Subject: Numerical Methods and Operational Research

Scientific Area:

Mathematics

80 Hours

Number of ECTS:

7,5 ECTS

Language:

Portuguese

# Overall objectives:

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 finiteprecision 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.

# Syllabus:

1 - Floating point systems and programming languages for numerical computation.
2 - Numerical error theory, conditioning, and numerical stability.
3 - Function interpolation and approximation.
4 - Numerical integration and differentiation.
5 - Direct and iterative methods for the solution of systems of linear equations.
6 - Solution of nonlinear equations and polynomial zeros.
7 - Numerical solution of systems of nonlinear equations.
8 - Numerical methods for the solution of initial-value problems in ordinary differential equations.
9 - Introduction to 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.

# Literature/Sources:

Campos Filho, F.F. , 2007 , Algoritmos Numéricos, 2.ª ed. , LTC
Burden, R.L., Faires, J.D., Burden, A.M. , 2016 , Numerical Analysis, 10th ed. , Cengage Learning
Chapra, S., Canale, R. , 2014 , Numerical Methods for Engineers, 7th ed. , McGraw-Hill
Quarteroni, A, Saleri, F., Gervasio, P. , 2014 , Scientific Computing with MATLAB and Octave, 4th ed. , Springer
Kharab, A., Guenther, R.B. , 2019 , An Introduction to Numerical Methods: A MATLAB Approach, 4th ed. , CRC Press
Santos, F.C., Duarte, J., Lopes, N.D. , 2019 , Fundamentos de Análise Numérica com Python 3 e R, 2.ª ed. , Sílabo
Santos, M.M., Hill, M.M. , 2015 , Investigação Operacional, Volume 1: Programação Linear, 3.ª ed. , Sílabo
Bazaraa, M.S., Jarvis, J.J., Sherali, H.D. , 2009 , Linear Programming and Network Flows, 4th ed. , Wiley
Tavares, L.V., Correia, F.N., Themido, I.H., Oliveira, R.C. , 1997 , Investigação Operacional , McGraw-Hill

# Assesssment methods and criteria:

Classification Type: Quantitativa (0-20)

Evaluation Methodology:
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).