Publication in the Diário da República: Despacho n.º 7795/2021 - 09/08/2021
6 ECTS; 2º Ano, 1º Semestre, 14,0 PL + 56,0 TP , Cód. 911212.
Lecturer
- João Manuel Mourão Patrício (2)
- Maria Manuela Morgado Fernandes Oliveira (1)(2)
(1) Docente Responsável
(2) Docente que lecciona
Prerequisites
Not applicable
Objectives
The acquisition of knowledge in Statistics, Complex Analysis and Transforms aims to provide
students with the necessary tools for the analysis of different problems, in the various
aspects of Electrical and Computer Engineering, as well as promoting the
development of analytical and reasoning skills that allow them to conceive and
implement solutions to these problems, facilitating decision-making.
Program
1. Probability:Revisions
1.1. Basics of Probability;
1.2. Random Variables;
1.3. Discrete and Continuous Theoretical Distributions: the Normal distribution;
1.4. Approximation of Binomial and Poisson distributions to Normal;
1.5. The Exponential distribution.
2. Distributions by Sampling
2.1. Statistical inference. Random sampling;
2.2. Central Limit Theorem;
2.3. Chebychev Inequality;
2.4. Theoretical sample distributions;
2.5. Distribution of the sample mean in a normal population;
2.6. Distribution of sample variance in a normal population;
2.7. Distribution of the sample proportion.
3. Parametric Estimation
3.1. Punctual estimation. Estimators and Estimates;
3.2. Properties of estimators;
3.3. Maximum Likelihood Estimation;
3.4. Interval estimation;
3.5. Confidence intervals for the mean of a normal population;
3.6. Confidence interval for the standard deviation and variance of a normal population;
3.7. Confidence interval for a proportion;
3.8. Choice of sample size.
4. Hypothesis Tests
4.1. Basic concepts;
4.2. Hypothesis tests for the mean of a normal population;
4.3. Hypothesis tests for the variance of a normal population;
4.4. Hypothesis tests for a proportion.
5. Introduction to Simple Linear Regression
5.1. Regression models;
5.2. Least squares method in simple linear regression;
5.3. Analysis of variance: ANOVA table;
5.4. Correlation and determination coefficients;
5.5. Inferences in the simple linear regression model.
6. Complex Numbers
6.1. Algebraic, trigonometric and polar form;
6.2. Powers and roots;
6.3. Geometry in the complex plane.
7. Analytical Functions
7.1. Complex variable functions;
7.2. Limits and continuity;
7.3. Analyticity;
7.4. Cauchy-Riemann equations;
7.5. Harmonic functions.
8. Elementary Functions
8.1. Exponential, trigonometric and hyperbolic functions;
8.2. Logarithmic function;
8.3. Power of complexes and inverse trigonometric functions;
8.4. Application to oscillatory systems.
9. Complex Integration
9.1. contours;
9.2. contour integrals;
9.3. Cauchy's integral theorem;
9.4. Integration of analytic functions.
10. Serial Development of Analytical Functions
10.1. Taylor series;
10.2. Power series;
10.3. Laurent series;
10.4. Zeros and singularities.
11. Residue Theory
11.1. Residue Theorem;
11.2. Application to the calculation of trigonometric and improper integrals.
12. Differential and Transformed Equations
12.1. Fundamental types of Differential Equations;
12.2. Fourier series;
12.3. Fourier transforms: definition, properties and their use in solving some types
of differential equations;
12.4. Laplace transforms: definition, properties and their use in solving some types
of differential equations
Evaluation Methodology
Bibliography
- Morriss, S. (2000). Programmable Logic Controllers. (Vol. 1). US: Prentice-Hall
- Novais, J. (2008). Programação de Autómatos, Método GRAFCET. (Vol. 1). Portugal: Fundação Calouste
- Siemens, S. (2003). Simatic, S7-200 Programmable Controller.. (Vol. 1). Alemanha: Siemens
(1993). Fundamentals of Complex Analysis for Mathematics, Science and Enginnering. New Jersey: Prentice-Hill
(1998). Variável Complexa. Lisboa: McGraw-Hill
(2004). Introdução Computacional à Probabilidade e Estatística. : Porto Editora
(2007). Estatística. : McGraw-Hill
Teaching Method
Theoretical and theoretical-practical classes, in which subjects related to
each of the program contents. Practical laboratory classes, in which specific software are used, and tutorial classes.
Software used in class
EXCEL Spreadsheet
