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Calculus 1

Limit and continuity. Derivatives. Applications of derivatives. Definite and indefinite integrals. Applications of definite integrals. Methods of integration.

Calculus 2

Vector functions. Functions of several variables. Limits of functions of several variables. Partial derivatives. Applications of partial derivatives. Directional derivatives and gradient vector. Multiple integrals. Infinite sequences and series. Line integrals. Green's theorem. Rotational and divergent. Surface integrals. Stokes' Theorem. Gauss's Theorem.

Calculus 3

First order linear differential equations. Second order linear differential equations. Higher order linear differential equations. Series of real numbers and power series. Series solutions of linear differential equations (including Bessel functions). Systems of differential equations. Laplace transform. Fourier transform. Fourier series. Introduction to partial differential equations (wave, heat and Laplace equations).

Euclidean vector spaces. Systems of equations. Linear transformations. Eigenvalues and eigenvectors. Diagonalization and other applications. Additional topics in linear algebra.

Mechanis 1

Objectives: To introduce students to the basic concepts of Mechanics through lectures, exercises and laboratory activities.
Topics: motion of a particle; Newton's laws of motion; gravitation; work and mechanical energy; conservation of energy.

Mechanics 2

Many-particle system (linear momentum, momentum, and collisions); rotation of rigid bodies (torque and angular momentum); dynamics of rotational motion; equilibrium and elasticity.

Charges and fields; electric potential; electric fields around conductors; electric currents; magnetic field; electromagnetic induction and Maxwell's equations; alternating current circuits; electric fields of matter; magnetic fields of matter.

Errors. Solution of equations in one variable. Interpolation and polynomial approximation. Numerical derivation and integration. Numerical solutions for ordinary differential equations. Solution of linear systems (direct and iterative methods). Solution of non-linear systems. Approximation theory. Introduction to numerical solutions of partial differential equations.

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Errors. Solution of equations in one variable. Interpolation and polynomial approximation. Numerical derivation and integration. Numerical solutions for ordinary differential equations. Solution of linear systems (direct and iterative methods). Solution of non-linear systems. Approximation theory. Introduction to numerical solutions of partial differential equations.

Physical basis of electronics, semiconductors, semiconductor diodes, rectifier diodes, applications; linear voltage sources: ac/dc conversion, basic concepts, capacitive filtering, voltage regulation, voltage regulators; special diodes: zener, led, applications in electronic circuits, junction transistor, transistor as electronic switch, signal amplifiers, operational amplifiers their basic configurations, optical couplers and their applications in electronic circuits. Data conversion and noise analysis, sensors and signal conditioning, actuators.

Fundamental concepts of thermodynamics; variables and equations of state; laws of thermodynamics; thermodynamic systems; thermodynamic potentials; phase transitions and mixtures.

Vector and tensor analysis; Green's functions; special functions.

Introduction to the fundamental ideas of quantum theory. The mathematical apparatus of Schrödinger's quantum mechanics. Formalization of Quantum Mechanics by stating the postulates. Spin 1/2 and two-level systems. The one-dimensional harmonic oscillator. Angular momentum. Particle in central potential. Hydrogen atom.

Topics: Crystal structures, reciprocal lattice, diffraction in crystals, crystal bonds, elasticity, phonons, lattice vibrations, thermal properties of insulators, Fermi gas: free electron models, energy bands, conduction theory, semiconductor materials.

Introduction to statistical methods. Statistical description of a system of particles. Statistical thermodynamics. Basic methods and results of statistical physics. Applications. Phase transitions. Quantum statistics. Systems with variable number of particles. Reversible processes and fluctuations.

Development of a group project with integrated solution involving different aspects of Engineering Physics.

Obs: This is a "scientific initiation" project, mentored by Dr. ZALEWSKI, Willian. Project done in the period 01/08/2017 - 31/07/2018.

Resume:

Variable stars are one of the main sources of information for astronomy, the study of the variation of brightness given in light curves, among other data, can provide information about their system, such as whether it has exoplanets or not. In this work, we analyze 36 systems with exoplanets identified from observations made by the NASA Kepler Space Telescope. In this analysis we look for patterns in the brightness variation that repeat in these systems that may be related to the existence of exoplanets. The patterns sought are morphological patterns present in the light curves of each system, the data are analyzed in time series forms, using techniques to find motifs, enabling temporal analysis of the phenomenon.

Keywords: astronomy, time series, clustering, machine learning.

Obs: This is a "scientific initiation" project, mentored by Dr. ZALEWSKI, Willian. Project done in the period 01/08/2018 - 31/07/2019.

Resume:

The study of DNA sequencing enables the development of new methods to diagnose diseases and the formulation of new drugs. Protein-coding genes constitute the functional part of DNA, where the basic biological instructions for gene expression (protein production) are located, and are composed of intron segments, non-coding sequences, and exons, sequences that will be translated into proteins. Advances in the automation of DNA sequencing have enabled the creation of large amounts of data, generating a high demand for more efficient methods of analysis. Computational techniques such as machine learning have been widely used, but the overall performance of these methods is still not considered satisfactory. In this work we use an aggregate of machine learning algorithms to identify the nucleotides that best identify the subsequence in order to identify intron and exon regions.

Keywords: machine learning, dna, classification, sequences.

Obs: This is a "scientific initiation" project, mentored by Dr. ZALEWSKI, Willian. Project done in the period 05/08/2019 - 31/10/2020.

Resume:

Advances in the automation of DNA sequencing have enabled the creation of large amounts of data, generating a high demand for more efficient analysis methods. Computational techniques such as machine learning (ML) offer the possibility of processing large amounts of data through various forms of analysis. In this context, in this work we aim to use the classifier Ensemble technique to combine different predictors and a weight system for the identification of introns and exons regions of gene sequences.

To achieve this goal we employ the use of the Python 3.0 programming language, through which we use the AM algorithms made freely available by the scikit-learn library together with our own lines of code. The method proposed in this paper consists in combining classifiers by means of the voting technique from a set of single-hypothesis predictors. Each predictor classifies a given sequence by assigning a weight, based on the classifier's performance on the training set.

To validate the proposed method we worked with the Molecular Biology (Splice-junction Gene Sequences) Data-Set database, which contains 3190 DNA sequences with 60 nucleotides each, classified into which type of junction they are intron-exon (IE) (767 sequences), exon-intron (EI) (768 sequences) or none (NE) (1655 sequences). As a result of the experimental evaluation, we could obtain an increase in accuracy in the performance of the voter we built (with classification accuracy of 91% for EI class, 92% for IE class and 94% for NE class), compared to the classifier that does not use the idea of custom weights provided by the library used (with classification accuracy of 93% (EI), 90% (IE) and 88% (NE)).

Considering the experimental evaluation performed in this study , we observe that our approach demonstrated interesting results for the studied dataset. The use of different prediction techniques combined for classification enabled higher performance in terms of the accuracy rate. More specifically, it is noteworthy that the combination of predictors obtained better results than any of the predictors evaluated individually.

Keywords: machine learning, dna, programming, classification, sequences.

Role: A monitor will be in the day to day of the course classes assisting both the professor and the students taking that subject during the monitoring semester.

Course: "Computer Programming for Chemical Engineering". Period: 16/08/2018 - 14/12/2018.

Course: "Computer Programming for Engineering Physics and Chemical Engineering". Period: 13/05/2019 - 06/08/2019.