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 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 optimizing 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 - Direct and iterative methods for the solution of systems of linear equations.
4 - Function interpolation and approximation.
5 - Numerical integration and differentiation.
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 - Mathematical formulation of linear programming problems.
10 - The Simplex method.
11 - Duality in linear programming.
12 - Sensitivity and post-optimization analysis.

Literature/Sources:

R. L. Burden, J. D. Faires, A. M. Burden , 2016 , Numerical Analysis , Cengage Learning
F. F. Campos Filho , 2007 , Algoritmos Numéricos , LTC
M. M. Hill, M. M. Santos , 2022 , Investigação Operacional, Volume 1: Programação Linear , Sílabo
L. V. Tavares, F. N. Correia, I. H. Themido, R. C. Oliveira , 1997 , Investigação Operacional , McGraw-Hill
M. S. Bazaraa, J. J. Jarvis, H. D. Sherali , 2009 , Linear Programming and Network Flows , Wiley
A. Quarteroni, F. Saleri, P. Gervasio , 2014 , Scientific Computing with MATLAB and Octave , Springer
S. R. Otto, J. P. Denier , 2005 , An Introduction to Programming and Numerical Methods in MATLAB , Springer
S. Chapra, R. Canale , 2014 , Numerical Methods for Engineers , McGraw-Hill
A. Kharab, R. B. Guenther , 2019 , An Introduction to Numerical Methods: A MATLAB Approach , CRC Press
F. C. Santos, J. Duarte, N. D. Lopes , 2019 , Fundamentos de Análise Numérica com Python 3 e R , Sílabo
A. Greenbaum,T. P. Chartier , 2012 , Numerical Methods: Design, Analysis, and Computer Implementation of Algorithms , Princeton Univ. Press
N. J. Higham , 2002 , Accuracy and Stability of Numerical Algorithms , SIAM
C. B. Moler , 2008 , Numerical Computing with MATLAB , SIAM
W. L. Winston , 2004 , Operations Research: Applications and Algorithms , Thomson/Brooks/Cole

Assesssment methods and criteria:

Classification Type: Quantitativa (0-20)

Evaluation Methodology:
The teaching methodology includes lectures and problem-solving classes, with the use of a 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 8); Test 3: weight 1/3 (topics 9 to 12).