1

2019-2020

01001681

Applied Mathematics

Portuguese

Face-to-face

SEMESTRIAL

6.0

Compulsory

1st Cycle Studies

Mathematical Analysis.

Detailed lectures (using some audio-visual devices) introducing and explaining concepts, principles and theories. In the theoretical-practical classes, students will solve problems with the guidance of the teacher.

The statistical software SPSS is used in the theoretical classes and in two practical classes, given in a computer room, to illustrate the main concepts of the syllabus.

To provide basic mathematical knowledge that prepares the students to model standard behaviors of random phenomena, which occur in Science and in Engineering contexts. To contribute to the acquisition of skills that enable describing, analyzing and interpreting real situations through random mathematical models.

1. Probability

Random phenomena. Definition of Probability. Conditional probability. Independent events.

2. Random variables and probability distributions

Real random variables discrete and continuous. Moments and parameters. Examples of discrete and continuous distributions. Central limit theorem.

3. Estimation

Introduction to statistical inference. Point estimation: estimators and sampling distributions, methods to obtain estimates. Confidence intervals: generalities, confidence intervals for a population mean, for a gaussian population variance and for a proportion.

4. Tests of Significance

Generalities, level of significance and power. Tests for a population mean, for a gaussian population variance and for a proportion. Qui-Square test for the goodness of fit.

5. Simple linear regression model

Estimation, confidence intervals and tests for the regression parameters. Prediction intervals.

Final

*Exam: 100.0%*

Continuous

*Two intermediate tests: 100.0%*

Murteira, B., C. S. Ribeiro, J. A. Silva, C. Pimenta - Introdução à Estatística, 2001, McGraw-Hill, Lisboa.

Guimarães, R., Sarsfield Cabral, J., Estatística, 1997, McGraw-Hill, Lisboa.

Moore, D., McCabe, G., Introduction to the practice of statistics, Freeman, New York, 2006.

Devore, J.L.,** Probability and statistics for engineering and the sciences****, **Duxbury, 2000.

Andrews, L.C., R.L. Phillips – Mathematical Techniques for engineers and scientists, 2003, Spie Press, Washington.

Ross, S. - Introduction to Probability and Statistics for engineers and scientists, 1987, Wiley.