Numerical and Statistical Methods

Basics of Mathematical Analysis and Linear Algebra.

During lectures the topics are introduced, supported by images to help concept understanding and to show examples. In the laboratory classes,
the students solve practical problems of Bioengineering in a PC using the software mentioned above in 3.3.4. There is a laboratorial component in
this course unity where a test is made in the computer or a team work or project, having a certain weight in the final score.

This curricular unit intends to introduce students to basic statistical concepts and methods in order to perform data analysis on Bioengineering
problems. At the completion of the curricular unit, students should be able to: demonstrate basic knowledge of statistics (descriptive statistics,
probability distributions, confidence intervals, hypothesis tests, correlation and simple linear regression). It also intends to introduce the
numerical methods as tools to solve engineering problems. Computer software packages such as MS Excel, SPSS, R and MATLAB are used
throughout the curricular unit. The student should be able to show basic knowledge of the computational used packages and to interpret
computer outputs. In general, the ability to analyze and solve problems through the application of acquired knowledge is developed. It is also
intended to develop lifelong learning and team working abilities.

Descriptive Statistics and Statistical Inference: population and sample; measurement levels; qualitative and quantitative variables. Univariate
descriptive statistics: displaying and summarizing data; frequencies distribution; measures of central tendency, variability, symmetry and
kurtosis. Bivariate descriptive statistics: linear correlation, coefficients; contingency tables; linear regression. Probability distributions: binomial and
normal distribution; sampling distributions and the Central Limit Theorem. Statistical Inference: basics of point and intervalar estimations;
confidence intervals.
Errors and Taylor series: error, uncertainty and significant digits; Taylor series; propagation of errors in calculations. Nonlinear equations: fixed
point, bisection and Newton methods. Systems of nonlinear equations: Newton’s method. Numerical Differentiation and Integration: derivation
formulas and integration rules.

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

• - Exame - 100.0%

NAO

Constantinides, A., Mostoufi, N., “Numerical Methods for Chemical Engineers with MATLAB Applications”, Prentice Hall, 1999.

Kharab, R,B.G., An Introduction to Numerical Methods- A Matlab Approach, Chapman&Hall, 2002.

Pedrosa, A. e Gama, S., Introdução Computacional à Probabilidade e Estatística, Porto Editora, 2004.

Montgomery, D.C. e Runger, G.C., Applied Statistics and Probability for Engineers, 3rd Edition, Wiley, 2003.

http: // www alea-estp.ine.pt Dossiers Didácticos: IV Estatística com o Excel. Uma aplicação das noções.

Santos, F. C., Fundamentos de Análise Numérica, Edições Sílabo, Lisboa, 2002.

Guimarães, R.C. e Cabral J., Estatística, 2.ª edição, Mc Graw Hill, 2009.

Robalo, A., Estatística – Exercícios, Vol I e II, Edições Sílabo, 1991.