Applied Mathematics to Chemical Engineering

Code:

EQ0076

Acronym:

MAEQ

Keywords
Classification	Keyword
OFICIAL	Physical Sciences (Mathematics)

Instance: 2012/2013 - 2S

Active?	Yes
E-learning page:	https://moodle.fe.up.pt/
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	77	Syllabus	2	-	6	56	162

Teaching language

Portuguese

Objectives

The use of statistical analysis tools is undoubtedly an advantage to the improvement and quality of processes. As far as applied mathematics knowledge is concerned, a special emphasis will be given to the use of R® in order to solve problems related to descriptive statistics. Personal and professional attitudes: identification and formulation of statistical analysis problems and their analytical resolution and using the computer, critical reasoning. Teamwork: creation of a teamwork, task management and leadership. Conceiving and implementing systems: modelling real situations, verification of objectives, and comparison of statistical simulation with real results.

Learning outcomes and competences

With the approval of this course the student is able to develop in-depth studies in statistics mainly applied to chemical engineering.

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 distribution Random variables Binomial probability distribution Poisson distribution 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 Student’s T-Distribution 8. Estimators and Moment Generating Function 9. Confidence intervals and hypothesis testing T test, F and chi2 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

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
Douglas C. Montgomery, George C. Runger; Applied Statistics and Probability for Engineers. ISBN: 0-471-17027-5
Carlos Daniel Paulino e João A. Branco; Exercícios de probabilidade e estatística. ISBN: 972-592-180-1

Teaching methods and learning activities

Laboratory classes- Problem solving using the computer (R Commander) Theoretical classes- examples and problems related to the themes of the course unit A reference book in English

Software

R Commander

keywords

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

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
MT - mini-tests	Exame		25,00
EF - final exam	Exame		75,00
	Total:	-	100,00

Eligibility for exams

Apply the general rules for assessing students existing in FEUP.

Calculation formula of final grade

For students who have no previous frequency in the discipline, the final classification (CF) is calculated by the equation:

CF = 0.25 + 0.75 * MT * EF

wherein:
MT = arithmetic average of the three best marks obtained in mini-tests (minimum grade of 6.0 values to obtain approval to discipline)
EF = marks obtained in the open recommended book Final Exam, with partial use of the R Commander (minimum grade of 6.0 values to obtain approval to discipline)

Students who have obtained frequency in earlier years may choose to perform only the final exam, and the final classification is then:

CF = EF

Examinations or Special Assignments

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. All students who make the mini-tests (having or not previous frequency) are required to obtain a minimum average grade of 6.0 values in the mini-tests to pass the course. Not performing a mini-test on the date set corresponds to zero mark.

Special assessment (TE, DA, ...)

An individual exam which covers all the themes of the course unit

Classification improvement

An individual exam which covers all the themes of the course unit