Mathematical Analysis I

Code:

EEC0003

Acronym:

AMAT1

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2018/2019 - 1S

Active?	Yes
Responsible unit:	Department of Electrical and Computer Engineering
Course/CS Responsible:	Master in Electrical and Computers Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MIEEC	270	Syllabus	1	-	8	77	216

Teaching language

Portuguese

Objectives

This course aims to:
1) Consolidate students’ knowledge and basic techniques of real analysis to solve practical problems;
2) Develop students’ skills to handle concepts;
3) Develop student’s independent and analytical reasoning;
4) Develop students’ skills to apply mathematical concepts to the resolution of practical problems;
5) Develop students’ skills to present their reasoning and solutions in a clear and accurate way; Students should be capable of identifying techniques of differential calculation, and should also be capable of correctly applying those techniques. CDIO Syllabus: 1.1, 1.2, 2.2, 2.3, 2.4, 3.2

Learning outcomes and competences

Learning Outcomes:
1) To correctly apply mathematical techniques included in the program.
2) To select the appropriate mathematical tools to solve problems.
3) To clearly display techniques involved in problem solving.
4) To analyse and criticise results obtained in problem solving. CDIO Syllabus: 1.1, 2.4

Working method

Presencial

Program

1- Revision of contents studied in Secondary School:
a) Calculation rules. Trigonometry. Geometry.
b) Real functions of a real variable. Limits, continuity and derivation
2- Indefinite integrals.
3- Definite integrals. Application to the calculation of areas
4- Improper integrals.
5- First order, linear and separable variables differential equations.
6- Linear differential equation of order n and constant coefficient.
7- Numerical successions (Revision). Finite Induction.
8- Numerical series.
9- Polynomial approximation and Taylor’s series.

Mandatory literature

Maria do Rosário de Pinho e Maria Margarida Ferreira; ;Análise Matemática 1, Apontamentos das Aulas Teóricas, 2007

Complementary Bibliography

Paula Rocha; Cálculo I, Universidade de Aveiro, 1999. ISBN: 972-8021-80-1 (vol 1)
William E. Boyce, Richard C. DiPrima; Elementary Differential Equations. ISBN: 0-471-09339-4
Sherman K. Stein Anthony Barcellos; Calculus and analytic geometry. ISBN: 0-07-061175-0
Robert A. Adams; Calculus. ISBN: 0-201-39607-6
Tom M. Apostol; Calculus. ISBN: 0-471-00005-1(v.1)
Spivak Michael; Calculus. ISBN: 0-521-86744-4

Teaching methods and learning activities

Theoretical classes:
These classes are the core of the course. Students are strongly encouraged to follow and participate on all these classes in order to ensure the necessary coordination and coherence among theoric, practise and individual study.
On theoretical classes it is made the motivation and presentation of the course subjects. Presentation of theoretical concepts, giving special emphasis to geometric interpretations and to their practical application. The demonstration of theoretical concepts is made, as long as it helps the understanding. Ilustration of the concepts with exercise resolution is also .

Theoretic-practical classes:
A selection of problems will be selected for each class. The students should try to solve them before the class. At the beginning of the class the students should present proof of such  work. In the class those problems will be discussed and, if need, solve. The Professor complete the class with   the discussion and solution of other problems.
The student must complement his study using the  other exercises from the Course Exercise Collection, studying  the sillabus and/or other suggested literature. 

Tutorial support for students during academic period:
Scheduled time will be appointed by each professor.

keywords

Physical sciences > Mathematics > Mathematical analysis

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	146,00
Frequência das aulas	70,00
Total:	216,00

Eligibility for exams

To obtain "frequency" in the course the student can not exceed the absence limit of practical classes (25% of the planned classes) and they should present the written work in 50% of TP classes. If the latter is not achieved, the student will loose "frequency" even though he/she does not exceed the number of absences at TPs

Dismissed from "frequency":
1) students with an official particular status (TE, ...)
2) studentswho has "frequency" in previous years  and are NOT registered in a TP class.

Calculation formula of final grade

To have a final classification, the student must have  "frequency"  in the course or be dismissed from such frequency.


The final classification will be obtained out of 
T1+T2+T3
or
"Exame de recurso"

The dates and rooms for the Tests will be defined by the Administration.

Grades:
T1: from 0 to 4
T2: from 0 to 7
T3: from 0 to 9
Exame de recurso: from 0 to 20.

A missing test corresponds to a 0 grade. There will be no second changes to take any of the tests.

Examinations or Special Assignments

Weekly written resolution of proposed problems to be presented at the beginning of each TP class except the first one.

Special assessment (TE, DA, ...)

Students with special status do not need to attend the TP classes. They may choose to go to the 3 tests or to the final exam.

Classification improvement

Final exam (época de recurso)