Mathematical Analysis I

Code:

EEC0003

Acronym:

AMAT1

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2014/2015 - 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	314	Syllabus	1	-	8	77	216

Teaching language

English

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

Roland E. Larson, Robert P. Hostetler, Bruce H. Edwards; Calculo. ISBN: 84-481-1770-0 brochada
Sherman K. Stein Anthony Barcellos; Calculus and analytic geometry. ISBN: 0-07-061175-0
Robert A. Adams; Calculus. ISBN: 0-201-39607-6
William E. Boyce, Richard C. DiPrima; Elementary Differential Equations. ISBN: 0-471-09339-4
Tom M. Apostol; Calculus. ISBN: 0-471-00005-1(v.1)

Teaching methods and learning activities

All the classes of this course are theoretical-practical classes. On them 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 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.

keywords

Physical sciences > Mathematics > Mathematical analysis

Evaluation Type

Distributed evaluation with 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	91,00
Frequência das aulas	119,00
Total:	210,00

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).

Dismissed from "frequency":
1) students with an official particular status (TE, ...)
2) students with a previous course registration.

Calculation formula of final grade

To have "frequency"  in the course or be dismissed from such frequency is mandatory.
The final classification will be obtained out of 
T1+T2+T3
or
"Exame de recurso"

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

A missing test corresponds to a 0 grade.

Classification improvement

Final exam (época de recurso)