Code: | EBE0018 | Acronym: | MNES |
Keywords | |
---|---|
Classification | Keyword |
OFICIAL | Basic Sciences |
Active? | Yes |
Responsible unit: | Population Studies |
Course/CS Responsible: | Master in Bioengineering |
Acronym | No. of Students | Study Plan | Curricular Years | Credits UCN | Credits ECTS | Contact hours | Total Time |
---|---|---|---|---|---|---|---|
MIB | 76 | Syllabus | 2 | - | 6 | 56 | 162 |
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.
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.
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.
Learning based on the presentation of the theoretic concepts and problem solving with EXCEL, OCTAVE and SPSS.
Designation | Weight (%) |
---|---|
Exame | 40,00 |
Teste | 60,00 |
Total: | 100,00 |
Designation | Time (hours) |
---|---|
Estudo autónomo | 106,00 |
Frequência das aulas | 56,00 |
Total: | 162,00 |
75% of the theoretical and practical lessons
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