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Elements of Mathtematics I

Code:

TPSI05

Sigla:

EM I

Áreas Científicas
Classificação	Área Científica
CNAEF	Mathematics

Ocorrência: 2022/2023 - 1S

Ativa?	Yes
Página Web:	https://moodle.ips.pt/2223/course/view.php?id=1341
Unidade Responsável:	Departamento de Matemática
Curso/CE Responsável:	Professional Technical Higher Education Courses in Technologies and Programming of Information Systems - ESTSetúbal

Ciclos de Estudo/Cursos

Sigla	Nº de Estudantes	Plano de Estudos	Anos Curriculares	Créditos UCN	Créditos ECTS	Horas de Contacto	Horas Totais
IPE	0	Plano de Estudos 2016/2017	1	-	6	60	162
TSPTB	32	Plano de Estudos_2015_16	1	-	6	60	162
TSPTSI	27	Plano de Estudos_2015_16	1	-	6	60	162

Língua de trabalho

Portuguese

Objetivos

The general objective of this course unit is to provide students with the basic mathematical knowledge required in the professional training of a top professional technician.

Resultados de aprendizagem e competências

By the end of term time, students should be able to:

1. Identify the properties of a real function.


2. Characterise inverse trigonometric functions.


3. Interpret the notion of limit of a function and calculate the limit of a function.


4. Analise the function continuity and apply the theorems of Bolzano and Weierstrass.


5. Interpret the concept of derivative of a function and calculate the derivative of a function at a point by definition.


6. Analise the differentiability of a function in an open interval and apply the derivative rules to calculate the derivative function.


7. Apply the theorems of Rolle, Lagrange and Cauchy.


8. Apply the Taylor's theorem to a k-times differentiable function.

Modo de trabalho

Presencial

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

Previous mathematical knowledge acquired through to secondary school, in particular fractional number and polynomials operations; equation and inequality solving; elementary properties of a real function.

Programa

1. Real Functions of Real Variable
1.1. Introduction to mathematical language and logical operations.
1.2. Generalities about real functions of real variable.
1.3. Study of inverse trigonometric functions.
1.4. Notion of limit; lateral boundaries; properties and operations.
1.5. Continuous functions, properties and continuity extension.
1.6. Fundamental theorems of continuous functions.

2. Differential Calculus in R
2.1. Notion of derivative of a function: definition and interpretations in geometric and physical terms; equations of the lines tangent and normal to the graph of a function at a point.
2.2. Lateral derivatives; differentiability and their properties; derivation rules; derived from the compound function and the inverse function; derived from inverse trigonometric functions; notion of differential.
2.3. Fundamental theorems of differentiable functions.
2.4. Derivatives of higher order; Taylor and Maclaurin formulas (Lagrange remnants). Application to the study of monotony, extremes and concavities.

Bibliografia Obrigatória

Departamento de Matemática; Textos de Apoio

Bibliografia Complementar

Apostol, T; Calculus – volume I, Wiley International Edition, 1967
Larson, R., Hostetler, R. P., Edwards, B. H.; Cálculo – Vol. I – 8ª edição, McGraw Hill, 2006
Campos Ferreira, J.; Introdução à Análise Matemática - 12ª edição, Fundação Calouste Gulbenkian, 2018. ISBN: 978-972-31-1388-4
Thomas, G.; Cálculo, Vol. 1 - 11ª Edição, Pearson, 2009

Métodos de ensino e atividades de aprendizagem

CU Elementos de Matemática II has a teaching load of 4 hours per week.

In the classes, the fundamental concepts of the different topics of the course program will be presented and the main results will be demonstrated. Students will carry out, under the guidance of the teacher, a set of exercises, with a view to a deeper understanding of the topics covered and a greater consolidation of knowledge. In class, students should acquire a global view of the themes and their interconnections, accompanied by a correct and objective formulation of mathematical definitions, the precise statement of propositions and the practice of deductive reasoning.

It will be up to the student, a posteriori, to carry out an autonomous study on the topics covered and deepen their knowledge, using the study material recommended in the CU bibliography and the support of the professor during the respective office hours.

The CU will have all the information centralized on the Moodle platform.

Tipo de avaliação

Distributed evaluation with final exam

Componentes de Avaliação

Designation	Peso (%)
Exame	0,00
Teste	100,00
Total:	100,00

Componentes de Ocupação

Designation	Tempo (Horas)
Estudo autónomo	102,00
Frequência das aulas	60,00
Total:	162,00

Obtenção de frequência

Fórmula de cálculo da classificação final

Avaliação especial (TE, DA, ...)

Special Assessment

Students covered by special rights referred to in the Regulation of Academic Activities and Guidelines for Assessment and School Performance of IPS Students must, until the second week of the beginning of the semester, contact the person responsible for the curricular unit, via email cristina.almeida@estsetubal.ips.pt to present their relevant specifics, under the terms provided for in the respective diplomas, otherwise they cannot be executed due to lack of objective conditions.

Melhoria de classificação

Rating Improvement

In accordance with Article 11 of the Academic Activities Regulation and Guidelines for the Assessment of Academic Performance by IPS Students, the classification improvement may occur in the academic year of enrollment, at the time of appeal, or in the academic year following the of approval, in any of the evaluation periods by exam, with the exception of the special season.

Observações

• Each summative test shall be of 90 minutes and each exam of 150 minutes.


• To perform any test or exam, an identification document with photo has to be presented.


• During assessment tests and examinatiom, only the enquiry form given by the teacher is allowed; handling or displaying any electronic equipment is prohibited.