Mathematical Analysis I

Code:

EMM0045

Acronym:

AMAT1

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2011/2012 - 1S

Active?	Yes
Responsible unit:	Metallurgy Section
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	44	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.

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.

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.
- Functions of several variables, definition, limits, continuity, graphics, partial derivates. Total increment and total differential. Derivative of an implicit function. Derivative of a compound function. Partial derivatives of different orders, level surface. Directional derivatives. Gradient. Taylor formula functions of two variables. Maximum and minimum.
- 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

Evaluation with final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Attendance (estimated)	Participação presencial	56,00
Study for final evaluation	Exame	50,00		2012-02-10
	Total:	-	0,00

Amount of time allocated to each course unit

Description	Type	Time (hours)	End date
Study of theoretical-practical classes	Estudo autónomo	56	2012-01-06
	Total:	56,00

Eligibility for exams

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Calculation formula of final grade

Exam = 100%

Examinations or Special Assignments

Not applicable

Special assessment (TE, DA, ...)

Students in accordance with line 4 of Article 3 of General Evaluation Rules of FEUP will be assessed based on a closed book written exam.

Classification improvement

In order to improve their grades, students have to enroll in this course unit in the following academic year.

Observations

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