genetic algorithms, fuzzy logic, and intelligent agents.

14 - Introduction to the Discrete Element Method. Particle modeling. Particle collision detection. Force application and method iteration. Time integration. Post-processing of results.

15 - Basic Concept of the Finite Element Method; Variational Formulations and Approximations; Discretization of a Structure; Elements and Interpolation Functions; Computation of the Element Matrix; Assembly of Element Matrices; Solution of the System of Equations; Applications in Structural Analysis, Heat Transfer, and Magnetic Field Evaluation; Execution of a Finite Element Program.

16 - Formulation of the linear programming problem; Geometric interpretation; Applications of linear programming: a production problem, a diet problem; Convex sets; Simplex method; The dual of the linear programming problem; Duality theorems.

17 - Solution methods for large-scale linear systems. Eigenvalues and eigenvectors. Eigensystems, decompositions (Schur, QR, singular value decomposition). Conditioning of eigensystems. Gerschgorin circles. Unitary and orthogonal transformations. Pseudo-inverse (generalized inverse) matrix. Greville’s method. Quadratic forms. Symmetric and Hermitian matrices.

18 - The best approximate solution of a system of algebraic linear equations. Least-squares method. Quadratic forms. Lagrange method. Rank of a quadratic form. Sylvester’s law of inertia for quadratic forms. Gram–Schmidt process. Symmetric and Hermitian matrices. Theorems on eigenvalues of symmetric matrices. Reduction of a quadratic form to canonical form by orthogonal transformation. Theorem on the extremal property of eigenvectors. Positive-definite quadratic forms. Sylvester’s criterion (with proof). Matrix functions. Regular functions. Application to ODEs. Calculation of the matrix exponential eAt. Two quadratic forms. Eigenvalues and eigenvectors of two matrices. D-orthogonalization of two vectors. Simultaneous reduction of two quadratic forms to canonical forms.

19 - Covers numerical methods with their computational implementation for the solution and optimization of linear and nonlinear systems. Errors and sources of error. Direct and iterative methods for solving linear systems of equations. Convergence criteria. Solution of nonlinear systems of equations. Local optimization by gradient descent. Global optimization. Curve fitting.

20 - Numerical methods with their computational implementation for solving problems in differential and integral calculus. Numerical differentiation and integration. Methods for ordinary differential equations and systems of ordinary differential equations. Consistency, stability, and convergence of methods. Boundary value problems. Finite difference method.

21 - Physical and Mathematical Classification of PDEs. Well-posed problems. Dirichlet, Neumann, and Robin problems. Evolution problems. Application of finite differences for solving PDEs. Methods for obtaining difference equations. Local and global approximation errors. Concepts of consistency, stability, and convergence. Lax’s theorem. Numerical schemes for solving PDEs (explicit and implicit schemes for parabolic, hyperbolic, and elliptic equations). Methods for stability analysis (Neumann method, Lax method, matrix methods), convergence. Methods for nonlinear equations.

22 - Basic concepts in industrial robotics: definitions, types of kinematic chains, types of joints, justifications and potential applications. Denavit–Hartenberg convention and tracing of reference coordinate systems of the links. Calculation of homogeneous transformation matrices. Mathematical formulation of the forward kinematics equation. Mathematical formulation of the inverse kinematics equation. Calculation of the Jacobian matrix. Mathematical formulation of the differential kinematics equation. Examples of kinematic modeling of typical serial robots. Computer-aided kinematic modeling.

23 - Fundamentals of Robot Dynamic Modeling, Importance, and Applications. Main components of an industrial robot: mechanism (serial, parallel, hybrid structure, types of joints), actuation (electric, pneumatic, or hydraulic), and control system. Methods for the mathematical formulation of the robot dynamic model. Representation of the dynamic model in compact matrix form: inertia matrix, matrix of centrifugal and Coriolis effects, vector of gravitational effects, vector of friction dynamics effects, and vector of joint torques and/or forces. Properties of the dynamic model of industrial robots and its application in control and stability analysis. Computational simulation of the robot dynamic model.

24 - Atomic Arrangements: Molecular structures, crystal structure, metallic structures, noncrystalline structures, phases. Structural Imperfections: impure phases, crystalline imperfections, atomic movements, vibrations in crystals. Phases and Material Properties, Material Deformation, Material Fracture. Mechanisms of atomic movement (diffusion). Reactions in the solid state, reaction rate, metastable phases. Modification of Properties through Microstructural Changes: physical properties (mechanical, thermal, and electrical) of materials, microstructure control. Solid-State Device Models, Band Theories. Structure of solids. Physical properties of materials. Properties of polymers and ceramics. Microstructural characterization of materials. Materials physics and semiconductor devices.

25 - Basic Concepts, Fundamental Principles, Overview, and Brief History of Feedback Control Systems. Modeling and linearization of dynamic systems for control. Transfer function, block diagram algebra, and dynamic response analysis. Design using the root locus method. Design based on frequency response. State-space control design. Computer-aided control system design.

26 - Introduction to Artificial Neural Networks. The biological neuron and the artificial neuron. Interconnection structures. Supervised and unsupervised learning. Learning algorithms. Error backpropagation. Competitive learning. Evolutionary neural networks. Self-organizing maps. Applications of neural networks.

27 - Introduction to Sensor and Actuator Microsystems. Introduction to MEMS and basic fabrication techniques for sensor and actuator microstructures. Introduction to physicalmathematical models of semiconductor devices at the meso-, micro-, and nanoscales. Development technology for micrometer-scale sensor and actuator devices. Historical aspects, main applications, and technological and commercial importance of MEMS. Main microfabrication techniques and compatibility with CMOS processes. Application examples. Substrate Microfabrication: silicon as a mechanical material; wet corrosion, isotropy and anisotropy, corrosion mechanisms; plasma corrosion, corrosion mechanisms; isotropic versus anisotropic corrosion and its relation to Si crystallography and other thin semiconductor films. Surface Microfabrication: structural and sacrificial layers; materials and properties of films used as structural and sacrificial layers; mechanical properties of films used as structural layers. Communication protocols. Integration of radio-frequency systems. Application examples. Encapsulation techniques and materials used. Specific applications. Methodologies for integrating microelectronics with sensors and actuators. Electronic compatibility and signal conditioning. Integration of microsystems with communication systems.

28 - Probability can be defined as the degree of belief in the occurrence of any event. Thus, statistics is the science that uses probabilistic theories to explain the frequency of occurrence of these events. These conditions are addressed in both observational and experimental studies, aiming to apply concepts and methods to support decision-making under uncertainty, scientifically justify such decisions, and enable the prediction of future phenomena. Therefore, the course Probability Theory and Statistics covers the study of descriptive statistics, probability calculation, and statistical inference, including processes related to the planning, execution, data analysis, and interpretation of results for a research hypothesis.

29 - Introduction to Heuristics and Metaheuristics; Search Heuristics; Genetic Algorithms; Simulated Annealing; Hill Climbing; Genetic Programming.

30 - The syllabus, course content, and bibliography for the course Special Topics will be defined by the Program Coordination for each edition of the course, upon request by a professor or a student’s request for credit transfer from a course taken in another program.

31 - Stack, Queue, and Tree Structures; Search Trees; Brute Force Method; Exhaustive Search; Greedy Algorithm; Divide and Conquer.

32 - Covers the Laplace transform, the inverse Laplace transform, and applications of the Laplace transform to ordinary differential equations and systems of ordinary differential equations.