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Elements of Mathtematics I

Code:

ARCI05

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=1578
Unidade Responsável:	Departamento de Matemática
Curso/CE Responsável:	Automation, Robotics and Industrial Control

Ciclos de Estudo/Cursos

Sigla	Nº de Estudantes	Plano de Estudos	Anos Curriculares	Créditos UCN	Créditos ECTS	Horas de Contacto	Horas Totais
ARCIL	29	Plano de Estudos_2015_16	1	-	6	60	162
TSPARC	25	Plano de Estudos_2015_16	1	-	6	60	162

Docência - Responsabilidades

Docente	Responsabilidade
Cristina Maria Ferreira de Almeida

Docência - Horas

Theorethical and Practical :

4,00

Type	Docente	Turmas	Horas
Theorethical and Practical	Totais	2	8,00
	Cristina Maria Ferreira de Almeida		4,00
	Cláudia Catarina Mendes Silva		4,00

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:

Identify the properties of a real function.

Characterise inverse trigonometric functions.

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

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

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

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

Apply the theorems of Rolle, Lagrange and Cauchy.

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 - 18.ª Edição, Fundação Calouste Gulbenkian, 2018
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 (%)
Teste	100,00
Exame	0,00
Total:	100,00

Componentes de Ocupação

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

Obtenção de frequência

If there is no indication to the contrary by the competent bodies, the tests and exams will be in person. If this is not possible, these evaluations will be carried out online and the evaluation rules and the respective procedures will be updated and published in a timely manner on the UC page in Moodle.

The achievement of this curricular unit can be obtained through two assessment processes: Continuous Assessment or Assessment by Exam.

Continuous evaluation:

Continuous assessment is based on the completion of two tests. Access to continuous assessment requires attendance of at least 75% of classes. Assigning by T1 and T2 the grades (from zero to 10 values, rounded to tenths) obtained in each of the 2 summative tests, the final classification CF (rounded to units) will be the plain sum of the two grades (CF=T1+T2).

The conditions for passing the continuous assessment are as follows:

If CF is greater than or equal to 10 and less than 18, the student passes on with a final grade equal to CF, provided that the classification in any of the tests (T1 and T2) the grade was greater than or equal to 3.5 values.

If CF (rounded to units) is greater than or equal to 18, the student must take an oral test, obtaining as a final grade the average of the classification obtained and of the referred oral test. If the student does not attend the oral test, the final classification will be 17 values.

Recovery of one of the tests:

The conditions for realization of the recovery of one of the tests will be as follows:

In order to meet the approval conditions (final sum greater than or equal to 10 and classification in both Tests greater than or equal to 3.5 values), a student who has a classification greater than or equal to 3.5 in one of the Tests has the option to perform the recovery of the lowest grade obtained in T1 and T2, on the same day and time of the 1st season Exam;

Passed students cannot recover a Test in order to improve their grade.

Exam Assessment:

Students who choose not to take the Continuous Assessment, or who, having opted for it, have not been approved, may take an Exam.

The approval conditions are as follows:

If the exam grade (rounded to units) is greater than or equal to 10 and less than 18, the student is approved with a final grade equal to the exam grade (rounded to units);

If the exam grade (rounded to units) is greater than or equal to 18, the student will have to take an oral exam, obtaining as a final grade the average of the classifications of the oral exam and the exam. If you do not attend the oral test, the final classification will be 17 points.

The tests have a time limit of 1 hour and 30 minutes the exams 2 hours and 30 minutes, being the Tests rated on a scale from 0 to 10 and the Exams on a scale from 0 to 20.

Fórmula de cálculo da classificação final

Final ranking calculation formula

CF = T1 + T2 (T1≥3.5 and T2≥3.5)

Exam evaluation (E)

If CF or E (rounded to units) is greater than or equal to 18, the student will have to take an oral exam, obtaining as a final grade the average of the classifications of the oral exam and the exam. If you do not attend the oral test, the final classification will be 17 points.

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.

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