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Numerical Analysis

Code:

INF32151

Sigla:

NA

Áreas Científicas
Classificação	Área Científica
OFICIAL	Matemática

Ocorrência: 2021/2022 - 2S

Ativa?	Yes
Página Web:	https://moodle.ips.pt/2122/course/view.php?id=91
Unidade Responsável:	Departamento de Matemática
Curso/CE Responsável:	Informatics Engineering

Ciclos de Estudo/Cursos

Sigla	Nº de Estudantes	Plano de Estudos	Anos Curriculares	Créditos UCN	Créditos ECTS	Horas de Contacto	Horas Totais
INF	345	Plano de Estudos	1	-	6	75	162

Língua de trabalho

Portuguese

Objetivos

The main objective of the Curricular Unit is to familiarize the student with computational methods that numerically approximate solutions of common questions in calculus. It is intended that the student learns various numerical methods, its application, its implementation on a computational tool and how to choose the most appropriate among them, considering the problem to be solved.

Resultados de aprendizagem e competências

Showing knowledge in:








Developing Skills in:





Acquisition of Competences in:

Modo de trabalho

Presencial

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

Integral and differential calculus with real functions in one real variável.

Programa

T1. NUMBER REPRESENTATION IN COMPUTER SYSTEMS AND ERRORS



T2. SYSTEMS OF LINEAR EQUATIONS







T3. NONLINEAR EQUATIONS




T4. POLINOMIAL INTERPOLATION




T5. NUMERICAL INTEGRATION

Bibliografia Obrigatória

César Fernández; Sebenta de Análise Numérica (Available in the Moodle platform)

Bibliografia Complementar

Atkinson KE; An introduction to numerical analysis, John Wiley & sons, 1990. ISBN: 0471624896
Correia dos Santos, F.M.; Fundamentos de Análise Numérica, Sílabo, 2002. ISBN: 9789726182863
Kharab, A.; Guenther, R.B.; An introduction to Numerical Methods - A Matlab approach, CRC press, 2018. ISBN: 9781315107042
Pina, H.; Métodos Numéricos, McGraw-Hill, 2010. ISBN: 9789728298043
Quarteroni, A.M.; Saleri, F.E.; Cálculo científico com Matlab e Octave, Springer Science & Business Media, 2007. ISBN: 9788847007185
Rao, S.S.; Applied numerical methods for engineers and scientists, Pearson, 2002. ISBN: 9780130894809
Scheid, F.; Análise Numérica, McGraw-Hill, 2000. ISBN: 972-9241-19-8

Métodos de ensino e atividades de aprendizagem

Student’s oriented study is performed through:




The objectives can be summarized as the knowledge of different algorithms, its properties, and all issues related to programming numerical methods on a computer. Thus theoretical sessions should serve for the solid presentation of the fundamentals. The presentation of contents, properties and exemples in theoretical-practical lessons, combined with the experimentation with these tools through specific exercises and Matlab programming should lead to the achivement of this course’s goals.

Exercise solving in theoretical-practical hours should serve for the assimilation of these notions, and its applications in different practical cases. Practical sessions with Matlab/Octave will develop the required skills in programming of scientific algorithms

Different supporting materials are available for the autonomous study: lecture notes, solved exercises, Matlab codes, formularies, web links, books (distributed at the classroom, Moodle page or IPS library)

Software

Matlab or Octave

Palavras Chave

Physical sciences > Mathematics > Computational mathematics
Physical sciences > Mathematics > Algorithms
Physical sciences > Mathematics > Mathematical analysis > Functions

Tipo de avaliação

Distributed evaluation with final exam

Componentes de Avaliação

Designation	Peso (%)
Teste	100,00
Total:	100,00

Componentes de Ocupação

Designation	Tempo (Horas)
Estudo autónomo	87,00
Frequência das aulas	75,00
Total:	162,00

Obtenção de frequência

The student may opt for continuous evaluation or final exam evaluation. Continuous evaluation is based on 2 written minitests and 1 written test. Minitests have a duration of 60 minutes and the corresponding evaluations (MT1,MT2) are in a scale of 20 values, rounded to the decimal figure. The continuous evaluation test has a duration of 120 minutes and the corresponding evaluation (T1) is in a scale of 20 values, rounded to the decimal figure.

In all evaluation processes, 1/5 of the rating is oriented to the evaluation of skills related to the implementation of numerical algorithms in computational tools, with the sintax of Matlab/Octave.

The final rating FR has a 25% component for each of the minitests, and a 50% component for the test, following the formula:

FR=0.25 x MT1+0.25 x MT2+0.5 x T1

A student with FR equal or higher than 9.5 values is approved in the Curricular Unit, with a global final grade determined by FR rounded to the closest integer. Evaluation by final exam is performed in the specific periods scheduled by ESTS, by a single written exam with a duration of 2h30m. The evaluation is in a scale of the integer values interval 0-20, with approval in the Curricular Unit for those students graded 10 or higher. Both in continuous or final exam evaluations, final grades equal or higher than 17 are confirmed only after an additional oral test (20min) evaluated in 20 values. For these students if the mean of the original rating and the oral test rating is lower than 16 or the student doesn’t attend, the global final grade will be 16.

Evaluation is preferentially presential, with the option of distance evaluation if there are legal restrictions that hinder this. Any time there is a distance evaluation by written test, the teacher can call any participant to an individual session to confirm the authorship of all answers, where the student shall explain and motivate all written argument that were given in the written answer, with a chance of the test being globally invalidated if these explanations are not satisfactory. Anytime that, as a result of a distance or presential evaluation, there exists a motivated fraud suspect situation, the Responsible for the Curricular Unit (RUC) can demand from the student a further complementary oral evaluation, with the structure determined by de decision 40/2021 of the Presidency of the IPS.

Fórmula de cálculo da classificação final

The final rating FR has a 25% component for each of the minitests, and a 50% component for the test, following the formula:

FR=0.25 x MT1+0.25 x MT2+0.5 x T1

Avaliação especial (TE, DA, ...)

Students that intend to apply for specific evaluation rules that are recognised within the IPS normatives, must communicate (no later than 14 days prior to the test) to any of the Teachers these circunstances. They shall present documentary evidence that these specific conditions and rules apply to their particular case.

In the case that this comunication is not stablished, all testing conditions that imply a planning by the evaluator may not apply due to lack of objective conditions.

Observações

Specific rules for written tests and exams:

• The presentation of ID is compulsory on all evaluation tests and exams.
• Students must fill in the incscription list to take part in any test or exam. This process will be open on the Moodle platform the week before the test.
• The student must bring the formatted exam sheets to any written evaluation process (one cover sheet and 4 additional A4 sheets)
• Calculating machines are authorized in tests and exams, as long as they comply with the rules declared in OficioCircular/S-DGE/2016/1798
• Using, handling or even carrying of nonauthorized electronic equipments, different from tha calculating machine, is prohibited during the tests/exams.

Tutorial support in the teaching period:

Prof. César Fernández (Responsável UC)
2ª feira 14h00-16h00
3ª feira 12h30-14h00

Prof.ª Carla Rodrigues (Co-Responsável UC)
Consultar na plataforma Moodle

Prof.ª Ana Barros
3ª feira 14h30-16h30
5ª feira 15h30-16h30

Tutorial support in the exams period will be determined after the corresponding exams schedule is approved.