Applied Mathematics to Chemical Engineering

Code:

EQ0076

Acronym:

MAEQ

Keywords
Classification	Keyword
OFICIAL	Physical Sciences (Mathematics)

Instance: 2016/2017 - 2S

Active?	Yes
Responsible unit:	Department of Chemical Engineering
Course/CS Responsible:	Master in Chemical Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MIEQ	76	Syllabus	2	-	6	56	162

Teaching language

Portuguese

Objectives

Framework:
The use of statistical analysis tools is undoubtedly an advantage to the improvement and quality of processes.

Specific aims:
- Acquisition of fundamental knowledge in statistics namely descriptive and inferential statistics enhancing the development of statistical literacy and reasoning
- Identification and formulation of problems of statistical analysis, its analytical resolution and computacional (through the use of application R®) fostering critical thinking.

Learning outcomes and competences

Students should be able to:

• Apply fundamental concepts in exploratory data analysis.
• Understand the basic concepts of probability and random variables.
• Understand the concept of the sampling distribution of a statistic, and in particular describe the behaviour of the sample mean.
• Understand the foundations for classical inference involving confidence intervals and hypothesis testing.
• Apply inferential methods relating to the means, variances and proportions.
• Apply and interpret basic summary and modelling techniques for bivariate data and use inferential methods in the context of simple linear models.
• Apply analysis of variance (ANOVA) method and interpret the results
• Use computational tools in statistical analysis
• Understand why statistics cannot prove conclusions but can suggest them
• Value the role that statistics can have in a research work

Working method

Presencial

Program

1. Data organisation and sampling graphic visualization and classification of statistical data. Random selection (sampling).
2. Numerical description of data and expected values. Trend estimation (mean, mode, median). Variation estimation (standard deviation – variance, dispersion). Percentiles and quartiles. How to compare data apparently incomparable (z values)
3. Probabilities. The fundamental counting principle. Mutually exclusive and independent events. Dependent events- conditional probability (Bayes’ formula). Statistical expectation
4. Random variables. Distribution Function and Probability Density Function. Joint distributions Conditional distributions Covariance and correlation
5. Discrete probabilities distributions: Uniform, Binomial, Hypergeometric and Poisson.
6. Continuous probability distributions: Uniform distribution. Normal distribution. Description and applications (rejection of outliers). Normality tests- graphic approximation (probit scale).
7. Sample distributions. Mean distribution and Central Limit Theorem. Chi-square, T-Student and F-Snedcor distribution
8. Estimators and Moment Generating Function.
9. Confidence intervals and hypothesis testing. T test, F test. Means, proportions and variance. How to estimate sample sizes.
10. Analysis of regression and experimental data. Simple linear regression. Standard error of estimate and residual variance. Regression parameters. Problem and meaning of correlation coefficient.
11. Analysis of Variance (ANOVA): One and two factors. Applications
12. Quality control

Mandatory literature

Ross, Sheldon M.; Introduction to probability and statistics for engineers and scientists. ISBN: 0-12-598059-0

Complementary Bibliography

Douglas C. Montgomery, George C. Runger; Applied Statistics and Probability for Engineers. ISBN: 0-471-17027-5
Rui Campos Guimarães, José A. Sarsfield Cabral; Estatística. ISBN: 978-84-481-5589-6
Dinis Duarte Pestana, Sílvio Filipe Velosa; Introdução à probabilidade e à estatística. ISBN: 972-31-0954-9
Bento Murteira... [et al.]; Introdução à estatística. ISBN: 978-84-481-6069-2
Carlos Daniel Paulino e João A. Branco; Exercícios de probabilidade e estatística. ISBN: 972-592-180-1

Teaching methods and learning activities

TP - Theoretical-practical classes of 90 + 60 minutes for presentation of the main concepts together with problem solving.

L - Laboratory classes of 90 minutes in computer rooms solving problems with or without the use of R + R Commander.

Software

R + R Commander

keywords

Physical sciences > Mathematics > Probability theory
Physical sciences > Mathematics > Applied mathematics > Engineering mathematics
Physical sciences > Mathematics > Statistics

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Designation	Weight (%)
Exame	75,00
Teste	25,00
Total:	100,00

Eligibility for exams

Obtaining frequency for regular students depends on:

• not exceeding a maximum of 3 laboratory class misses and
• obtain a minimum grade of 6 in distributed evaluation (AD).

Students with frequency from previous years do not need to attend classes. Students who wish to attend must obey the above rules.

Calculation formula of final grade

The final classification (CF) is calculated by the equation:

CF = max(0.25 x AD + 0.75 x EF,EF)

wherein:
AD = arithmetic average of the three best marks obtained in mini-tests
EF = marks obtained in the open recommended book Final Exam, with partial use of the R Commander

The final exam consists in two parts: theorethical (TP) and pratical (P). The final mark is calculated by the equation:

EF = 0.6 x TP + 0.4 x P

Conditions for course approval:

• minimum grade of 6 values on AD
• minimum grade of 6 values on TP
• minimum grade of 6 values on P

The realization of the mini-tests is mandatory for all students without previous frequency. The other may choose as venue and must communicate its decision to the teacher in the first week of classes. Not performing a mini-test on the date set corresponds to zero mark.

Special assessment (TE, DA, ...)

An exam at the corresponding seasons.

Classification improvement

Improvement of classification can be attempted in the Recurso season. The computation formula is identical to the one used in final classification described above.