Métodos Quantitativos em Engenharia
Instance: 2004/2005 - 1S
Cycles of Study/Courses
Teaching language
Portuguese
Objectives
To transmite solid knowledge for application of quantitative methods at specialization level or at the professional activity
levels, giving the student a set of mathematical tools needed
to deal with some engeneering problems. To educate him
for an easy translation into a mathematical reasoning in the analysis of problems and in an adequate formulation of these.
Program
Numerical resolution of Differential Equations:
1. Ordinary Differential Equations:
Initial Value Problems (P.V.I.); One-step methods;
Multiple-step methos (Adams-Bashforth, Adams-Multon, Predictor-corrector); Runge-Kutta methods; Stability and instability, Stiffness, Gear's method (BDF Backward-Difference-Formulae);
Boundary values problems; Classical methods.
2. Partial Differential Equations: explicit methods;
stability; implicit methods; semi-direct methods.
Statistical techniques:
1. Typology of variables and data organization. Brief notions
of sampling theory. Dealing with different types of data.
2. Monte Carlo simulation. The principles of simulation.
Simulating samples under different kinds of probabilistic lows. Simulation of stochastic systems.
3. Multilinear regression.
4. Time series (tendency, parameter estimation, simulation)
5. Queues.
6. Brief notion of probabilistic fiability.
Mandatory literature
Atkinson, Kendall E.;
An^introduction to numerical analysis. ISBN: 0-471-62489-6
Augusti, Giuliano;
Probabilistic methods in structural engineering. ISBN: 0-412-22230-2
Leitch, Roger D.;
Reliability analysis for engineers. ISBN: 0-19-856371-X
J. Ortega, W. Poole; Numerical Methods for Differencial Equations
Rubinstein; Simulation and Monte Carlo Method
Stewart, G. W.;
Afternotes goes to graduate school. ISBN: 0-89871-404-4
Guia do Utilizador Matlab
Teaching methods and learning activities
Subject essentialy supported by learning methods together with practical developpements. The intuitive setlement of notions is encouraged as well as the computational ability.
Subjects are presented during theoretical classes using
case studies and looking for applications in the optional areas of the student.
During other classes the student is tutored in the application of the knowledge he aquired in selected problems.
The use of the software (MATLAB) is encouraged as a working tool, mainly in the execution of the proposed practical projects.
Software
Matlab, mainly.
Others: Maple, SPSS
Evaluation Type
Distributed evaluation without final exam
Eligibility for exams
see school regulations