Numerical Analysis

Code:

M2018

Acronym:

M2018

Level:

200

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2022/2023 - 1S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Mathematics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:B	0	Official Study Plan	3	-	6	56	162
L:CC	17	study plan from 2021/22	2	-	6	56	162
			3
L:F	0	Official Study Plan	2	-	6	56	162
			3
L:G	2	study plan from 2017/18	2	-	6	56	162
			3
L:M	66	Official Study Plan	2	-	6	56	162
L:MA	0	Official Study Plan	2	-	6	56	162
L:Q	1	study plan from 2016/17	3	-	6	56	162

Teaching language

Portuguese

Objectives

The main aim of this subject is given a mathematical problem,  to 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

Presencial

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. Newton-Cotes formulas. Simple and composite rules of rectangles, trapezium and Simpson. Truncation errors. Finite differences formulas for numerical differentiation. Truncation errors. 

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

 

 

Mandatory literature

Pina Heitor; Métodos numéricos. ISBN: 972-8298-04-8

Complementary Bibliography

Quarteroni Alfio; Numerical mathematics. ISBN: 0-387-98959-5

Teaching methods and learning activities

Lectures, problems  and computational projects.

Software

Maxima
Python
Matlab

keywords

Physical sciences > Mathematics

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Teste	60,00
Trabalho laboratorial	40,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	98,00
Frequência das aulas	53,00
Trabalho escrito	3,00
Trabalho laboratorial	8,00
Total:	162,00

Eligibility for exams

A minimum of  3 points in the practical classification (CP).
To obtain frequency, a minimum  of 3  points is required in the practical classification.

Calculation formula of final grade

Theoretical classification (CT): Sum of the classifications of 2 or 3 tests (6 or 4 points each) or a final exam (12 points)
To be approved, a minimum rate of 3 points is required in the theoretical classification.



Practical classification (CP): sum of classifications obtained in 4 practical tests (2 points each)
Final classification (CF): CT+CP

Special assessment (TE, DA, ...)

One final exam (theoretical and practical) in the appeal exam period.

Classification improvement

Only for the Theoretical classification (CT) in the appeal exam period.