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Graduate Program in Mathematical Modeling

Graduate Program in Mathematical Modeling

Detalhes
Quarta, 11 Julho de 2018

Master's and Doctoral Degree

Grade 4

Structure of the Curriculum


Total amount of class hours: 480
Total amount of credits: 32
Version: 2015/1


Master of Science Degree

Obligatory Subjects

Code Subject School Hours Credits Summary
P0075 Scientific Computing I 60 4
Notions of Programming Logic. Conceptualization of 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. Sub-Algorithms
P0076 Ordinary Differential Equations 60 4
First order differential equations. Theorems of existence and oneness. Methods of resolution. Differential equations of order n. Theorems of existence and oneness. Methods of resolution. Linear differential equations. Linear differential equations solutions theory. Systems of differential equations. Theorems of existence and oneness. Laplace transform and its application to differential equations. Theory of stability. Stability settings. Stability of linear and non-linear systems. The second Lyapunov method. Lyapunov theorems. Applications of Ordinary Differential Equations
P0078 Numeric Methods 60 4
Numerical methods of algebra. Linear systems. Direct and iterative methods. Criteria for convergence and acceleration. Systems of nonlinear equations and optimization problems. Convergence criteria. Newton's method. Methods of descent (by coordinates, by gradient). Interpolation and numerical derivation. Numerical Integration. Ordinary Differential Equations and Systems. The problem of Initial Value (of Cauchy). Runge-Kutta methods (explicit and implicit). Methods Predictor-Corrector (Adams, Milne). Consistency, stability, and convergence of methods. Border Value Problem. Shooting Methods. Finite difference methods. Approximate analytical methods.
P0077 Mathematical Modeling I 30 2
Basic concepts in mathematical modeling: definitions, applications, and characterization. Modeling techniques: white box, black box, gray box. Main steps of mathematical modeling: problem definition (parameters, variables), formulation of the phenomenon, determination of parameters, experimentation, validation, analytical and/or numerical resolution, analysis and modification. Examples of applications of mathematical modeling in problems of mechanical systems.
P0079 Introduction to Research 30 2
The proposed study themes will approach research as a factor of knowledge production; Criteria of scientific knowledge; Nature and assumptions of scientific knowledge; Phases of the construction and elaboration of the research project; Presentations on funding and research promotion agencies and the applicability of didactic strategies in science. In addition, the art of scientific writing and the processes of reviewing and publishing scientific journals will be addressed.
Total: 240 16

Subjects of Applied Research

Code Subject School Hours Credits Summary
P0081 Seminar on the Thesis 30 2
This course marks the moment of presentation and collective discussion of the master's research project, regarding the delimitation of the subject, the definition of the problem, the objectives, the theoretical- methodological mediation and the schedule. Scheduled for the month of March and April of the third semester of the course, the Thesis Seminar course consists of an expanded and collective discussion of the master's research intentions, providing contributions from colleagues and invited teachers for these sessions.
P0082 Thesis Work 90 6
This course aims to offer a space for the student to perform the practical and theoretical activities related to the execution and writing of the Thesis document.
P0080 Research Work 30 2
This course aims to offer a space for the student to start the research work, which will be developed during the Master Course. In this context, the definition of the research project is defined with regard to the delimitation of the topic, the definition of the problem, as well as the survey of the material that will support the research and the bibliographic review. In order to receive the credits of this subject, the master must present proof of publication of the article, of the research initiated in this discipline, in a scientific and/or periodic quality event, as established in Table 5 of the Program Rules
Total: 150 10

Complementary Subjects

Code Subject School Hours Credits Summary
P9587 Teaching Practice Internship 30 2
Development of teaching activities in the Degree in Law and related areas. It is a compulsory course for all Master's students who hold a CAPES scholarship.
Obligatory for holders of CAPES grants
P6706 Methodology of Higher Education 30 2 -
Total: 60 4

Elective Subjects

Code Subject School Hours Credits Summary
P0085 Scientific Computing II 30 2
Computational modeling at system and subsystem level. Block diagram. Use of computational tools with block diagram and customized libraries. Simulation of systems in continuous time and in discrete time. Simulation of dynamic systems applied in different areas of science. Interface with high level languages.
P0097 Computational Fluid Dynamics (Cfd) 30 2
Partial Differential Equations. Problems of Dirichlet, Neuman, Robin. Application of finite differences to solve the partial differential equations. Understanding Consistency, Stability, Convergence. Numerical methods of solving partial differential equations (explicit and implicit schemes of 1st, 2nd and 3rd order). Flows with and without viscosity. Deduction of Navier-Stokes equations. Numerical methods of solving the Navier-Stokes equations. Several formulations of the pressure-velocity problem, current function). Equations of Euler, Reynolds. Models of turbulence.
P0098 Dynamics of Fluids in Porous Media 30 2
Introduction. Porous Media (Basics, definitions, classification). Porosity. Fundamental Equations in Porous Media (Conservation of Mass, Moment and Energy). Tortuosity and Permeability. Equation of Homogeneous Fluid Movement. Darcy's Law, Isotropic and Anisotropic Permeability. Derived from Darcy's Law. Equations of Continuity and Conservation in Homogeneous Flow. Initial and Contour Value Problems.
P0089 Dynamics of Nonlinear Systems 30 2
Basic concepts in nonlinear systems: definitions, types of nonlinearities (dynamic x static, soft x hard), motivation and justification of application, autonomous and non-autonomous systems. Typical examples of nonlinearities. Behavior of non-linear systems: comparison with linear systems, points of equilibrium and classification, limit cycles, bifurcations, chaos. Characterization of the dynamics of nonlinear systems: multiple attractors, limit cycles, chaotic dynamics. Analysis of nonlinear systems: phase plane, trajectory, phase portrait, singular points, stability, Lyapunov method. Methods of control of nonlinear systems.
P0087 Partial Differential Equations I 30 2
Fourier series and integrals. Partial Differential Equations. Theorems of existence and oneness. Problems of values in the contour. Problems of Sturm-Liouville. Development in self-functions. The equation of the One-dimensional Wave. One-dimensional Heat Diffusion. Variable Separation Method (Product Method): Homogeneous and Non-Homogeneous Problem
P0088 Partial Differential Equations II 30 2
Partial Differential Equations. Vibrant Membrane. Two-dimensional wave equation. Two-dimensional Heat Diffusion. Variable Separation Method (Product Method): Homogeneous and Non-Homogeneous Problem. Laplacian in Polar Coordinates. Circular Membrane. The equation of Bessel. Laplace equation. Potential.
P0099 Transport Phenomena 30 2
Introduction. Main concepts. Heat transfer, mass, linear momentum. Control of magnitudes. Laws of Fourier, Fick, Newton, Statics of Fluids. Heat transfer by radiation. Fluid fields and basic equations (Euler): conservation of the mass of linear momentum, energy. Navier-Stakes equations. Laminar flow of fluids in incomprehensible cases. Turbulent flow of viscous fluids. The analogy of Reynolds. Mass transfer by convection. Free convection heat transfer. Flow through porous media.
P0101 Identification of Systems I 30 2
Introduction. Equations the difference. Transform Z. Time Series. Classification of systems. Identification of linear systems. Linear estimators: types and properties. Treatment of data. Linear models and structure. Validation of models. Case Study.
P0102 Identification of Systems II 30 2
Introduction. Identification of non-linear systems. Nonlinear estimators: types and properties. Treatment of data. Nonlinear models and structure. Validation of models. Case Study.
P0084 Instrumentation and Data Acquisition 30 2
Energy Conversion. Metrology. Laboratory environment and standardization. Constructive aspects of test benches. Measures of magnitudes. Measurement techniques and methods. Theory of errors and uncertainties. Basic methods for data processing. Use of software for processing and presentation of information. Measuring systems. The instrument. Basic Principles of Transduction. Transducers: Sensors and Actuators. Conditioning and basic structures of signal conditioning. Electrical and electronic instruments: analog and digital. Automatic, intelligent and virtual instruments. Characterization of an instrument. General aspects in instrumentation. Techniques of acquisition and transection of data in instrumentation. Computerized systems for instrumentation. Cards for data acquisition. Applications and design.
P0086 Artificial intelligence 30 2
Main concepts of Artificial Intelligence; Historical Notes of A. I. and its impact on society; Main AI techniques: search systems and heuristics, artificial neural networks, genetic algorithms, fuzzy logic and intelligent agents.
P0109 Discrete Element Methods 30 2
Introduction to the Discrete Element Method. Particle modeling. Particle collision detection. Application of forces and iteration of the method. Temporal integration. Post Processing of results.
P0090 Finite Element Methods 30 2
Basic Concept of the Finite Element Method; Variable Formulations and Approximations; Discretization of a Structure; Elements and Functions of Interpolation, Element Matrix Computation; Assembly of the Matrices of the Elements; Solution of the System of Equations; Applications in Structural Analysis, Heat Transfer and Magnetic Field Evaluation; Execution of a Finite Element program.
P0091 Optimization Methods 30 2
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; Theorems of duality.
P0093 Matrix Methods I 30 2
Solution methods of large linear systems. Eigenvalues and eigenvectors. Self-systems, decompositions (from Schur, QR, in singular values). The condition of self-systems. Circles of Gerschgorin. Unitary and orthogonal transformations. Pseudo-Inverse Matrix (Generalized). Greville's method. Quadratic Forms. Symmetric and Hermitian Matrices.
P0094 Matrix Methods II 30 2
The best approximation of the system of algebraic linear equations. Least squares method. Quadratic Forms. Lagrange method. Position of the Quadratic Form. Law of inertia of Sylvester's Quadratic Forms. Gram- Schmidt process. Symmetric and Hermitian Matrices. Theorems about eigenvalues of the symmetric matrix. Reduction of Quadratic form to canonical form by orthogonal transformation. Theorem on extreme properties of eigenvectors. Positive definite quadratic forms. Sylvester Criterion (with demonstration). Matrix Functions. Regular Functions. Application for EDO. Calculation of matrix etA. Two Quadratic Forms. Eigenvalues and eigenvectors of two matrices. D-orthogonalization of two vectors. Simultaneous reduction of two Quadratic Forms to canonical forms.
P0096 Numerical Methods for Partial Differential Equations 30 2
Physical and Mathematical Classification of EDP. Problems well put. Problems of Dirichlet, Neuman, Robin. Problems of Evolution. Application of finite differences to solve EDP. Methods of obtaining equations for differences. Local and global approach error. Understanding Consistency, Stability, Convergence. Lax's theorem. Numerical solution schemes of the EDP (explicit and implicit schemes for parabolic, hyperbolic, elliptic equations). Methods for stability analysis (Neumann methods, Lax methods, Matrix methods), convergence. Methods for nonlinear equations.
P0107 Kinematic Modeling of Industrial Robots 30 2
Basic concepts in industrial robotics: definitions, types of kinematic chains, types of joints, justifications and potential applications. The Denavit-Hatenberg Convention and the design of the reference coordinate systems for links. Calculation of homogeneous transformation matrices. Mathematical formulation of the direct 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-assisted kinematic modeling.
P0108 Dynamic Modeling of Industrial Robots 30 2
Fundamentals of dynamic modeling of robots, importance, and applications. Main components of an industrial robot: mechanism (serial, parallel, mixed structure, types of joints), drive (electric, pneumatic or hydraulic) and control system. Methods for mathematical formulation of the dynamic model of robots. Representation of the dynamic model in compact matrix form: inertia matrix, matrix of centrifugal and Coriolis effects, vector of gravitational effects, vector of the effects of friction dynamics and vector of torques and/or joint forces. Properties of the dynamic model of industrial robots and its application in control and stability analysis. Computational simulation of the dynamic robot model.
P0083 Mathematical Modeling II 30 2
Modeling as a scientific method of knowledge: examples of mathematical models: classical models of physics (mechanical and electrical systems); ECONOMIC models (economic growth model, Leontiev model); models of population dynamics (Malthus, Verhulst, Lotka-Volterra); compartmental models (epidemiological, immunological, etc.). Main steps of Mathematical Modeling: formulation of the problem in terms of the phenomenon; experimentation; formulation of the problem in terms of the mathematical model.
P0100 Constitutive Models of Materials 30 2
Atomic Arrays: Molecular structures, crystalline structure, metallic structure, non-crystalline structures, phases. Structural imperfections: impure phases, crystalline imperfections, atomic movements, crystal vibrations. Phases and properties of materials, deformation of materials, ruptures of materials. Mechanisms of atomic motion (diffusion). Solid state reactions, reaction velocity, metastable phases. Modifications of the properties through changes of the microstructure: physical properties (mechanical, thermal and electrical) of materials, control of microstructures. Solid State Device Models, Band Theories. The Structure of Solids. Physical Properties of Materials. Properties of Polymers and Ceramics. Microstructural Characterization of Materials. Physics of Materials and Semiconductor Devices.
P0103 Control Systems Design 30 2
Basic concepts, fundamental principles, overview and a brief history of control systems with feedback. Modeling and linearization of dynamic systems for control. Transfer function, block diagrams algebra and dynamic response analysis. Design by the roots place method. Design based on frequency response. Control project in state space. The design of computer aided control systems.
P0110 Artificial neural networks 30 2
Introduction to the Discrete Element Method. Particle modeling. Particle collision detection. Application of forces and iteration of the method. Temporal integration. Post Processing of results.
P0106 Sensors and Actuators, Technologies and Applications 30 2
Introduction to microsystems sensors and actuators. Introduction to MEMS and the basic techniques of manufacturing sensor and actuator microstructures. Introduction to physical-mathematical models of semiconductor devices in meso, micro and manometric scale. Technology development of sensing devices and actuators in micrometric scale. Historical aspects, main applications, technological and commercial importance of MEMS. Main techniques of microfabrication, compatibility with CMOS processes. Application examples. Micro substrate manufacturing. Silicon as a mechanical material. Wet corrosion, isotropy and anisotropy, corrosion mechanism. Plasma corrosion, corrosion mechanisms. Isotropic versus anisotropic corrosion, relationship with Si crystallography and other semiconductor thin films. Micromanufacturing in Surface, 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 Radiofrequency systems. Application examples. Encapsulation techniques, Materials used. Specific applications. Methodologies of integration of Microelectronics and Sensors Actuators. Electronic compatibility and signal conditioning. Integration of Microsystems and Communication Systems.
P0095 Theory of Probability and Statistics 30 2
The discipline of Probability and Statistical Theory deals with the analysis of quantitative and qualitative categorized and numeric data, the definition of probability and its distribution (Binomial and Poisson, Normal, T and F and Chi-square). Also, from the study of parametric and non-parametric analysis, regressions and correlation and multivariate analysis. However, it will cover the study of descriptive statistics, the calculation of probabilities and statistical inference. Including, the processes related to the planning, execution, data analysis and interpretation of the results of a hypothesis of research from experimental designs, bringing together the use of computational programs.
P0092 Search-based Optimization Techniques 30 2
Introduction to Heuristics and Metaheuristics; Search Heuristics; Genetic Algorithms; Simulated Annealing; Hill Climbing; Genetic Programming.
P0104 Special Topics in Software Engineering 30 2
Software Process Models; Software Requirements and Specification; Methods for Analysis and Design; Reuse of Software; Development of model-driven software; Software Verification and Validation; Fault Tolerance; Software quality.
P0105 Special Topics in Scientific Programming 30 2
Software Process Models; Software Requirements and Specification; Methods for Analysis and Design; Reuse of Software; Development of model-driven software; Software Verification and Validation; Fault Tolerance; Software quality.
Total: 840 56

Doctorate degree

Complementary Subjects

Code Subject School Hours Credits Summary
P9587 Teaching Internship (obligatory for holders of grants from CAPES) 30 2
Development of teaching activities in the Degree in Law and related areas. It is a compulsory course for all Master's degree students who hold a CAPES scholarship.
P6706 Methodology of Higher Education 30 2 -
Total: 60 4

Subjects on Applied Research

Code Subject School Hours Credits Summary
P9739 Qualification Exam 60 4
This course aims to offer a space for the student to carry out the practical and theoretical activities related to the execution and writing of the qualification examination document, for presentation and defense before an Examining Committee composed of three professors of the Program, one of whom is its supervisor , and two teachers outside the Program. Foreseen for the sixth semester of the Course, the course allows the student a critical evaluation of his research proposal, carried out by other teachers together with his supervisor, so that he can improve it, correct it and reorient it before its completion.
P9735 Thesis Seminar 30 2
This discipline marks the moment of presentation and collective discussion of the doctoral research project, regarding the delimitation of the subject, the definition of the problem, the objectives, the theoretical-methodological mediation and the schedule. Foreseen for the third semester of the course, the Thesis Seminar consists of an expanded and collective discussion of the doctorate's research intentions, offering contributions from colleagues and teachers invited to these sessions.
P9736 Research Work I 30 2
This course aims to offer a space for the student to start the research work, which will be developed during the PhD course. In this context, the definition of the research project is defined with regard to the delimitation of the topic, the definition of the problem, as well as the survey of the material that will support the research and the bibliographic review. In order to receive the credits of this subject, the doctoral student must present proof of publication of an article, of the research begun in this discipline, in a scientific and / or periodic quality event, as established in Table 5 of the Program's Rules of Procedure.
P9737 Research Work II 30 2
This course aims to offer a space for the student to continue the research work, initialized in the discipline of Research Paper I and presented in the subject Seminar of Thesis. The activities developed in this discipline aim at valuing the researcher's training, and can be worked in the form of seminars, production and publication of articles, communications of works in scientific events, exchanges with lines and research programs, or other activities that contribute decisively to the process of training researchers. In order to receive credits related to this subject, the doctoral student must present proof of the publication of an article, in a scientific and / or periodic quality event, as established in Table 5 of the Program Rules.
P9738 Research Work III 30 2
This course aims to offer a space for the student to continue the research work, initialized in the disciplines of Research Work I and II, which is being developed during the PhD course. The activities developed in this discipline aim at valuing the researcher's training, and can be worked in the form of seminars, production and publication of articles, communications of works in scientific events, exchanges with lines and research programs, or other activities that contribute decisively to the process of training researchers. In order to receive credits related to this subject, the doctoral student must present proof of the publication of an article, in a scientific and / or periodic quality event, as established in Table 5 of the Program Rules.
P9740 Working on the Doctorate Thesis 30 2
This course aims to offer a space for the student to perform the practical and theoretical activities, defined in the Qualification Exam, referring to the execution and writing of the final thesis document.
Total: 210 14

Elective Subjects

Code Subject School Hours Credits Summary
P0085 Scientific Computation II 30 2
Computational modeling at system and subsystem level. Block diagram. Use of computational tools with block diagram and customized libraries. Simulation of systems in continuous time and in discrete time. Simulation of dynamic systems applied in different areas of science. Interface with high level languages.
P0097 Computational Fluids Dynamics (Cfd) 30 2
Partial Differential Equations. Problems of Dirichlet, Neuman, Robin. Application of finite differences to solve the partial differential equations. Understanding Consistency, Stability, Convergence. Numerical methods of solving partial differential equations (explicit and implicit schemes of 1st, 2nd and 3rd order). Flows with and without viscosity. Deduction of Navier-Stokes equations. Numerical methods of solving the Navier-Stokes equations. Several formulations of the pressure-velocity problem, current function). Equations of Euler, Reynolds. Models of turbulence.
P0098 Dynamics of Fluids in Porous Media 30 2
Introduction. Porous Media (Basics, definitions, classification). Porosity. Fundamental Equations in Porous Media (Conservation of Mass, Moment and Energy). Tortuosity and Permeability. Equation of Homogeneous Fluid Movement. Darcy's Law, Isotropic and Anisotropic Permeability. Derived from Darcy's Law. Equations of Continuity and Conservation in Homogeneous Flow. Initial and Contour Value Problems.
P0089 Dynamics of Non Linear Systems 30 2
Basic concepts in nonlinear systems: definitions, types of nonlinearities (dynamic x static, soft x hard), motivation and justification of application, autonomous and non-autonomous systems. Typical examples of nonlinearities. Behavior of non-linear systems: comparison with linear systems, points of equilibrium and classification, limit cycles, bifurcations, chaos. Characterization of the dynamics of nonlinear systems: multiple attractors, limit cycles, chaotic dynamics. Analysis of nonlinear systems: phase plane, trajectory, phase portrait, singular points, stability, Lyapunov method. Methods of control of nonlinear systems.
P0087 Partial Differential Equations I 30 2
Fourier series and integrals. Partial Differential Equations. Theorems of existence and uniqueness. Problems of values in the contour. Problems of Sturm-Liouville. Development in self-functions. Equation of the One-dimensional Wave. One-dimensional Heat Diffusion. Variable Separation Method (Product Method): Homogeneous and Non Homogeneous Problem
P0088 Partial Differential Equations II 30 2
Partial Differential Equations. Vibrant Membrane. Two-dimensional wave equation. Two-dimensional Heat Diffusion. Variable Separation Method (Product Method): Homogeneous and Non Homogeneous Problem. Laplacian in Polar Coordinates. Circular Membrane. Equation of Bessel. Laplace equation. Potential.
P0099 Transport Phenomena 30 2
Introduction. Main concepts. Heat transfer, mass, linear momentum. Control of magnitudes. Laws of Fourier, Fick, Newton, Statics of Fluids. Heat transfer by radiation. Fluid fields and basic equations (Euler): conservation of the mass of linear momentum, energy. Navier-Stakes equations. Laminar flow of fluids in incomprehensible cases. Turbulent flow of viscous fluids. Analogy of Reynolds. Mass transfer by convection. Free convection heat transfer. Flow through porous media.
P0101 System Identification I 30 2
Introduction. Equations the difference. Transform Z. Time Series. Classification of systems. Identification of linear systems. Linear estimators: types and properties. Treatment of data. Linear models and structure. Validation of models. Case Study.
P0102 System Identification II 30 2
Introduction. Identification of non-linear systems. Nonlinear estimators: types and properties. Treatment of data. Nonlinear models and structure. Validation of models. Case Study.
P0084 Instrumentation and Data Acquisition 30 2
Energy Conversion. Metrology. Laboratory environment and standardization. Constructive aspects of test benches. Measures of magnitudes. Measurement techniques and methods. Theory of errors and uncertainties. Basic methods for data processing. Use of software for processing and presentation of information. Measuring systems. The instrument. Basic Principles of Transduction. Transducers: Sensors and Actuators. Conditioning and basic structures of signal conditioning. Electrical and electronic instruments: analog and digital. Automatic, intelligent and virtual instruments. Characterization of an instrument. General aspects in instrumentation. Techniques of acquisition and transection of data in instrumentation. Computerized systems for instrumentation. Cards for data acquisition. Applications and design.
P0086 Artificial Intelligence 30 2
Main concepts of Artificial Intelligence; Historical Notes of I.A and its impact on society; Main AI techniques: search systems and heuristics, artificial neural networks, genetic algorithms, fuzzy logic and intelligent agents.
P0109 Discrete Element Methods 30 2
Introduction to the Discrete Element Method. Particle modeling. Particle collision detection. Application of forces and iteration of the method. Temporal integration. Post Processing of results.
P0090 Finite Element Methods 30 2
Basic Concept of the Finite Element Method; Variable Formulations and Approximations; Discretization of a Structure; Elements and Functions of Interpolation, Computation of the Element Matrix; Assembly of the Matrices of the Elements; Solution of the System of Equations; Applications in Structural Analysis, Heat Transfer and Magnetic Field Evaluation; Execution of a Finite Element program.
P0091 Optimization Methods 30 2
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; Theorems of duality.
P0093 Matrix Methods I 30 2
Solution methods of large linear systems. Eigenvalues and eigenvectors. Self-systems, decompositions (from Schur, QR, in singular values). The condition of self-systems. Circles of Gerschgorin. Unitary and orthogonal transformations. Pseudo-Inverse Matrix (Generalized). Greville's method. Quadratic Forms. Symmetric and Hermitian Matrices.
P0094 Matrix Methods II 30 2
The best approximation of the system of algebraic linear equations. Least squares method. Quadratic Forms. Lagrange method. Position of the Quadratic Form. Law of inertia of Sylvester's Quadratic Forms. Gram-Schmidt process. Symmetric and Hermitian Matrices. Theorems about eigenvalues of the symmetric matrix. Reduction of Quadratic form to canonical form by orthogonal transformation. Theorem on extreme properties of eigenvectors. Positive definite quadratic forms. Sylvester Criterion (with demonstration). Matrix Functions. Regular Functions. Application for EDO. Calculation of matrix eA. Two Quadratic Forms. Eigenvalues and eigenvectors of two matrices. D-orthogonalization of two vectors. Simultaneous reduction of two Quadratic Forms to canonical forms.
P0096 Numerical Methods for Partial Differential Equations 30 2
Physical and Mathematical Classification of EDP. Problems well put. Problems of Dirichlet, Neuman, Robin. Evolution Problems. Application of finite differences to solve EDP. Methods of obtaining equations for differences. Local and global approach error. Understanding Consistency, Stability, Convergence. Lax's theorem. Numerical schemes of solution of the EDP (explicit and implicit schemes for parabolic, hyperbolic, elliptic equations). Methods for stability analysis (Neumann methods, Lax methods, Matrix methods), convergence. Methods for nonlinear equations.
P0107 Kinematic Modeling of Industrial Robots 30 2
Basic concepts in industrial robotics: definitions, types of kinematic chains, types of joints, justifications and potential applications. Denavit-Hatenberg Convention and the mapping of reference coordinate systems for links. Calculation of homogeneous transformation matrices. Mathematical formulation of the direct 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 assisted kinematic modeling.
P0083 Mathematical Modeling II 30 2
Modeling as scientific method of knowledge: Examples of mathematical models: classical models of physics (mechanical and electrical systems); economic models (economic growth model, Leontiev model); models of population dynamics (Malthus, Verhulst, Lotka-Volterra); compartmental models (epidemiological, immunological, etc.). Main steps of Mathematical Modeling: formulation of the problem in terms of the phenomenon; experimentation; formulation of the problem in terms of the mathematical model.
P0100 Constitutive Models of Materials 30 2
Atomic Arrays: Molecular structures, crystalline structure, metallic structure, non-crystalline structures, phases. Structural imperfections: impure phases, crystalline imperfections, atomic movements, crystal vibrations. Phases and properties of materials, deformation of materials, ruptures of materials. Mechanisms of atomic motion (diffusion). Solid state reactions, reaction velocity, metastable phases. Modifications of the properties through changes of the microstructure: physical properties (mechanical, thermal and electrical) of materials, control of microstructures. Solid State Device Models, Band Theories. Structure of Solids. Physical Properties of Materials. Properties of Polymers and Ceramics. Microstructural Characterization of Materials. Physics of Materials and Semiconductor Devices.
P0103 Control Systems Design 30 2
Basic concepts, fundamental principles, overview and brief history of control systems with feedback. Modeling and linearization of dynamic systems for control. Transfer function, block diagrams algebra and dynamic response analysis. Design by the roots place method. Design based on frequency response. Control project in state space. Design of computer-aided control systems.
P0106 Sensors and Actuators, Technologies and Applications 30 2
Introduction to microsystems sensors and actuators. Introduction to MEMS and the basic techniques of manufacturing sensor and actuator microstructures. Introduction to physical-mathematical models of semiconductor devices in meso, micro and manometric scale. Technology development of sensing devices and actuators in micrometric scale. Historical aspects, main applications, technological and commercial importance of MEMS. Main techniques of microfabrication, compatibility with CMOS processes. Application examples. Micro substrate manufacturing. Silicon as mechanical material. Wet corrosion, isotropy and anisotropy, corrosion mechanism. Plasma corrosion, corrosion mechanisms. Isotropic versus anisotropic corrosion, relationship with Si crystallography and other semiconductor thin films. Micro manufacturing in Surface, 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 Radiofrequency systems. Application examples. Encapsulation techniques, Materials used. Specific applications. Methodologies of integration of Microelectronics and Sensors Actuators. Electronic compatibility and signal conditioning. Integration of Microsystems and Communication Systems.
P0095 Theory of Probability and Statistics 30 2
The discipline of Probability and Statistical Theory deals with the analysis of quantitative and qualitative categorized and numeric data, the definition of probability and its distribution (Binomial and Poisson, Normal, T and F and Chi-square). Also, from the study of parametric and non-parametric analysis, regressions and correlation and multivariate analysis. However, it will cover the study of descriptive statistics, the calculation of probabilities and statistical inference. Including, the processes related to the planning, execution, data analysis and interpretation of the results of a hypothesis of research from experimental designs, bringing together the use of computational programs.
P0092 Search-based Optimization Techniques 30 2
Introduction to Heuristics and Metaheuristics; Search Heuristics; Genetic Algorithms; Simulated Annealing; Hill Climbing; Genetic Programming.
P0104 Special Topics in Software Engineering 30 2
Software Process Models; Software Requirements and Specification; Methods for Analysis and Design; Reuse of Software; Development of model-driven software; Software Verification and Validation; Fault Tolerance; Software quality.
P0105 Special Topics in Scientific Programming 30 2
Software Process Models; Software Requirements and Specification; Methods for Analysis and Design; Reuse of Software; Development of model-driven software; Software Verification and Validation; Fault Tolerance; Software quality.
P0108 Dynamic Modeling of Industrial Robots 30 2
Fundamentals of dynamic modeling of robots, importance and applications. Main components of an industrial robot: mechanism (serial, parallel, mixed structure, types of joints), drive (electric, pneumatic or hydraulic) and control system. Methods for mathematical formulation of the dynamic model of robots. Representation of the dynamic model in the compact matrix form: inertia matrix, matrix of centrifugal and Coriolis effects, vector of gravitational effects, vector of the effects of friction dynamics and vector of torques and / or joint forces. Properties of the dynamic model of industrial robots and its application in control and stability analysis. Computational simulation of the dynamic robot model.
P0110 Artificial neural networks 30 2
Introduction to the Discrete Element Method. Particle modeling. Particle collision detection. Application of forces and iteration of the method. Temporal integration. Post Processing of results.
Total: 840 56

Obligatory Subjects

Code Subject School Hours Credits Summary
P0075 Scientific Computing I 60 4
Notions of Programming Logic. Conceptualization of 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. Sub-Algorithms.
P0076 Differential Equations 60 4
Differential equations of the first order. Theorems of existence and uniqueness. Methods of resolution. Differential equations of order n. Theorems of existence and uniqueness. Methods of resolution. Linear differential equations. Linear differential equations solutions theory. Systems of differential equations. Theorems of existence and uniqueness. Laplace transform and its application to differential equations. Theory of stability. Stability settings. Stability of linear and non-linear systems. The second Lyapunov method. Lyapunov theorems. Applications of Ordinary Differential Equations.
P0070 Introduction to Research 30 2
The proposed study themes will approach research as a factor of knowledge production; criteria of scientific knowledge; nature and assumptions of scientific knowledge; phases of the construction and elaboration of the research project; presentations on funding and research promotion agencies and the applicability of didactic strategies in science. In addition, it will address the art of scientific writing and the processes of reviewing and publishing scientific journals.
P0078 Numeric Methods 60 4
Numerical methods of algebra. Linear systems. Direct and iterative methods. Criteria for convergence and acceleration. Systems of nonlinear equations and optimization problems. Convergence criteria. Newton's method. Methods of descent (by coordinates, by gradient). Interpolation and numerical derivation. Numerical Integration. Ordinary Differential Equations and Systems. Problem of Initial Value (of Cauchy). Runge-Kutta methods (explicit and implicit). Methods Predictor-Corrector (Adams, Milne). Consistency, stability and convergence of methods. Border Value Problem. Shooting Methods. Finite difference methods. Approximate analytical methods.
P0077 Mathematical Modeling I 30 2
Basic concepts in mathematical modeling: definitions, applications and characterization. Modeling techniques: white box, black box, gray box. Main steps of mathematical modeling: definition of the problem (parameters, variables), formulation of the phenomenon, determination of parameters, experimentation, validation, analytical and / or numerical resolution, analysis and modification. Examples of applications of mathematical modeling in problems of mechanical systems.
Total: 240 16

Graduate Program in Mathematical Modeling

Detalhes
Quarta, 11 Julho de 2018

Master's and Doctoral Degree

Grade 4

Scholarships for Master of Science


UNIJUÍ Masters Scholarships: are granted in quotas defined annually. Partial scholarships are granted, of 50% of the monthly fee, in addition to full scholarships. In order to win the scholarship, it is necessary to obey a ranking order of the students in the selection process established by the Program and not have an employment relationship with UNIJUÍ. In addition, you must have at least two shifts a week to dedicate yourself to the activities of the Program when you benefit from a partial scholarship, and four shifts a week when you benefit from a full scholarship. Check out the resolution (Portuguese only).


Master and Doctorate scholarships:


Development agency that grant through specific notices and regulations: CAPES / FAPERGS grants, CNPq grants, and CAPES grants.


Graduate Program in Mathematical Modeling

Detalhes
Quarta, 11 Julho de 2018

Master's and Doctoral Degree

Grade 4

Linguistic Proficiency


Within a period of 24 months, and before the Thesis Defense Banking, the student must  have passed a foreign language proficiency examination carried out by the Department of UNIJUÍ responsible for the area of letters or by an external institution officially accredited for this purpose by the Official bodies of promotion to the Stricto Sensu Postgraduate Courses in the Country.


The approval of the proficiency exam for the Master's Course must be in a foreign language. The English, Spanish, French, Italian and German languages are accepted by the Program.


Graduate Program in Mathematical Modeling

Detalhes
Quarta, 11 Julho de 2018

Master's and Doctoral Degree

Grade 4

History and Proposal of the Program


Mathematical Modeling is a scientific area that extensively uses Mathematics and Scientific Computing. It uses mathematical and computational methods in the elaboration of mathematical models and the search for solutions to current problems in the most diverse areas of knowledge.

Currently modeling is used in areas such as mathematics, physics, condensed matter physics, systems identification, dynamical systems, mechanical systems control, grain storage and drying, gap control strategies in the production of petroleum, wireless sensor networks, mobile robotics, mathematical modeling through metaheuristics; plant breeding, physiology of cultivated plants, veterinary medicine, production of new materials for engineering, control and automation of systems, microelectronics among others.

Mathematical modeling has the improvement of production processes as its fundamental theme, especially in the regional agro-industrial sector and in all of Brazil, as well as the training of professionals to work in higher education.

The Master's degree lasts 24 months and offers 25 vacancies yearly. 32 credits, that is, 480 hours, are organized and offered on a semester basis, with classes on Mondays, Tuesdays, and Wednesdays.

The Doctorate degree lasts 48 months and offers yearly 10 vacancies.  48 credits, that is, 720 hours, are offered from Monday to Wednesday.


Target Audience


The Program covers professionals with a higher education diploma in Mathematics, Physics, Engineering, Agrarian Sciences, Veterinary Medicine, Computing and / or related areas.


Graduate Program in Mathematical Modeling

Detalhes
Quarta, 11 Julho de 2018

Master's and Doctoral Degree

Grade 4

Faculty and Coordinator


Permanent Faculty


Name E-mail Title Lattes Master Doctorate
Airam Teresa Zago Romcy Sausen (Coordenador) airam@unijui.edu.br Doctor View lattes
Antonio Carlos Valdiero valdiero@unijui.edu.br Doctor View lattes
Fabricia Carneiro Roos Frantz frfrantz@unijui.edu.br Doctor View lattes
Fernanda da Cunha Pereira fernanda.cunha@unijui.edu.br Doctor View lattes
José Antonio Gonzalez da Silva jose.gonzales@unijui.edu.br Doctor View lattes
Luiz Antônio Rasia rasia@unijui.edu.br Doctor View lattes
Manuel Martin Perez Reimbold manolo@unijui.edu.br Doctor View lattes
Manuel Osorio Binelo manuel.binelo@unijui.edu.br Doctor View lattes
Paulo Sérgio Sausen sausen@unijui.edu.br Doctor View lattes
Rafael Zancan Frantz rzfrantz@unijui.edu.br Doctor View lattes
Sandro Sawicki sawicki@unijui.edu.br Post doctoral View lattes

Graduate Program in Mathematical Modeling

Detalhes
Quarta, 11 Julho de 2018

Master's and Doctoral Degree

Grade 4

Concentration area and lines of research


Mathematical Modeling (MM) is an area of knowledge that is essentially interdisciplinary, not restricted to any technical-scientific discipline that can be found in the curricula of math, engineering or even computing courses. MM studies the simulation of real systems from the application of mathematics aiming to describe and predict mathematically the behavior of a phenomenon. In this area of knowledge human resources are developed to use the mathematical tool in the placement and resolution of problems in different areas of knowledge contributing to the development of the region and the country. Professionals with this profile are scarce in Brazil, especially in regions far away from large centers. Professionals qualified in MM have a different profile from any others, since besides the knowledge in mathematics and computing they distinguish themselves from other professionals by the knowledge in the subject areas contemplated by the MM, among them the physics, mathematics, computation and Engineering, among others.


Line: Mathematical Modeling Applied to Biosystems Engineering

The line of Mathematical Modeling Research Applied to Biosystems Engineering aims to use mathematical modeling applied in an interdisciplinary way in the areas of engineering, physics, chemistry and biological sciences for technological development and innovation in the fields of agriculture, post-harvest technology, veterinary, systems automation, sensors, bioenergy, natural resources and sustainability.


Line: Computational Modeling, Optimization and Systems Control

The line of Research Computational Modeling, Optimization and Control of Systems comprises study, application and / or development of mathematical models and computational modeling techniques for the solution of interdisciplinary problems. This line also includes researches that apply techniques of optimization and control of dynamic systems as well as problems related to non-linear systems covering the use of mathematical / computational models in the perspective of support to decision making processes, emphasizing the fundamental theoretical questions and their applications.

See Study regulations and study guide


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