﻿ Numerical and Statistical Methods - Construção e ReabilitaçãoInstituto Politécnico de Tomar

# Bachelor's Degree in Construção e Reabilitação

## Numerical and Statistical Methods

Publication in the Diário da República: Despacho nº 9398/2015 - 18/08/2015

6 ECTS; 1º Ano, 2º Semestre, 30,0 T + 45,0 TP

Lecturer

Prerequisites
Not applicable

Objectives
(a) Provide the basic foundations of some of the main statistical techniques, descriptive and inferential, for Data Analysis.
(b) Provide some of the basic concepts of Numerical Methods for the Resolution of Systems of Linear Equations, Numerical Integration, etc.

Program
PART I

1. Exploratory data analysis
1.1. General information
1.2. Fundamental statistical terms and concepts
1.3. Sampling Theory: Random and non-random methods
1.4. Classification of data
1.5. Tabular and graphical representation of univariate data: discrete and continuous
1.6. Measures of location, dispersion and shape

2. Bivariate analysis
2.1. General information
2.2. The dispersion diagram
2.3. Analysis of the degree of association between variables
2.4. Pearson's linear correlation coefficient
2.5. Minimum squares method
2.6. Forecast with the regression line
2.7. Quality of the adjustment (coefficient of determination)

3. Elementary concepts of statistical inference
3.1. Theory of the estimation (punctual and by intervals)
3.1.1. Population mean confidence interval
3.2. Decision theory (hypothesis testing)
3.2.1. Testing the expected value of a population
3.2.2. Probability of significance
3.3. Confidence Intervals versus Hypothesis Testing

PART II

4. Numerical Methods for Systems of Linear Equations
4.1. Indirect or Iterative Methods:
4.1.1. Jacobi iterative method;
4.1.2. Iterative method of Gauss-Seidel.

5. Numerical Methods for Equations and Systems of Nonlinear Equations
5.1. Location of roots;
5.2. Iterative methods:
5.2.1. Method of bisection;
5.2.2. Fixed point method;
5.2.3. Newton's method;
5.2.4. Secant method and False Rope method;
5.3. Newton's method for systems of non-linear equations.

6. Polynomial interpolation
6.1. Lagrange interpolator polynomial;
6.2. Newton's interpolator polynomial;
6.3. Hermite interpolator polynomial.
6.4. Segmented interpolation and inverse interpolation.
7. Derivation and Numerical Integration
7.1. Numerical Derivation;
7.2. Newton-Cotes formulas;
7.3. Simple Trapeze and Simpson rules;
7.4. Compound Trapeze and Simpson formulas;
7.5. Gaussian formulas.

Evaluation Methodology
Exam-based assessment: the student will pass if the mark obtained is equal or higher than 10 (out of 20) with a minimum of 3 marks in both parts (i.e. considering the Numerical Methods part and the Statistical Methods part marked from 0 to 10).

Bibliography
- Pina, H. (1995). Métodos Numéricos. Lisboa: McGraw-Hill
- Burden, R. e Faires, J. (1993). Numerical Analysis. New York: PWS Publishing Company
- Grilo, L. (2013). Probabilidades e Estatística. Conceitos Teórico-Práticos. (Vol. 1). Tomar, Portugal.: Instituto Politécnico de Tomar
- Murteira, B. (1994). Análise Exploratória de Dados ? Estatística Descritiva. (Vol. 1). Lisboa - Portugal: McGraw Hill

Teaching Method
Lectures focusing on theoretical concepts and theoretical-practical lessons involving problem-solving.

Software used in class
The Excel spreadsheet and the IBM SPSS statistical package are occasionally used to solve some exercises.