Numeric and Statistical Methods

Code:

EBE0018

Acronym:

MNES

Keywords
Classification	Keyword
OFICIAL	Basic Sciences

Instance: 2012/2013 - 2S

Active?	Yes
Course/CS Responsible:	Master in Bioengineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MIB	67	Syllabus	2	-	7	56	189

Teaching language

Portuguese

Objectives

The course aims to contribute for the development of a general and integrated vision of Numerical and Statistical Methods in the Bioengineering professional context.

Learning outcomes and competences

To offer a vision ofthe Numerical and Statistical Methods in Bioengineering and its importance for the professional practice in Engineering;

 

To provide knowledge and comprehension of concepts, methods and aplications and topics in Numerical and Statistical Methods relevant for Bioengineering;

 

To support the development, in the context of Numerical and Statistical Methods, of the analytical, communication and learning skills required for the professional exercise;

 

To develop critical skilss, in particular, in data  collection, analysis and treatment.

Working method

Presencial

Program

Numerical Methods module

1. Computational arithmetics. Binary representations. Floating point representation rounding errors.

2. System of linear equations. Gaussian elimination. Pivot. Determinant and inversion of a matrix.

3. Non linear equations. Methods: fixed point, bisection, secant and Newton. Stopping criteria. Convergence.

4. System of non linear equations. Newton´s method. Stopping criteria. Convergence.

5. Polynomial interpolation. Approximation errors. Divided differences. Newton´s interpolating polynomial with divided differences. Truncation error.

 

6. Numerical integration. Simple formulae: trapezoidal, Simpson and 3/8. Truncation errors. Composite formulae. Application to intervals with different length.

 

Statistical methods module

7. Descriptive statistics. Measurement scales. Location and dispersion measures. Graphical methods. Introduction to SPSS.

8. Probability. Independence and conditional probability. Bayes theorem.

9. random variables: discrete and continuous. Probability distributions. Expected value and variance of a random variable.

10. Discrete distributions: uniform, binomial, and Poisson. Continuous distributions: uniform, normal, and exponential.

11. Sampling distributions. Central Limit Theorem. Confidence intervals: mean; difference of means; variance; ratio of variances; proportion and difference of proportions.

12. Hypothesis testing: Type I and Type II Errors. Tests: mean; difference of means; variance; ratio of variances; proportion and difference of proportions. Power of a test.

13. Analysis of Variance. Complete random design and Factorial design.

14. Regression and correlation. Simple linear regression. Non linear regression. Correlation. Multiple linear regression. Analysis of errors.

Mandatory literature

Erwin Kreyszig; Advanced engineering mathematics. ISBN: 0-471-59989-1
Heitor Pina; Métodos numéricos. ISBN: 972-8298-04-8
Jerrold H. Zar; Biostatistical analysis. ISBN: 978-0-206502-3
Robert R. Sokal and F. James Rohlf; Biometry. ISBN: 978-0-7167-2411-7
Baldi, B.; Moore D.S.; The practice of statistics in the life sciences, W.H. Freeman and Company, 2012. ISBN: ISBN 1-4292-7272-4
Robert Ho.; Handbook of univariate and multivariate data analysis and interpretation with SPSS. ISBN: 1584886021 (alk. paper)

Teaching methods and learning activities

Learning based on the presentation of the theoretic concepts and problem solving with EXCEL and SPSS.

Software

SPSS 17.0

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Attendance (estimated)	Participação presencial	68,00
Compulsory	Exame		50,00
Compulsory	Trabalho escrito		50,00
	Total:	-	100,00

Eligibility for exams

80% of all the theoretical and pratical classes.

Calculation formula of final grade

Evaluation will have the following components:

• Exercises

• Test: in the planned period.

• Exam: in the exam period for Normal and Repeated exams

Classification= 0.5xFE + 0.25 PI+0.25 E

where:

• PI– test classification(minimum of 7.5 marks out of 20)

• E – Exam

• FE – Exercises

Students who have not reached the minimum classification of 7.5 in the Test will have an Exam weighted by 0.5.