Subject: Numerical Computing and Analysis

Scientific Area:

Mathematics

80 Hours

Number of ECTS:

7,5 ECTS

Language:

Portuguese

# Overall objectives:

1 - This course aims to 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.

# Syllabus:

1 - Floating point systems and programming languages for numerical computing.
2 - Numerical error theory, conditioning, and numerical 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 - introduction to finite difference methods for partial differential equations.

# Literature/Sources:

R. L. Burden, J. D. Faires, A. M. Burden , 2016 , Numerical analysis , Cengage Learning
H. Pina , 2010 , Métodos numéricos (9789725922842) , Escolar
A. Quarteroni, R. Sacco, F. Saleri , 2007 , Numerical mathematics , Springer-Verlag
M. R. Valença , 1993 , Métodos numéricos , Livraria Minho
A. Quarteroni, F. Saleri, P. Gervasio , 2014 , Scientific computing with MATLAB and Octave , Springer-Verlag
J.H. Mathews, K.D. Fink , 2004 , Numerical methods using MATLAB , Pearson Prentice Hall
F.F. Campos Filho , 2007 , Algoritmos numéricos , LTC
D.M. Claudio, J.M. Marins , 2000 , Cálculo numérico computacional: teoria e prática , Atlas
N.J. Higham , 2002 , Accuracy and stability of numerical algorithms , SIAM
M. Ruggiero, V. Lopes , 1996 , Cálculo numérico: aspetos teóricos e computacionais , Makron Books
S.R. Otto, J.P. Denier , 2005 , An introduction to programming and numerical methods in MATLAB , Springer-Verlag
J. Stoer, R. Bulirsch , 2010 , Introduction to numerical analysis , Springer

# 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 4 of the syllabus); Test #2 : weight 1/3 (topics 5 to 7); Test #3 : weight 1/3 (topics 8 and 9).