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Mathematical Methods I

Code:

TGI41

Sigla:

MMI

Áreas Científicas
Classificação	Área Científica
OFICIAL	Matemática

Ocorrência: 2022/2023 - 1T

Ativa?	Yes
Página Web:	https://moodle.ips.pt/2223/course/view.php?id=1735
Unidade Responsável:	Departamento de Matemática
Curso/CE Responsável:	Industrial Management and Techinology

Ciclos de Estudo/Cursos

Sigla	Nº de Estudantes	Plano de Estudos	Anos Curriculares	Créditos UCN	Créditos ECTS	Horas de Contacto	Horas Totais
TGI	79	Plano de Estudos 2016	1	-	4	44	108

Língua de trabalho

Portuguese

Objetivos

The general objective of this course unit is to provide students with the mathematical knowledge about functions of a real variable and differential calculus.

Resultados de aprendizagem e competências

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

1. Analyse the properties of functions of a real variable.


2. Calculate the derivative of a function at a point by definition and its lateral derivatives.


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


4. Calculate the equations of the tangent and normal straight lines at a point.


5. Apply the L'Hospital's rule in limit calculus.


6. Analyse the monotony of a function and its relative extremum.

Modo de trabalho

B-learning

Programa

1. Functions of a Real Variable
1.1. Generalities on functions of a real variable.
1.2. Notion of limit; lateral boundaries; properties and operations.
1.3. Continuous functions, properties and continuity extension; fundamental theorems of continuous functions.
1.4. Study of inverse trigonometric functions.

2. Differential Calculus
1.1. Derivative of a function: concept, geometrical perspective and lateral derivatives.
1.2. Differentiability of a function and derivative rules.
1.3. Fundamental theorems of differentiation and L'Hospital's rule.
1.4. Study of monotony and extremum of a function and optimization problems.

Bibliografia Obrigatória

Larson, R., Robert P. H. e Edwards, Bruce H.; Cálculo - Volume 1 - 8ª edição, McGraw Hill, 2006. ISBN: 9788586804564

Bibliografia Complementar

Campos Ferreira, J.; Introdução à Análise Matemática - 12ª edição, Fundação Calouste Gulbenkian, 2018. ISBN: 978-972-31-1388-4
Thomas, G.; Cálculo, Volume 1 - 11ª Edição, Pearson, 2009. ISBN: 978-85-88639-31-7

Métodos de ensino e atividades de aprendizagem

The teaching approach applied in this course unit is the student-centered approach based on flipped learning. In this context, learning materials are available on the IT platform Moodle along with a set of learning activities for students to perform in order to achieve the learning outcomes.

Tipo de avaliação

Distributed evaluation without final exam

Componentes de Avaliação

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

Componentes de Ocupação

Designation	Tempo (Horas)
Estudo autónomo	86,00
Frequência das aulas	22,00
Total:	108,00

Obtenção de frequência

The approval in this UC (curricular unit) can be obtained through two assessment processes: Continuous Evaluation or Exam Evaluation.

CONTINUOUS EVALUATION
The Continuous Evaluation presupposes the accomplishment of 4 summative tests.
Assigning by MT1, MT2, MT3 and MT4 the grades (from zero to 5 values, rounded to tenths) obtained in each of the 4 summative tests, the final classification CF (rounded to units) will be the plain sum of the four grades.

The approval conditions are as follows:

1. 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 sums (MT1+MT2) and (MT3+MT4) is greater than or equal to 3.5 values.
   
   


2. If a student fails the approval conditions referred in point 1, the student can recover the lowest grade obtained in (MT1+MT2) and (MT3+MT4) by performing a recovery test on the date of the normal period exam, provided that (MT1+MT2) or (MT3+MT4) is greater than or equal to 3.5 values. 

EVALUATION BY EXAM
Students who have not obtained approval for Continuous Assessment may take an exam, being approved as long as they obtain a grade of 10 or higher.

NOTE: In any of the evaluation processes, whenever the final classification is greater than or equal to 18 values, the student must carried out an oral test, obtaining as a final grade the average of the classifications of the written test and of the said oral test . If the student does not attend the oral test, the final classification will be 17 values.

Fórmula de cálculo da classificação final

CF = MT1 + MT2 + MT3 + MT4
or
Exam evaluation

Avaliação especial (TE, DA, ...)

Working students, high-level athletes, association leaders and students under the Religious Freedom Law must address, until the second academic week of the semester, to the head of the Curricular Unit to present their pertinent specificities, in accordance with the terms of the respective diplomas under penalty of failure to enforce them for lack of objective conditions.

Melhoria de classificação

In this course unit passed students of this academic year may only apply to their improvement classification in the supplementary period exam.

Observações

• Each summative test shall be of 60 minutes, the recovery test of 90 minutes and each exam of 150 minutes.


• To perform the recovery test and/or exams, an identification document with photo has to be presented.


• Handling or displaying any electronic equipment is prohibited, except school calculators (non-graphing).