Numeric and Statistical Methods

Code:

EBE0018

Acronym:

MNES

Keywords
Classification	Keyword
OFICIAL	Basic Sciences

Instance: 2018/2019 - 2S

Active?	Yes
Responsible unit:	Population Studies
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	71	Syllabus	2	-	6	56	162

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.

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

Learning outcomes and competences

Knowledge and understanding

The principles, concepts and techniques associated with Numerical and Statistical Methods applied to the study of Bioengineering systems.

The possibilities, theoretical and practical limits and compromises inherent in modelling Bioengineering systems.

The possibilities, theoretical and practical limits and compromises inherent to collect and analyse data in Bioengineering systems.

Cognitive skills

Use of a wide range of techniques and computer based tools for modelling, predicting and evaluating the behaviour of systems.

Develop and apply numerical, statistical and mathematical skills to describe and analyse the behaviour of Bioengineering systems.

Compare different approaches to fulfilling the requirements of Bioengineering system.

Interpret and critically analyse literature on Bioengineering systems.

Appreciate economic, commercial, social and political issues which may influence the decision over systems in Bioengineering.

 Key skills

Communicate effectively about Bioengineering systems.

Improve own learning and performance.

Professional and practical skills

Apply the principles, concepts and techniques of modelling and analysis bioengineering systems in a
professional context.

Working method

Presencial

Program

 Numerical Methods

1.Computational arithmetic. Binary representation. Floating point and rounding errors.

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

3. Nonlinear 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. Approximations errors. Divided differences. Newton´s divided diferences interpolating polynomials. Truncation errors.

6. Numerical integration. Newton-Cotes formulas: trapezoidal, Simpson and 3/8. Truncation errors. Multiple segments rules. Intervals with unequal  segments.

Statistical methods

7. Descriptive statistics. 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. Cumulative density functions. 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, difference of
proportions.

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

13. Analysis of Variance. Experimental design. Completely at random, factorial design. Analysis of errors.

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

 

Mandatory literature

Steven Chapra, Raymond Canale; Numerical Methods for Engineers (6th Edition), McGraw-Hill International Editions, 2010. ISBN: 978–0–07–340106–5
Zar Jerrold H.; Biostatistical analysis. ISBN: 978-0-13-206502-3

Complementary Bibliography

Heitor Pina; Métodos Numéricos, McGraw-Hill International Editions, 1995. ISBN: 972-9298-04-8
Sokal Robert E.; Biometry. ISBN: 978-0-7167-2411-7
Erwin Kreyszig; Advance Engineering Mathematics, John Wiley & Sons, 1988. ISBN: 0-471-85824-2
G. Lindfield, J. Penny; Numerical Methods, Academic Press, 2012. ISBN: 978-0-12-386942-5
Landau Sabine; «A» handbook of statistical analyses using SPSS. ISBN: 1-58488-369-3

Teaching methods and learning activities

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

keywords

Physical sciences > Mathematics > Statistics > Biometrics
Physical sciences > Mathematics > Applied mathematics > Numerical analysis

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Designation	Weight (%)
Exame	40,00
Teste	60,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	106,00
Frequência das aulas	56,00
Total:	162,00

Eligibility for exams

75% of the theoretical and practical lessons

Calculation formula of final grade

Evaluation will have the following components:

• Exercises
• Exam: in the Normal exam period

Classification= 0.6xFE + 0.4 E

where:

• E – Exam
• FE – Exercises

Approval requires that a minimal mark of 7.5 in each exercise and in the exam. Students that do not obtain a pass mark, can applt for Resit Exam but, in this case, it´s weight is 100%.

Classfication= Resit Exam