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Mathematical Analysis I

Code:

CVN002

Sigla:

AMI

Áreas Científicas
Classificação	Área Científica
OFICIAL	Matemática e Informática

Ocorrência: 2020/2021 - 1S

Ativa?	Yes
Unidade Responsável:	Matemática e Informática
Curso/CE Responsável:	Undergraduate in Civil Engineering (evening course)

Ciclos de Estudo/Cursos

Sigla	Nº de Estudantes	Plano de Estudos	Anos Curriculares	Créditos UCN	Créditos ECTS	Horas de Contacto	Horas Totais
CIVN	29	Study Plan	1	-	6	75	162

Língua de trabalho

Portuguese

Objetivos

The goal is to carry on developing the mathematical reasoning initiated in highschool education, in order to be able to meet the demands of other curricular units. On completing this curricular unit, students should have acquired the necessary skills in differential calculus and integration of functions of one variable, including the fundamental theorems of calculus.

Resultados de aprendizagem e competências

Not applicable

Modo de trabalho

Presencial

Programa

Limits and continuity: Basics on real valued functions. Exponential and logarithmic function. Trigonometric inverse functions. Continuity and limit. Mean Value and Weierstrass Theorems.
Differential calculus: Derivative concept, rules; differentiability and continuity; higher order derivatives, applications. Rolle’s, Lagrange’s, Cauchy’s and L’Hôpital’s Theorem. Taylor’s formula and its applications. Integral calculus: Antiderivatives by inspection, by parts, by substitution and integration of rational functions. Integral calculus of real functions. Integrability conditions; properties of integrable functions. Indefinite integral, derivative of an indefinite integral, Fundamental Theorem of Calculus, Barrow’s formula. Integration by parts and by substitution. Application of integral calculus to the computation of area, volume of revolution solids and curve length. Moments, center of mass and centroids.

Bibliografia Obrigatória

T. Apostol; Calculus, Vol. I, second edition, Wiley, 1967
J. Campos Ferreira; Introdução à Análise Matemática, Fundação Gulbenkian, 8a ed., 2005
Larson, Hostetler e Edwards; Cálculo, Vol. 1, 8a edição, McGraw-Hill, 2006
Cálculo Diferencial e Integral, Vol. I; N. Piskounov, Lopes da Silva Editora, 1967
C. Sarrico; Análise Matemática, Leitura e exercícios, 1a edição, Gradiva, 1997

Bibliografia Complementar

Departamento de Matemática do IST; Exercícios de Análise Matemática I e II, IST Press, 2005. ISBN: 978-989-8481-83-2
M. Ferreira e I. Amaral; Matemática, Exercícios, Primitivas, Integrais, edições sílabo, 1996
B. Demidovitch; Problemas e Exercícios de Análise Matemática, Editora Mir, 1997

Métodos de ensino e atividades de aprendizagem

Theoretical classes with lecturing periods with application examples followed by small tasks to be done by the students in order to consolidate the contents previously taught. Practical classes dedicated to problem solving, individually or in small groups.
The assessment will be done through a final written exam or, alternatively by student option, by two written tests each one contributing 50% to the final assessment.

Classes held at a distance due to the pandemic situation.

 

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

Not applicable

Fórmula de cálculo da classificação final

Continuous evaluation:
2 tests, with a weight of 50% each;
Exam:
100% of the exam grade.

If it is not possible to carry out the test and/or examination in person, because of the pandemic, an oral test may be required of all students who obain a rating greater  than or equal to 9,5 values. The final classification will be the classification obtained in the oral exam.