Applied Mathematics to Chemical Engineering

Code:

EQ0076

Acronym:

MAEQ

Keywords
Classification	Keyword
OFICIAL	Physical Sciences (Mathematics)

Instance: 2011/2012 - 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	99	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 Matlab® 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.

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

Complementary Bibliography

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

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

Excel
R Commander

Evaluation Type

Distributed evaluation with final exam

Eligibility for exams

To be admitted to exams, students:
• have to attend classes
• and reach a minimum grade of 10 out 20 in the continuous assessment (CA) component

Continuous Assessment grade will be based on the average grade of a group assignment (GA) (maximum of 4 students) plus professor’s opinion (PO) regarding students’ performance in laboratory classes.

A written and individual final exam (FE) (minimum grade of 30%) – students can use the book mentioned in the bibliography and calculator, and partially use R Commander. It will last 3 hours.

Calculation formula of final grade

Formulas which will be used to assess students in both components:
Continuous Assessment= 0.80*GA +0.20*PO
Final Grade = 0.30 CA + 0.70 FE

Examinations or Special Assignments

A group assignment starting 26.04 until 29.04

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