Numerical and Statistical Methods

Basic concepts of Mathematical Analysis and Linear Algebra.

Teaching method will be essentially expository in theoretical classes, in order to introduce concepts. Theoretical-practical and practical classes will be dedicated to problem solving, including their analysis, choice and/or implementation of the most appropriate technique/method, resolution and interpretation of results, under the guidance of the teacher. Problem solving will be initiated “by hand” to help understand the methods and will continue with the support of software appropriate to the contents of the CU, particularly in practical classes (operating in a laboratory environment).

With this Curricular Unit (CU) it is intended that the student knows how to apply some methods and techniques of Statistics and Numerical Analysis. The student will develop skills in statistical data analysis: data organization, statistical treatment, including Statistical Inference, reading and interpretation of results. The student also acquires skills in numerical problem solving, a fundamental approach in Engineering, when analytical solutions to problems are not possible, time-consuming or complex. The student will also develop his/her reasoning and problem solving skills with the support of computational tools.

Part I: Statistical Methods

1. Descriptive Statistics

Aims of descriptive statistics. Notions of population and sample. Data types and measurement scales. Univariate descriptive statistics: displaying and summarizing data; frequencies distribution; measures of central tendency, variability, symmetry and kurtosis. Bivariate descriptive statistics: contingency tables; scatter diagrams, linear correlation, coefficients; linear regression.

 2. Probability Distributions

Binomial, Poisson and Normal distributions. Sampling distributions (introduction). Central Limit Theorem.

 3. Introduction to Statistical Inference

Aims of statistical inference. Point and interval estimations. Confidence intervals for population parameters. Test of hypotheses.

Use of statistical software (MS Excel and/or SPSS) as a support tool in problem solving.

Part II: Numerical Methods

 4. Introduction

Introduction and motivation for the use of numerical methods in Bioengineering. Error estimation in iterative methods.

 5. Nonlinear Equations

Introduction. Location of roots. Graphical method. Bisection, false position, one-point iteration, Newton-Raphson and secant methods.

 6. Methods for Solving Linear Systems

Introduction. Iterative methods of Jacobi and Gauss-Seidel.

 7. Polynomial Interpolation

Introduction. Newton’s interpolating polynomial (divided differences). Lagrange interpolating polynomial.

 8. Numerical integration

Trapezoidal and Simpson rules.

Use of MS Excel and Matlab applications, including the implementation of some algorithms in VBA and Matlab, as support tools in problem solving.

• - Exame - 100.0%

• - Trabalho prático em computador - 30.0%
• - Dois Testes escritos - 70.0%

NAO

Main Bibliography:

Canova, F., Santos, L. & Marques, M. (2021). Apontamentos e exercícios de apoio às aulas. ISEC (available on academic platforms  Moodle and InforEstudante)

Chapra, S.C. & Canale, R.P. (2008). Métodos Numéricos para Engenharia (5ª ed.). São Paulo [etc.]:  McGraw Hill. (ISEC library: 3-4-118)

Pedrosa, A. & Gama, S. (2018). Introdução Computacional à Probabilidade e Estatística com Excel (3ª ed.). Porto: Porto Editora. (ISEC library: 3-3-236)

Complementary Bibliography:

Ross, S.M. (2021). Introduction to Probability and Statistics for Engineers and Scientists (6th ed.). UK: Elsevier Inc.