Mathematical Analysis I

Code:

EMM0045

Acronym:

AMAT1

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2016/2017 - 1S

Active?	Yes
Web Page:	http://consultoriodigitalmatematica.pt.vu/
Responsible unit:	Department of Metallurgical and Materials Engineering
Course/CS Responsible:	Master in Metallurgical and Materials Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MIEMM	38	Syllabus since 2006/2007	1	-	6	56	162

Teaching language

Portuguese

Objectives

Justification The mathematical analysis is an indispensable tool for a engineer. Objectives Provide the requisite mathematical foundations for the formation of an engineering professional.

Learning outcomes and competences

Skills and Learning Outcomes To achieve with proficiency the knowledge of mathematical analysis and be able to apply it in engineer’s problem solving. Make a contribution for achieve a critical thinking and a correct time management.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

12º years of scolarship

Program

- Implicit function: definition and properties. Inverse function. Curves in parametric and polar coordinates. Differential and its applications. Taylor’s formula and McLaurin’s formula. - Indefinite integral: Primitive and indefinite integral. Definition and properties. Immediate integration and almost immediate integration. Integration by change of variables. Expression integrals containing 2nd level trinomial. Integration by parts. Integration of rational fractions. Integration of trigonometric functions. Change of trigonometric variables. - Definite integral. Definition and properties. Newton-Leibniz formula. Geometrical meaning. Change of variable. Improper integral. Areas in cartesian coordinates. Areas in polar and parametric coordinates. Derivative of arc length. Curve length in cartesian coordinates. Curve length in polar and parametric coordinates. Curvature and radius of curvature. Volumes in cartesian coordinates. Volumes in parametric coordinates. Work done by variable forces. Centre of gravity of an arc and an area.

Mandatory literature

N. Piskounov ; trad. de António Eduardo Pereira Teixeira, Maria José Pereira Teixeira; Cálculo diferencial e integral
B. Demidovitch; Problemas e exercícios de análise matemática. ISBN: 978-972-592-283-5

Teaching methods and learning activities

Theoretical-practical classes: presentation of the content of the course unit and problem solving by the students.

keywords

Physical sciences > Mathematics > Mathematical analysis
Physical sciences > Mathematics > Mathematical analysis > Functions
Physical sciences > Mathematics

Evaluation Type

Distributed evaluation without final exam

Assessment Components

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

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	114,00
Frequência das aulas	48,00
Total:	162,00

Eligibility for exams

Gets frequency to this UC, in the current school year, every student that: - Regularly registered in UC and does not exceed the maximum number of absences. All students duly registered in UC, can perform the tests and examinations that are proposed and used for evaluation.
Regarding the assessment there are three different times, and they were the following:
1) First Test (T1);
2) Second Test (T2);
3) Exam resource (E) (all matter) - to be marked.
Remarks:
a) classifications of tests from previous years are not considered.
b) if a student misses one test, the rating assigned to this test, to calculate the final average, is zero values.

Calculation formula of final grade

For the final grade of the UC student must have or be exempt from such frequency. In these conditions, any student can choose to get approved by tests or final exam resource (E). If a student does not obtain approval for tests, he can still do the test resource. 

The final grade of UC is (scale 0-20): 
- Arithmetic average of T1 and T2; 
- The grade of the exam recourse (E).

Examinations or Special Assignments

Not applicable

Internship work/project

Not applicable

Special assessment (TE, DA, ...)

Students who are under special statutes or having the or who have had previous years frequency, are exempt frequency. The approval can be obtained by performing the tests (T1 and T2) or exam resource (E), the final classification is done according to the previous point.

Classification improvement

Students who wish to undertake improvement of classification shall be subject to an exam.

Observations

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