Description

Theory
1

Laboratory
3

Instructors

Luís Manuel Silva

Contents

1 Software (2/15)
1.1 EXCEL
1.2 Octave/Matlab
1.3 Python

2 Complements on numerical analysis (5/15)
2.1 Numerical resolution of algebraic equations by Newton and secant methods.
2.2 Numerical resolution of a system of nonlinear equations by Newton-Raphson method.
2.2 Matrices and systems of equations.
2.3 Numerical resolution of equations and systems of ordinary differential equations
2.4 Stiff character of ordinary differential equation systems.

3 Optimization (6/15)
3.1 Necessary and sufficient conditions
3.2 Optimization of a one-variable function by direct and indirect methods
3.3 Optimization of an unconstrained and constrained multi-variable function
3.4 Least Squares Problems
3.5 Lagrangean function

4 Experimental design (2/15)
4.1 2^k factorial design
4.2 2-level fractional factorial designs

Learning Outcomes

Generally, it is pretended at end of this course the student should be able to:
1 - Select and apply the most suitable methods for numerical problem solving in chemical engineering
2 - Operate and program in several computational platforms for scientific calculation.
3 - Conceive a design of experiments in order to test the possible cause-effect relationships.
4 - Integrate algorithms from different syllabus modules to solve a complex problem.

Specifically, the student should be able to:

1 - Perform repeated calculations automatically using Excel and Octave
2 - Describe the numerical methods taught in this u.c. as well as manually performing two consecutive iterations
3 - Create functions and scripts in Octave software editor
4 - Evaluate local and global errors and distinguish between truncation and round-off error
5 - Apply Octave functions in numerical ODE resolution
6 - Calculate the condition number in a root-finding problem
7 - Analyze the stiff character of an ODE system
8 - Apply direct and indirect methods to solve univariate optimization problems.
9 - Formulate constrained optimization problems
10 - State the necessary and sufficient conditions for a stationary point to be a minimizing point
11 - Solve least-squares problems in 3 situations: 1) parameter estimation; 2) nonlinear equation systems resolution and 3) process data reconciliation
12 - Identify constrained stationary points by formulating the Lagrangean function
13 - Perform an ANOVA in order to identify the significant factors/interactions in a design of experiments.
14 - Implement a design of experiments from a python package