Mathematical Analysis

Code:

EIC0004

Acronym:

AMAT

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2010/2011 - 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	214	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.

At the end of this course, the learning outcomes are:

1. To solve derivatives of functions, draw graphics and study functions in general
2. To solve integrals and use them in various engineering applications
3. To use different integration techniques and differential equations
4. To use series and polynomials, to dominate the approximation concepts.

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	90,00
Fisrt examination	Exame	1,50
Second Examination	Exame	1,50
3rd Examination	Exame	3,00
Regular Practice	Teste	24,00
	Total:	-	0,00

Amount of time allocated to each course unit

Description	Type	Time (hours)	End date
Preparation for exams	Estudo autónomo	22
Weekly study hours	Estudo autónomo	24
	Total:	46,00

Eligibility for exams

All registered students are allowed to attend exams.
Students, who are repeating the course, do not need to attend classes. However, they have to attend to the exams.

Calculation formula of final grade

Final Mark will be based on the average mark of the three mini-tests.
At the the third test, on top of the third part to be examined, students can choose to repeat first part or second part.

Examinations or Special Assignments

Three mini-tests will take place, and they are closed book tests.
Students will be informed about the dates of the tests beforehand. Students should consult ‘FICHEIRO’ ‘AVISOS’ on the course page on SIFEUP.

Classification improvement

At the the third test, on top of the third part to be examined, students can choose to repeat first part or second part.

Observations

Language of instruction is Portuguese.