Subject: Numerical Methods and Operational Research
Scientific, Cultural, Social and Ethical Formation
Number of ECTS:
1 - Provide the students with basic knowledge on numerical methods for solving mathematical problems in science and engineering, emphasizing the analysis of the errors involved in the numerical approximations, the effects of finite-precision computer arithmetic, the construction and implementation of numerical algorithms, and the analysis of their theoretical properties.
2 - To give students the concept/philosophy of structuring and optimisation of simplified models to support solving linear programming problems.
1 - Floating point systems and programming languages for numerical computation.
2 - Numerical error theory, conditioning, and stability.
3 - Direct and iterative methods for the solution of systems of linear equations.
4 - Solution of nonlinear equations and polynomial zeros.
5 - Numerical solution of systems of nonlinear equations.
6 - Function interpolation and approximation.
7 - Numerical integration and differentiation.
8 - Numerical methods for the solution of initial-value problems in ordinary differential equations.
9 - Finite difference methods for partial differential equations.
10 - Mathematical formulation of linear programming problems.
11 - The Simplex method
12 - Duality in linear programming.
13 - Sensitivity and post-optimisation analysis.
R. L. Burden, J. D. Faires, A. M. Burden , 2016 , Numerical analysis , Cengage Learning
F. F. Campos Filho , 2007 , Algoritmos numéricos , LTC
A. Quarteroni, R. Sacco, F. Saleri , 2007 , Numerical mathematics , Springer-Verlag
M. R. Valença , 1993 , Métodos numéricos , Livraria Minho
M. M. Hill, M. M. Santos , 2009 , Investigação operacional: programação linear , Sílabo
L. V. Tavares, R.C. Oliveira, I.H. Themido, F.N. Correia , 1996 , Investigação Operacional , McGraw-Hill
M. S. Bazaraa, J. J. Jarvis, H. D. Sherali , 2010 , Linear programming and network flows , Wiley
A. Quarteroni, F. Saleri, P. Gervasio , 2014 , Scientific computing with MATLAB and Octave , Springer-Verlag
Assesssment methods and criteria:
Classification Type: Quantitativa (0-20)
The teaching methodology includes lectures and problem-solving classes, with the use of whiteboard, notebook, and video projector. The adopted evaluation methodology consists of three individual written tests: Test 1 : weight 1/3 (topics 1 to 5 of the syllabus); Test 2 : weight 1/3 (topics 6 to 9); Test 3 : weight 1/3 (topics 10 to 13).