Mathematical Analysis

Code:

EIC0004

Acronym:

AMAT

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2009/2010 - 1S

Active?	Yes
Responsible unit:	Mathematics Section
Course/CS Responsible:	Master in Informatics and Computing Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MIEIC	239	Syllabus since 2009/2010	1	-	6	70	162

Teaching language

Portuguese

Objectives

This course aims to acquaint students with the differential and integral calculus, in order to make them able to apply basic tools of mathematical analysis in problem solving related with subjects of this degree. This course also aims to expand students’ knowledge, so that they can solve new kinds of problems.

Program

Revision of the contents studied in Secondary School
Polynomial function; divisibility; zeros; factorization
Rational function; simple fractions; decomposition of rational functions
Functions and derivatives (composed, inverted, continuity, graphs)
Implicit function and its derivatives
Mean value theorem (Taylor’s theorem). Applications
Anti-derivatives and integration; 1st and 2nd theorems; Average theorem; Calculation of areas
First order differential equations
Improper integrals
Numerical series
Polynomial and Taylor series
Hyperbolic functions, definition and properties; inverse hyperbolic functions
Curves; polar coordinates, length of curves, curve rotation around coordinate axis; curvature
Integration R2 and R3; double and triple integrals

Mandatory literature

Apostol, Tom M.; Calculus. ISBN: 84-291-5001-3
APONTAMENTOS ELABORADOS PELO REGENTE E DISPONIBILIZADOS NO SIFEUP NA PÁGINA DA DISCIPLINA
SALLAS-HILLE-ETGEN ; CALCULUS ONE AND SEVERAL VARIABLES;WILEY

Complementary Bibliography

Erwin Kreyszig; Adanced Engineering Mathematics, Wiley

Teaching methods and learning activities

Concepts and important results are presented in theorectical classes ,whit geometrical interpretation,with engeneering applications.Some construtive demonstrations are presented.In theorectical-practical classes,the students are guided to the resolution of selected problems.

keywords

Physical sciences > Mathematics > Mathematical analysis > Functions

Evaluation Type

Distributed evaluation without final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Attendance (estimated)	Participação presencial	85,00
Evaluation	Exame	6,00
	Total:	-	0,00

Amount of time allocated to each course unit

Description	Type	Time (hours)	End date
Personal Study (weekly)	Estudo autónomo	39
Preparation first examination	Estudo autónomo	6
Preparation second examination	Estudo autónomo	6
Preparation third examination	Estudo autónomo	12
	Total:	63,00

Eligibility for exams

Students have to achieve at least a 6 out of 20 in the three mini-tests, according to General Evaluation Rules of FEUP.
Students, who are repeating the course, do not need to attend classes. However, they have to attend to the tests.

Calculation formula of final grade

Final Mark will be based on the mark of the three mini-tests (1st- 6 + 2nd- 6 + 3rd- 8+4). The first and second tests will have three questions, which worth the same.
The third test will be composed by five questions, in which three of them are related with the corresponding subject (8 values= 3+3+2), and two values will be given to the question in which the students had the most difficulty to answer, while the other two questions (4 values= 2+2) will cover themes of the first and second mini-tests.

Examinations or Special Assignments

Three mini-tests will take place, and they are closed book tests. The first and second mini-test will last 90 minutes, while the third test lasts 150 minutes. If necessary, a final exam will be placed.
Students will be informed about the dates of the tests beforehand. Students should consult ‘FICHEIRO’ ‘AVISOS’ on the course page on SIFEUP.

Special assessment (TE, DA, ...)

It will take place an exam for students with a special status (working students …) that did not complete the course in the previous year.

Classification improvement

An exam, according to General Evaluation Rules of FEUP

Observations

Language of instruction is Portuguese.