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Programming and Numerical Computing

Code:

CVN039

Sigla:

PCN

Áreas Científicas
Classificação	Área Científica
OFICIAL	Matemática e Informática

Ocorrência: 2022/2023 - 2S

Ativa?	Yes
Unidade Responsável:	Departamento de Matemática e Informática
Curso/CE Responsável:	Undergraduate in Civil Engineering (evening course)

Ciclos de Estudo/Cursos

Sigla	Nº de Estudantes	Plano de Estudos	Anos Curriculares	Créditos UCN	Créditos ECTS	Horas de Contacto	Horas Totais
CIVN	9	Study Plan	2	-	4	67,5	108

Língua de trabalho

Portuguese - Suitable for English-speaking students

Objetivos

It is intended that the student acquires programming and numerical calculus skills.

At the end of the course, the student should be able to:

• Understand the basic programming principles that will allow the student to adapt to new programming languages;


• Develop logical reasoning;


• Understand and apply numerical methods to solve mathematical problems: nonlinear equations, polynomial approximation of functions, numerical integration and ordinary differential equations;


• Implement the algorithms obtained from the numerical methods and apply them to Civil Engineering problems;


• Recognize the advantages, disadvantages and limitations of each method;

Develop teamwork skills.

Resultados de aprendizagem e competências

Not applicable

Modo de trabalho

Presencial

Pré-requisitos (conhecimentos prévios) e co-requisitos (conhecimentos simultâneos)

Previous knowledge about real functions (continuity, differentiability, integration) and about ordinary differential equations.

Programa

1. Introduction to programming: constants, variables, operators (arithmetic, relational and logical), functions (2 weeks)


2. Pseudocode: structure of na algorithm, declaration of variables, assignment of values,, comments, input and output data, basic structures (sequential, conditional and repetition) (3 weeks);


3. Error theory: absolute error, relative error, propagation of errorsn(1 week)


4. Calculation of roots of nonlinear functions: fixed point, bisection, secant and Newton-Raphson methods (1 week);


5. Function interpolation: Lagrange and Newton methods (2 weeks)


6. Numerical integration: (2 weeks)
   
   
   
   1. Problems arising from Civil Engineering that require numerical integration
   
   
   2. Difference between algebraic integration and numerical integration
   
   
   3. Rules for numerical integration: Newton-Cotes and Gauss quadrature
   
   
   
   


7. Numerical resolution of ordinary differential equations (odes) (4 weeks);
   
   
   
   1. Introduction to the numerical resolution of odes
   
   
   2. Euler and Runge-Kutta methods
   
   
   
   

Bibliografia Obrigatória

Chapra, S.C., Canale, R. P.; ;Numerical Methods for Engineers - 7th edition, McGraw-Hill, 2015
Correia dos Santos, F., Duarte, J., Lopes, N. D.; Fundamentos de Análise Numérica com Python 3 e R – 2ª edição, Edições Sílabo, 2019
Guttag, J. V;; Introduction to Computation and Programming Using Python, MIT Press

Bibliografia Complementar

Liang, Y.D.; Introduction to Programming Using Python, Pearson, 2013
Quarteroni, A., Salero, F. ; Cálculo Científico com Matlab e Octave, Springer, 2006
Burden, R. L., Faires, D. J.,Burden, A. M.; Numerical Analysis – 10th Edition, Engage, 2016

Métodos de ensino e atividades de aprendizagem

In the theoretical-practical classes, the concepts will be introduced, with the help of application exemples whenever possible, trying to stimulate the interest, reasoning and critical thinking of the sudents.

The laboratory classes will take place in computer rooms and will be dedicated to the resolution of programming exercises that allow the student to put into practice the knoweledge acquired. A programming language will be introduced in order to implement the concepts.

Team work will be encouraged.

The continous assessment will be made trough 3 assignments , 1 written test and a final project.

The assessmente during the exams periodo is made throught an written exam and a project (that can be the same that was done during the semester).

Software

Jupyter notebook
Python3

Tipo de avaliação

Distributed evaluation without final exam

Componentes de Avaliação

Designation	Peso (%)
Teste	30,00
Trabalho escrito	70,00
Total:	100,00

Componentes de Ocupação

Designation	Tempo (Horas)
Elaboração de projeto	12,00
Estudo autónomo	37,50
Frequência das aulas	52,50
Trabalho escrito	6,00
Total:	108,00

Obtenção de frequência

Not applicable

Fórmula de cálculo da classificação final

Continuous assessment

• 10%*assignment1+10%*assigment2+10%*assignment3+30%*test+40%*project

Final assessment

• 70% exame + 40% project


• Not applicable 100% exam because the project represents a crucial role of integration of the various components of knowledge through its application to solve an actual problem and it allows the student to consolidate his/her programming skills