Numerical Methods

Instance: 2020/2021 - 2S

Cycles of Study/Courses

Last updated on 2021-02-12.

Fields changed: Objectives, Resultados de aprendizagem e competências, Métodos de ensino e atividades de aprendizagem, Fórmula de cálculo da classificação final, Avaliação especial, Bibliografia Complementar, Obtenção de frequência, Tipo de avaliação, Modo de trabalho, Software de apoio à Unidade Curricular, Componentes de Avaliação e Ocupação, Melhoria de classificação

Teaching language

Objectives

Given a mathematical problem, study sufficient conditions for the existence and unicity of its solution, to establish a constructive method to solve it, to study and control the errors  involved, to give an algoritmh for the solution and to implement it in a computer and to study and interpret the numerical results.

Learning outcomes and competences

Students must show skills in solving numerically mathematical problems in the areas described.

Working method

Program

Computer Arithmetic and numerical errors. Representation of numbers and arithmetic operations. Errors and their propagation. Systems of linear equations. Triangular systems and Gaussian elimination.

Nonlinear equations. Order of convergence of a sequence. Root finding methods: bisection method,  fixed point method , Newton method and variants.

Polynomial interpolation. Lagrange and Newton in divided differences methods. Interpolation using splines. Generalized polynomial approximation of a set of values in the sense of least squares.
 
Numerical differentiation and numerical integration. Finite differences formulas for numerical differentiation. Truncation errors. Newton-Cotes formulas. Simple and composite rules of rectangles, trapezium and Simpson. Truncation errors.

Numerical integration of differential equations. Euler methods, "predictor-corrector", Taylor and Runge-Kutta. Truncation errors.

Mandatory literature

Teaching methods and learning activities

Lectures and computational exercices.

Software

keywords

Evaluation Type

Assessment Components

Amount of time allocated to each course unit

Eligibility for exams

Calculation formula of final grade

Exam classification.

Special assessment (TE, DA, ...)

Classification improvement