Mathematical Analysis

Code:

EIC0004

Acronym:

AMAT

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2020/2021 - 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	249	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 Informatics and Computing Engineering. This course also aims to expand students’ knowledge, so that they can address new methodologies applied to engineering problems. At the end of the 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 and understand approximation concepts based on series and polynomials.

Learning outcomes and competences

As a result of this course, students should be aquainted with the following matters:
1. To study functions, solve derivatives and draw graphics
2. To solve integrals and use them in various engineering applications
3. To use differential equations and Laplace Transform
4. To understand approximation concepts using series and polynomials.

Working method

Presencial

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

Knowledge of pre-calculus at the level of the high school program of Math A.

Program

1-      Differenciation
a.      Applications to engineering problems
b.      Limits
2-      Integration
a.   Indefinite integral
b.   Definite integral
c.   Fundamental Theorem
d.  Integration Techniques
e.  Application of integration - Areas and Volumes
3-      Differential Equations
             a.       First Order Differential Equations
             b.      Second Order Differential Equations
4-      Laplace Transform and their use to solve Differential Equations
5-      Series
a.       Convergence criteria
b.      Trigonometric series, power series ...
6-      Function approximation
a.       Taylor series
b.      Fourier series

Mandatory literature

Carlos A. Conceição António; Análise Matemática 1 - Conteúdo teórico e aplicações, AEFEUP, 2017. ISBN: 978-989-98632-3-1
Madureira, Luísa; Problemas de equações diferenciais ordinárias de Laplace . ISBN: 972-752-065-0
Madureira Maria Luísa Romariz; Problemas de integrais de linha e superfície e de séries de Fourier., Universidade do Porto. Faculdade de Engenharia, 2018. ISBN: 978-989-99559-2-9

Complementary Bibliography

Apostol, Tom M; Calculus. ISBN: 84-291-5001-3
Banner, Adrian; The calculus lifesaver: all the tools you need to excel at calculus., Princeton University Press, 2007
Roland E. Larson; Cálculo. ISBN: 85-86804-56-8 (v. 1)

Teaching methods and learning activities

At the theoretical lectures (T) one presents and discusses the proposed program at a theoretical level with the support of applied examples. The theoretical and practical classes (TP) are intended for analysis and applied problem solved by the students. One aims to use the acquired skills at the theoretical lectures to address and correctly solve typical examples and problems. This methodology allows to develop the student´s skills as weel as knowledge and mathematical reasoning to solve problems with increasing level of complexity.

keywords

Physical sciences > Mathematics > Mathematical analysis > Differential equations
Physical sciences > Mathematics > Mathematical analysis > Functions

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	92,00
Frequência das aulas	70,00
Total:	162,00

Eligibility for exams

In order to attend mini-tests or exam, students need to to be in conformity with the general standards of evaluation of FEUP.
Students repeating the course, do not need to attend classes.

Calculation formula of final grade

The grade will be calculated taking into account the average of two mini-tests.
To obtain approval it is required an average higher than or equal to 9.5 (out of 20) and a minimum of 5 (out of 20) in each of the minitests.
The student that has not obtained approval can attend an “appeal exam” on the subject of ONE of the minitests or on the entire matter.
The student that has already obtained approval can attend the “appeal exam” assessing the TOTALITY of matter.

Examinations or Special Assignments

The grade will be calculated taking into account the average of two mini-tests. Three assessment mini-tests (closed-book) will take place during the semester. The date, time, duration and classrooms of the assessment tests, as well as for the appeal test, will be communicated well in advance.

Internship work/project

n/a

Special assessment (TE, DA, ...)

It will be done through a special exam, provided that it is required at convenient dates. Students with special conditions (TE, DA, ..), although exempt of  classes, MUST attend the mini-tests and submit themselves to the rules of the general evaluation of the course.

Classification improvement

The student that has already obtained approval can attend the “appeal exam” assessing the totality of matter or only one of the mini-tests.

Observations

Language of instruction is Portuguese.