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# Mathematical Analysis I

 Code: EEC0003 Acronym: AMAT1

Keywords
Classification Keyword
OFICIAL Mathematics

## Instance: 2011/2012 - 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 390 Syllabus (Transition) since 2010/2011 1 - 8 87 216
Syllabus 1 - 8 87 216

### Teaching - Hours

 Lectures: 0,00 Recitations: 5,50
Type Teacher Classes Hour
Recitations Totals 8 44,00
Maria Margarida de Amorim Ferreira 11,00
Vitor Manuel Martins Cicouro de Pêra 11,00
Maria do Rosário Marques Fernandes Teixeira de Pinho 5,50
Nuno Alexandre Lopes Moreira da Cruz 11,00
Fernando Manuel Ferreira Lobo Pereira 5,50

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

### Program

Program:
1- Revision of contents studied in Secondary School
a) Calculation rules. Trigonometry.
b) Numerical successions. Finite Induction.
c) 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- Laplace transform
8- Numerical series
9- Polynomial approximation and Taylor’s series

### Mandatory literature

George F. Simmons; Calculus with Analytic Geometry, McGrawHill. ISBN: 0-07-057642-4
Stein, Sherman K.; Calculus and Analytic Geometry. ISBN: 0-07-061175-0
Adams, Robert A.; Calculus. ISBN: 0-201-39607-6
Larson, Hostetler e Edwards, Barcellos; Calculo, (Vols. 1,2)
Apostol, Tom M.; Calculus
Boyce, William E.; Elementary differential equations and boundary value problems. ISBN: 0-471-31999-6
Maria do Rosário de Pinho e Maria Margarida Ferreira; Análise Matemática 1, Apontamentos das Aulas Teóricas , 2007

### Complementary Bibliography

Wylie, C. Ray Jr.; Advanced engineering mathematics

### Teaching methods and learning activities

Theoretical Classes:
Presentation of theoretical concepts, giving special emphasis to geometric interpretations and to their practical application.
The demonstration of theoretical concepts is always made, as long as it helps the understanding. After the presentation of a theoretical concept, the students will do some exercises related to that. Throughout classes, we look for the participation of the students, not only to do exercises, but also to introduce new concepts.

Theoretical-Practical Classes:
Solving exercises that illustrate and clarify the contents studied in theoretical classes.
Practical Classes:
Orientation of the study of this course and clarification of any doubts that might come up with the resolution of the proposed exercises. Division of the class into groups of 3 or 4 students. In each practical class some of the groups will be randomly chosen. Each group will have one of its elements going to solve the problem on the board. This person is also randomly chosen. The exercise will be one of a list of 3 or 4 exercises previously indicated by the teacher.
The participation in these practical classes will be a part of the continuous evaluation of this course.

### keywords

Physical sciences > Mathematics > Mathematical analysis

### Evaluation Type

Distributed evaluation with final exam

### Assessment Components

Description Type Time (hours) Weight (%) End date
Attendance (estimated) Participação presencial 93,50
Written test Exame 1,00
Written test Exame 1,00
Written test Exame 1,00
Final exam Exame 2,50
Solving suggested problems Teste 30,00
Total: - 0,00

### Amount of time allocated to each course unit

Description Type Time (hours) End date
Individual study Estudo autónomo 87 2012-02-10
Total: 87,00

### Eligibility for exams

Regardless of the distributed component evaluation, any student who was not dismissed from frequency and exceeded the absence limit of practical classes (25% of the planned classes) will NOT be allowed to do this course’s exam. Furthermore, each and every student who hasn’t exceeded the absence limit will be allowed to do the exam, regardless of his classification in the distributed component.

### Calculation formula of final grade

The final classification will be obtained out of the exam grade and the grade of the evaluation in practical classes, according to the following:
MAX {0.2×P + 0.8×E, E}
P represents the grade of the distributed evaluation of practical classes and E represents the grade of the exam. They both range from 0 to 20. The result will, then, be rounded to units.

### Special assessment (TE, DA, ...)

The students that, in 2004/2005, have either the military status or that of working student are dismissed from frequency and from the distributed component.

### Classification improvement

Classification improvement is made with a final written exam. Its result represents 100% of the final classification.

### Observations

Language of instruction: Portuguese.